ordinal_type compareToAnalytic( std::ifstream &inputFile,
const Kokkos::DynRankView<ValueType,testMatProperties...> testMat,
const ValueType reltol,
const ordinal_type iprint,
const TypeOfExactData analyticDataType ) {
INTREPID2_TEST_FOR_EXCEPTION( testMat.rank() != 2, std::invalid_argument,
">>> ERROR (compareToAnalytic): testMat must have rank 2");
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream outNothing;
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&outNothing, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
std::string line;
ValueType testentry;
ValueType abstol;
ValueType absdiff;
ordinal_type i = 0, j = 0;
ordinal_type err = 0;
while (! inputFile.eof() && i < static_cast<ordinal_type>(testMat.dimension(0)) ) {
std::getline(inputFile,line);
std::istringstream linestream(line);
std::string chunk;
j = 0;
while( linestream >> chunk ) {
ordinal_type num1;
ordinal_type num2;
std::string::size_type loc = chunk.find( "/", 0);
if( loc != std::string::npos ) {
chunk.replace( loc, 1, " ");
std::istringstream chunkstream(chunk);
chunkstream >> num1;
chunkstream >> num2;
testentry = (ValueType)(num1)/(ValueType)(num2);
abstol = ( std::fabs(testentry) < reltol ? reltol : std::fabs(reltol*testentry) );
absdiff = std::fabs(testentry - testMat(i, j));
if (absdiff > abstol) {
++err;
*outStream << "FAILURE --> ";
}
*outStream << "entry[" << i << "," << j << "]:" << " "
<< testMat(i, j) << " " << num1 << "/" << num2 << " "
<< absdiff << " " << "<?" << " " << abstol << "\n";
}
else {
std::istringstream chunkstream(chunk);
if (analyticDataType == INTREPID2_UTILS_FRACTION) {
chunkstream >> num1;
testentry = (ValueType)(num1);
}
else if (analyticDataType == INTREPID2_UTILS_SCALAR)
int main(int argc, char *argv[]) {
// feenableexcept(FE_DIVBYZERO | FE_INVALID | FE_OVERFLOW);
typedef ROL::Vector<RealT> V;
typedef ROL::Objective<RealT> OBJ;
typedef ROL::BoundConstraint<RealT> CON;
using Teuchos::RCP;
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
// This little trick lets us print to std::cout only if a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
RealT zero(0);
RCP<V> x0;
RCP<V> x;
RCP<V> g;
RCP<OBJ> obj;
RCP<CON> con;
RCP<OBJ> model;
ROL::ZOO::getHS2(obj,con,x0,x);
g = x->dual().clone();
// Need to evaluate the gradient to construct the model
obj->gradient(*g,*x,zero);
model = Teuchos::rcp(new ROL::ColemanLiModel<RealT>(*obj,*con,*x,*g));
RCP<V> s = x->clone();
RCP<V> v = x->clone();
RCP<V> u = x->clone();
ROL::RandomizeVector(*s,-1.0,1.0);
ROL::RandomizeVector(*u,-1.0,1.0);
ROL::RandomizeVector(*v,-1.0,1.0);
model->checkGradient(*s,*v);
model->checkHessVec(*s,*v);
model->checkHessSym(*s,*u,*v);
return 0;
}
std::vector<Real> Objective<Real>::checkHessSym( const Vector<Real> &x,
const Vector<Real> &hv,
const Vector<Real> &v,
const Vector<Real> &w,
const bool printToStream,
std::ostream & outStream ) {
Real tol = std::sqrt(ROL_EPSILON);
// Compute (Hessian at x) times (vector v).
Teuchos::RCP<Vector<Real> > h = hv.clone();
this->hessVec(*h, v, x, tol);
Real wHv = w.dot(h->dual());
this->hessVec(*h, w, x, tol);
Real vHw = v.dot(h->dual());
std::vector<Real> hsymCheck(3, 0);
hsymCheck[0] = wHv;
hsymCheck[1] = vHw;
hsymCheck[2] = std::abs(vHw-wHv);
// Save the format state of the original outStream.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(outStream);
if (printToStream) {
outStream << std::right
<< std::setw(20) << "<w, H(x)v>"
<< std::setw(20) << "<v, H(x)w>"
<< std::setw(20) << "abs error"
<< "\n";
outStream << std::scientific << std::setprecision(11) << std::right
<< std::setw(20) << hsymCheck[0]
<< std::setw(20) << hsymCheck[1]
<< std::setw(20) << hsymCheck[2]
<< "\n";
}
// Reset format state of outStream.
outStream.copyfmt(oldFormatState);
return hsymCheck;
} // checkHessSym
int HDIV_WEDGE_I1_FEM_Test01(const bool verbose) {
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (1)// (verbose)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
typedef typename
Kokkos::Impl::is_space<DeviceSpaceType>::host_mirror_space::execution_space HostSpaceType ;
*outStream << "DeviceSpace:: "; DeviceSpaceType::print_configuration(*outStream, false);
*outStream << "HostSpace:: "; HostSpaceType::print_configuration(*outStream, false);
*outStream
<< "===============================================================================\n"
<< "| |\n"
<< "| Unit Test (Basis_HDIV_WEDGE_I1_FEM) |\n"
<< "| |\n"
<< "| 1) Conversion of Dof tags into Dof ordinals and back |\n"
<< "| 2) Basis values for VALUE and DIV operators |\n"
<< "| |\n"
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n"
<< "| Denis Ridzal ([email protected]), |\n"
<< "| Kara Peterson ([email protected]). |\n"
<< "| |\n"
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n"
<< "| Trilinos website: http://trilinos.sandia.gov |\n"
<< "| |\n"
<< "===============================================================================\n";
typedef Kokkos::DynRankView<ValueType,DeviceSpaceType> DynRankView;
typedef Kokkos::DynRankView<ValueType,HostSpaceType> DynRankViewHost;
#define ConstructWithLabel(obj, ...) obj(#obj, __VA_ARGS__)
const ValueType tol = tolerence();
int errorFlag = 0;
// for virtual function, value and point types are declared in the class
typedef ValueType outputValueType;
typedef ValueType pointValueType;
Basis_HDIV_WEDGE_I1_FEM<DeviceSpaceType,outputValueType,pointValueType> wedgeBasis;
*outStream
<< "\n"
<< "===============================================================================\n"
<< "| TEST 1: constructors and exceptions |\n"
<< "===============================================================================\n";
try {
ordinal_type nthrow = 0, ncatch = 0;
#ifdef HAVE_INTREPID2_DEBUG
// Define array containing the 6 vertices of the reference WEDGE and 6 other points.
DynRankView ConstructWithLabel(wedgeNodes, 12, 3);
// Generic array for the output values; needs to be properly resized depending on the operator type
const auto numFields = wedgeBasis.getCardinality();
const auto numPoints = wedgeNodes.dimension(0);
const auto spaceDim = wedgeBasis.getBaseCellTopology().getDimension();
// exception #1: GRAD cannot be applied to HDIV functions
DynRankView ConstructWithLabel(vals, numFields, numPoints, spaceDim );
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_GRAD));
// exception #2: CURL cannot be applied to HDIV functions
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_CURL));
// Exceptions 3-7: all bf tags/bf Ids below are wrong and should cause getDofOrdinal() and
// getDofTag() to access invalid array elements thereby causing bounds check exception
// exception #3
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getDofOrdinal(3,0,0));
// exception #4
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getDofOrdinal(1,1,1));
// exception #5
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getDofOrdinal(0,4,1));
// exception #6
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getDofTag(11));
// exception #7
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getDofTag(-1));
// Exceptions 8-15 test exception handling with incorrectly dimensioned input/output arrays
// exception #8: input points array must be of rank-2
DynRankView ConstructWithLabel(badPoints1, 4, 5, 3);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(vals, badPoints1, OPERATOR_VALUE));
// exception #9 dimension 1 in the input point array must equal space dimension of the cell
DynRankView ConstructWithLabel(badPoints2, 4, 2);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(vals, badPoints2, OPERATOR_VALUE));
// exception #10 output values must be of rank-3 for OPERATOR_VALUE
DynRankView ConstructWithLabel(badVals1, 4, 3);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(badVals1, wedgeNodes, OPERATOR_VALUE));
// exception #11 output values must be of rank-2 for OPERATOR_DIV
DynRankView ConstructWithLabel(badVals2, 4, 3, 1);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(badVals2, wedgeNodes, OPERATOR_DIV));
// exception #12 incorrect 0th dimension of output array (must equal number of basis functions)
DynRankView ConstructWithLabel(badVals3, wedgeBasis.getCardinality() + 1, wedgeNodes.dimension(0), 3);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(badVals3, wedgeNodes, OPERATOR_VALUE));
// exception #13 incorrect 0th dimension of output array (must equal number of basis functions)
DynRankView ConstructWithLabel(badVals4, wedgeBasis.getCardinality() + 1, wedgeNodes.dimension(0));
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(badVals4, wedgeNodes, OPERATOR_DIV));
// exception #14 incorrect 1st dimension of output array (must equal number of points)
DynRankView ConstructWithLabel(badVals5, wedgeBasis.getCardinality(), wedgeNodes.dimension(0) + 1, 3);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(badVals5, wedgeNodes, OPERATOR_VALUE));
// exception #15 incorrect 1st dimension of output array (must equal number of points)
DynRankView ConstructWithLabel(badVals6, wedgeBasis.getCardinality(), wedgeNodes.dimension(0) + 1);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(badVals6, wedgeNodes, OPERATOR_DIV));
// exception #16: incorrect 2nd dimension of output array (must equal the space dimension)
DynRankView ConstructWithLabel(badVals7, wedgeBasis.getCardinality(), wedgeNodes.dimension(0), 4);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(badVals7, wedgeNodes, OPERATOR_VALUE));
#endif
} catch (std::logic_error err) {
*outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
*outStream << err.what() << '\n';
*outStream << "-------------------------------------------------------------------------------" << "\n\n";
errorFlag = -1000;
}
*outStream
<< "\n"
<< "===============================================================================\n"
<< "| TEST 2: correctness of tag to enum and enum to tag lookups |\n"
<< "===============================================================================\n";
try{
const auto numFields = wedgeBasis.getCardinality();
const auto allTags = wedgeBasis.getAllDofTags();
// Loop over all tags, lookup the associated dof enumeration and then lookup the tag again
const auto dofTagSize = allTags.dimension(0);
// Loop over all tags, lookup the associated dof enumeration and then lookup the tag again
for (size_type i = 0; i < dofTagSize; i++) {
const auto bfOrd = wedgeBasis.getDofOrdinal(allTags(i, 0), allTags(i, 1), allTags(i, 2));
const auto myTag = wedgeBasis.getDofTag(bfOrd);
if( !( (myTag(0) == allTags(i, 0)) &&
(myTag(1) == allTags(i, 1)) &&
(myTag(2) == allTags(i, 2)) &&
(myTag(3) == allTags(i, 3)) ) ) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " getDofOrdinal( {"
<< allTags(i, 0) << ", "
<< allTags(i, 1) << ", "
<< allTags(i, 2) << ", "
<< allTags(i, 3) << "}) = " << bfOrd <<" but \n";
*outStream << " getDofTag(" << bfOrd << ") = { "
<< myTag(0) << ", "
<< myTag(1) << ", "
<< myTag(2) << ", "
<< myTag(3) << "}\n";
}
}
// Now do the same but loop over basis functions
for( int bfOrd = 0; bfOrd <numFields; bfOrd++) {
const auto myTag = wedgeBasis.getDofTag(bfOrd);
const auto myBfOrd = wedgeBasis.getDofOrdinal(myTag(0), myTag(1), myTag(2));
if( bfOrd != myBfOrd) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " getDofTag(" << bfOrd << ") = { "
<< myTag(0) << ", "
<< myTag(1) << ", "
<< myTag(2) << ", "
<< myTag(3) << "} but getDofOrdinal({"
<< myTag(0) << ", "
<< myTag(1) << ", "
<< myTag(2) << ", "
<< myTag(3) << "} ) = " << myBfOrd << "\n";
}
}
}
catch (std::logic_error err){
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 3: correctness of basis function values |\n"\
<< "===============================================================================\n";
outStream -> precision(20);
// VALUE: Each row pair gives the 5x3 correct basis set values at an evaluation point
double basisValues[] = {
0, -0.500000, 0, 0, 0, 0, -0.500000, 0, 0, 0, 0, -2.00000, 0, 0, 0, \
0.500000, -0.500000, 0, 0.500000, 0, 0, 0, 0, 0, 0, 0, -2.00000, 0, \
0, 0, 0, 0, 0, 0, 0.500000, 0, -0.500000, 0.500000, 0, 0, 0, \
-2.00000, 0, 0, 0, 0, -0.500000, 0, 0, 0, 0, -0.500000, 0, 0, 0, 0, \
0, 0, 0, 2.00000, 0.500000, -0.500000, 0, 0.500000, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 2.00000, 0, 0, 0, 0, 0.500000, 0, -0.500000, 0.500000, 0, \
0, 0, 0, 0, 0, 2.00000, 0.125000, -0.250000, 0, 0.125000, 0.250000, \
0, -0.375000, 0.250000, 0, 0, 0, -2.00000, 0, 0, 0, 0.250000, \
-0.375000, 0, 0.250000, 0.125000, 0, -0.250000, 0.125000, 0, 0, 0, \
-1.00000, 0, 0, 1.00000, 0.125000, -0.375000, 0, 0.125000, 0.125000, \
0, -0.375000, 0.125000, 0, 0, 0, 0, 0, 0, 2.00000, 0.125000, \
-0.500000, 0, 0.125000, 0, 0, -0.375000, 0, 0, 0, 0, -0.250000, 0, 0, \
1.75000, 0, -0.250000, 0, 0, 0.250000, 0, -0.500000, 0.250000, 0, 0, \
0, -1.25000, 0, 0, 0.750000, 0.250000, -0.250000, 0, 0.250000, \
0.250000, 0, -0.250000, 0.250000, 0, 0, 0, -1.00000, 0, 0, 1.00000};
// DIV: each row pair gives the 5 correct values of the divergence of the 5 basis functions
double basisDivs[] = {
// 6 vertices
1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0,
// 6 other points
1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0,
1.0, 1.0, 1.0, 1.0, 1.0
};
try{
DynRankViewHost ConstructWithLabel(wedgeNodesHost, 12, 3);
wedgeNodesHost(0,0) = 0.0; wedgeNodesHost(0,1) = 0.0; wedgeNodesHost(0,2) = -1.0;
wedgeNodesHost(1,0) = 1.0; wedgeNodesHost(1,1) = 0.0; wedgeNodesHost(1,2) = -1.0;
wedgeNodesHost(2,0) = 0.0; wedgeNodesHost(2,1) = 1.0; wedgeNodesHost(2,2) = -1.0;
wedgeNodesHost(3,0) = 0.0; wedgeNodesHost(3,1) = 0.0; wedgeNodesHost(3,2) = 1.0;
wedgeNodesHost(4,0) = 1.0; wedgeNodesHost(4,1) = 0.0; wedgeNodesHost(4,2) = 1.0;
wedgeNodesHost(5,0) = 0.0; wedgeNodesHost(5,1) = 1.0; wedgeNodesHost(5,2) = 1.0;
wedgeNodesHost(6,0) = 0.25; wedgeNodesHost(6,1) = 0.5; wedgeNodesHost(6,2) = -1.0;
wedgeNodesHost(7,0) = 0.5; wedgeNodesHost(7,1) = 0.25; wedgeNodesHost(7,2) = 0.0;
wedgeNodesHost(8,0) = 0.25; wedgeNodesHost(8,1) = 0.25; wedgeNodesHost(8,2) = 1.0;
wedgeNodesHost(9,0) = 0.25; wedgeNodesHost(9,1) = 0.0; wedgeNodesHost(9,2) = 0.75;
wedgeNodesHost(10,0)= 0.0; wedgeNodesHost(10,1)= 0.5; wedgeNodesHost(10,2)= -0.25;
wedgeNodesHost(11,0)= 0.5; wedgeNodesHost(11,1)= 0.5; wedgeNodesHost(11,2)= 0.0;
const auto wedgeNodes = Kokkos::create_mirror_view(typename DeviceSpaceType::memory_space(), wedgeNodesHost);
Kokkos::deep_copy(wedgeNodes, wedgeNodesHost);
// Dimensions for the output arrays:
const auto numFields = wedgeBasis.getCardinality();
const auto numPoints = wedgeNodes.dimension(0);
const auto spaceDim = wedgeBasis.getBaseCellTopology().getDimension();
// Check VALUE of basis functions: resize vals to rank-3 container:
{
DynRankView ConstructWithLabel(vals, numFields, numPoints, spaceDim);
wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_VALUE);
const auto vals_host = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), vals);
Kokkos::deep_copy(vals_host, vals);
for (int i = 0; i < numFields; i++) {
for (size_type j = 0; j < numPoints; j++) {
for (size_type k = 0; k < spaceDim; k++) {
int l = k + i * spaceDim + j * spaceDim * numFields;
if (std::abs(vals_host(i,j,k) - basisValues[l]) > tol) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed value: " << vals_host(i,j,k)
<< " but reference value: " << basisValues[l] << "\n";
}
}
}
}
}
// Check DIV of basis function: resize vals to rank-2 container
{
DynRankView ConstructWithLabel(vals, numFields, numPoints);
wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_DIV);
const auto vals_host = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), vals);
Kokkos::deep_copy(vals_host, vals);
for (int i = 0; i < numFields; i++) {
for (size_type j = 0; j < numPoints; j++) {
int l = i + j * numFields;
if (std::abs(vals_host(i,j) - basisDivs[l]) > tol) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";
*outStream << "} computed divergence component: " << vals_host(i,j)
<< " but reference divergence component: " << basisDivs[l] << "\n";
}
}
}
}
} catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
}
*outStream
<< "\n"
<< "===============================================================================\n"
<< "| TEST 4: correctness of DoF locations |\n"
<< "===============================================================================\n";
try {
const auto numFields = wedgeBasis.getCardinality();
const auto spaceDim = wedgeBasis.getBaseCellTopology().getDimension();
// Check exceptions.
ordinal_type nthrow = 0, ncatch = 0;
#ifdef HAVE_INTREPID2_DEBUG
{
DynRankView ConstructWithLabel(badVals, 1,2,3);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getDofCoords(badVals) );
}
{
DynRankView ConstructWithLabel(badVals, 4,3);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getDofCoords(badVals) );
}
{
DynRankView ConstructWithLabel(badVals, 5,2);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getDofCoords(badVals) );
}
#endif
if (nthrow != ncatch) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << "# of catch ("<< ncatch << ") is different from # of throw (" << ncatch << ")\n";
}
DynRankView ConstructWithLabel(bvals, numFields, numFields, spaceDim);
DynRankView ConstructWithLabel(cvals, numFields, spaceDim);
// Check mathematical correctness.
wedgeBasis.getDofCoords(cvals);
wedgeBasis.getValues(bvals, cvals, OPERATOR_VALUE);
// Check mathematical correctness
DynRankViewHost ConstructWithLabel(normals, numFields,spaceDim); // normals at each point basis point
normals(0,0) = 0.0; normals(0,1) = -2.0; normals(0,2) = 0.0;
normals(1,0) = 2.0; normals(1,1) = 2.0; normals(1,2) = 0.0;
normals(2,0) = -2.0; normals(2,1) = 0.0; normals(2,2) = 0.0;
normals(3,0) = 0.0; normals(3,1) = 0.0; normals(3,2) = -0.5;
normals(4,0) = 0.0; normals(4,1) = 0.0; normals(4,2) = 0.5;
auto cvals_host = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), cvals);
Kokkos::deep_copy(cvals_host, cvals);
auto bvals_host = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), bvals);
Kokkos::deep_copy(bvals_host, bvals);
for (ordinal_type i=0;i<numFields;++i) {
for (ordinal_type j=0;j<numFields;++j) {
ValueType normal = 0.0;
for(size_type d=0;d<spaceDim;++d) {
normal += bvals_host(i,j,d)*normals(j,d);
}
const ValueType expected_normal = (i == j);
if (std::abs(normal - expected_normal) > tol || isnan(normal)) {
errorFlag++;
std::stringstream ss;
ss << "\nNormal component of basis function " << i << " at (" << cvals_host(j,0) << ", " << cvals_host(j,1)<< ", " << cvals_host(j,2) << ") is " << normal << " but should be " << expected_normal << "\n";
*outStream << ss.str();
}
}
}
} catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
}
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
int HCURL_WEDGE_I1_FEM_Test01(const bool verbose) {
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (verbose)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
typedef typename
Kokkos::Impl::is_space<DeviceSpaceType>::host_mirror_space::execution_space HostSpaceType ;
*outStream << "DeviceSpace:: "; DeviceSpaceType::print_configuration(*outStream, false);
*outStream << "HostSpace:: "; HostSpaceType::print_configuration(*outStream, false);
*outStream
<< "\n"
<< "===============================================================================\n"
<< "| |\n"
<< "| Unit Test (Basis_HCURL_WEDGE_I1_FEM) |\n"
<< "| |\n"
<< "| 1) Conversion of Dof tags into Dof ordinals and back |\n"
<< "| 2) Basis values for VALUE and CURL operators |\n"
<< "| |\n"
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n"
<< "| Denis Ridzal ([email protected]), |\n"
<< "| Kara Peterson ([email protected]). |\n"
<< "| Kyungjoo Kim ([email protected]). |\n"
<< "| |\n"
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n"
<< "| Trilinos website: http://trilinos.sandia.gov |\n"
<< "| |\n"
<< "===============================================================================\n";
typedef Kokkos::DynRankView<ValueType,DeviceSpaceType> DynRankView;
typedef Kokkos::DynRankView<ValueType,HostSpaceType> DynRankViewHost;
#define ConstructWithLabel(obj, ...) obj(#obj, __VA_ARGS__)
const ValueType tol = tolerence();
int errorFlag = 0;
// for virtual function, value and point types are declared in the class
typedef ValueType outputValueType;
typedef ValueType pointValueType;
Basis_HCURL_WEDGE_I1_FEM<DeviceSpaceType,outputValueType,pointValueType> wedgeBasis;
*outStream
<< "\n"
<< "===============================================================================\n"
<< "| TEST 1: Basis creation, exception testing |\n"
<< "===============================================================================\n";
try{
ordinal_type nthrow = 0, ncatch = 0;
#ifdef HAVE_INTREPID2_DEBUG
// Define array containing the 4 vertices of the reference WEDGE and its center.
DynRankView ConstructWithLabel(wedgeNodes, 12, 3);
// Generic array for the output values; needs to be properly resized depending on the operator type
const ordinal_type numFields = wedgeBasis.getCardinality();
const ordinal_type numPoints = wedgeNodes.dimension(0);
const ordinal_type spaceDim = wedgeBasis.getBaseCellTopology().getDimension();
DynRankView vals ("vals", numFields, numPoints);
DynRankView vals_vec ("vals", numFields, numPoints, spaceDim);
{
// exception #1: GRAD cannot be applied to HCURL functions
// resize vals to rank-3 container with dimensions (num. basis functions, num. points, arbitrary)
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(vals_vec, wedgeNodes, OPERATOR_GRAD) );
// exception #2: DIV cannot be applied to HCURL functions
// resize vals to rank-2 container with dimensions (num. basis functions, num. points)
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_DIV) );
}
// Exceptions 3-7: all bf tags/bf Ids below are wrong and should cause getDofOrdinal() and
// getDofTag() to access invalid array elements thereby causing bounds check exception
{
// exception #3
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getDofOrdinal(3,0,0) );
// exception #4
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getDofOrdinal(1,1,1) );
// exception #5
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getDofOrdinal(0,4,1) );
// exception #6
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getDofTag(numFields) );
// exception #7
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getDofTag(-1) );
}
// Exceptions 8- test exception handling with incorrectly dimensioned input/output arrays
{
// exception #8: input points array must be of rank-2
DynRankView ConstructWithLabel(badPoints1, 4, 5, 3);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(vals, badPoints1, OPERATOR_VALUE) );
}
{
// exception #9 dimension 1 in the input point array must equal space dimension of the cell
DynRankView ConstructWithLabel(badPoints2, 4, 2);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(vals, badPoints2, OPERATOR_VALUE) );
}
{
// exception #10 output values must be of rank-3 for OPERATOR_VALUE
DynRankView ConstructWithLabel(badVals1, 4, 3);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(badVals1, wedgeNodes, OPERATOR_VALUE) );
// exception #11 output values must be of rank-3 for OPERATOR_CURL
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(badVals1, wedgeNodes, OPERATOR_CURL) );
}
{
// exception #12 incorrect 0th dimension of output array (must equal number of basis functions)
DynRankView ConstructWithLabel(badVals2, numFields + 1, numPoints, 3);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(badVals2, wedgeNodes, OPERATOR_VALUE) );
}
{
// exception #13 incorrect 1st dimension of output array (must equal number of points)
DynRankView ConstructWithLabel(badVals3, numFields, numPoints + 1, 3);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(badVals3, wedgeNodes, OPERATOR_VALUE) );
}
{
// exception #14: incorrect 2nd dimension of output array (must equal the space dimension)
DynRankView ConstructWithLabel(badVals4, numFields, numPoints, 4);
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(badVals4, wedgeNodes, OPERATOR_VALUE) );
// exception #15: incorrect 2nd dimension of output array (must equal the space dimension)
INTREPID2_TEST_ERROR_EXPECTED( wedgeBasis.getValues(badVals4, wedgeNodes, OPERATOR_CURL) );
}
#endif
// Check if number of thrown exceptions matches the one we expect
if (nthrow != ncatch) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << "# of catch ("<< ncatch << ") is different from # of throw (" << nthrow << ")\n";
}
} catch (std::logic_error err) {
*outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
*outStream << err.what() << '\n';
*outStream << "-------------------------------------------------------------------------------" << "\n\n";
errorFlag = -1000;
};
*outStream
<< "\n"
<< "===============================================================================\n"
<< "| TEST 2: correctness of tag to enum and enum to tag lookups |\n"
<< "===============================================================================\n";
try{
const ordinal_type numFields = wedgeBasis.getCardinality();
const auto allTags = wedgeBasis.getAllDofTags();
// Loop over all tags, lookup the associated dof enumeration and then lookup the tag again
const ordinal_type dofTagSize = allTags.dimension(0);
for (ordinal_type i = 0; i < dofTagSize; ++i) {
auto bfOrd = wedgeBasis.getDofOrdinal(allTags(i,0), allTags(i,1), allTags(i,2));
const auto myTag = wedgeBasis.getDofTag(bfOrd);
if( !( (myTag(0) == allTags(i,0)) &&
(myTag(1) == allTags(i,1)) &&
(myTag(2) == allTags(i,2)) &&
(myTag(3) == allTags(i,3)) ) ) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " getDofOrdinal( {"
<< allTags(i,0) << ", "
<< allTags(i,1) << ", "
<< allTags(i,2) << ", "
<< allTags(i,3) << "}) = " << bfOrd <<" but \n";
*outStream << " getDofTag(" << bfOrd << ") = { "
<< myTag(0) << ", "
<< myTag(1) << ", "
<< myTag(2) << ", "
<< myTag(3) << "}\n";
}
}
// Now do the same but loop over basis functions
for( ordinal_type bfOrd = 0; bfOrd < numFields; ++bfOrd) {
const auto myTag = wedgeBasis.getDofTag(bfOrd);
const auto myBfOrd = wedgeBasis.getDofOrdinal(myTag(0), myTag(1), myTag(2));
if( bfOrd != myBfOrd) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " getDofTag(" << bfOrd << ") = { "
<< myTag(0) << ", "
<< myTag(1) << ", "
<< myTag(2) << ", "
<< myTag(3) << "} but getDofOrdinal({"
<< myTag(0) << ", "
<< myTag(1) << ", "
<< myTag(2) << ", "
<< myTag(3) << "} ) = " << myBfOrd << "\n";
}
}
} catch (std::logic_error err){
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
*outStream
<< "\n"
<< "===============================================================================\n"
<< "| TEST 3: correctness of basis function values |\n"
<< "===============================================================================\n";
outStream -> precision(20);
// VALUE: Each row pair gives the 9x3 correct basis set values at an evaluation point: (P,F,D) layout
const ValueType basisValues[] = {
1.00000, 0, 0, 0, 0, 0, 0, -1.00000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0.500000, 0, 0, 0, 0, 0, 0, 1.00000, 1.00000, 0, 0, 1.00000, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.500000, 0, 0, 0, 0, \
0, 0, -1.00000, 0, 0, -1.00000, -1.00000, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0.500000, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
1.00000, 0, 0, 0, 0, 0, 0, -1.00000, 0, 0, 0, 0.500000, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00000, 1.00000, 0, 0, 1.00000, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0.500000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, -1.00000, 0, 0, -1.00000, -1.00000, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0.500000, 0.500000, 0.250000, 0, -0.500000, 0.250000, 0, \
-0.500000, -0.750000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.125000, \
0, 0, 0.125000, 0, 0, 0.250000, 0.375000, 0.250000, 0, -0.125000, \
0.250000, 0, -0.125000, -0.250000, 0, 0.375000, 0.250000, 0, \
-0.125000, 0.250000, 0, -0.125000, -0.250000, 0, 0, 0, 0.125000, 0, \
0, 0.250000, 0, 0, 0.125000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.750000, \
0.250000, 0, -0.250000, 0.250000, 0, -0.250000, -0.750000, 0, 0, 0, \
0.250000, 0, 0, 0.125000, 0, 0, 0.125000, 0.125000, 0.0312500, 0, 0, \
0.0312500, 0, 0, -0.0937500, 0, 0.875000, 0.218750, 0, 0, 0.218750, \
0, 0, -0.656250, 0, 0, 0, 0.375000, 0, 0, 0.125000, 0, 0, 0, \
0.312500, 0, 0, -0.312500, 0, 0, -0.312500, -0.625000, 0, 0.187500, \
0, 0, -0.187500, 0, 0, -0.187500, -0.375000, 0, 0, 0, 0.250000, 0, 0, \
0, 0, 0, 0.250000, 0.250000, 0.250000, 0, -0.250000, 0.250000, 0, \
-0.250000, -0.250000, 0, 0.250000, 0.250000, 0, -0.250000, 0.250000, \
0, -0.250000, -0.250000, 0, 0, 0, 0, 0, 0, 0.250000, 0, 0, 0.250000
};
// CURL: each row pair gives the 9x3 correct values of the curls of the 9 basis functions: (P,F,D) layout
const ValueType basisCurls[] = {
0, -0.500000, 2.00000, 0, 0, 2.00000, -0.500000, 0, 2.00000, 0, \
0.500000, 0, 0, 0, 0, 0.500000, 0, 0, -0.500000, 0.500000, 0, 0, \
-0.500000, 0, 0.500000, 0, 0, 0.500000, -0.500000, 2.00000, 0.500000, \
0, 2.00000, 0, 0, 2.00000, -0.500000, 0.500000, 0, -0.500000, 0, 0, \
0, 0, 0, -0.500000, 0.500000, 0, 0, -0.500000, 0, 0.500000, 0, 0, 0, \
0, 2.00000, 0, 0.500000, 2.00000, -0.500000, 0.500000, 2.00000, 0, 0, \
0, 0, -0.500000, 0, 0.500000, -0.500000, 0, -0.500000, 0.500000, 0, \
0, -0.500000, 0, 0.500000, 0, 0, 0, -0.500000, 0, 0, 0, 0, -0.500000, \
0, 0, 0, 0.500000, 2.00000, 0, 0, 2.00000, 0.500000, 0, 2.00000, \
-0.500000, 0.500000, 0, 0, -0.500000, 0, 0.500000, 0, 0, 0.500000, \
-0.500000, 0, 0.500000, 0, 0, 0, 0, 0, -0.500000, 0.500000, 2.00000, \
-0.500000, 0, 2.00000, 0, 0, 2.00000, -0.500000, 0.500000, 0, 0, \
-0.500000, 0, 0.500000, 0, 0, 0, 0, 0, 0, 0.500000, 0, -0.500000, \
0.500000, 0, 0, 0, 2.00000, 0, -0.500000, 2.00000, 0.500000, \
-0.500000, 2.00000, -0.500000, 0.500000, 0, 0, -0.500000, 0, \
0.500000, 0, 0, 0.125000, -0.250000, 2.00000, 0.125000, 0.250000, \
2.00000, -0.375000, 0.250000, 2.00000, -0.125000, 0.250000, 0, \
-0.125000, -0.250000, 0, 0.375000, -0.250000, 0, -0.500000, 0.500000, \
0, 0, -0.500000, 0, 0.500000, 0, 0, 0.250000, -0.375000, 1.00000, \
0.250000, 0.125000, 1.00000, -0.250000, 0.125000, 1.00000, -0.250000, \
0.375000, 1.00000, -0.250000, -0.125000, 1.00000, 0.250000, \
-0.125000, 1.00000, -0.500000, 0.500000, 0, 0, -0.500000, 0, \
0.500000, 0, 0, 0.125000, -0.375000, 0, 0.125000, 0.125000, 0, \
-0.375000, 0.125000, 0, -0.125000, 0.375000, 2.00000, -0.125000, \
-0.125000, 2.00000, 0.375000, -0.125000, 2.00000, -0.500000, \
0.500000, 0, 0, -0.500000, 0, 0.500000, 0, 0, 0.125000, -0.500000, \
0.250000, 0.125000, 0, 0.250000, -0.375000, 0, 0.250000, -0.125000, \
0.500000, 1.75000, -0.125000, 0, 1.75000, 0.375000, 0, 1.75000, \
-0.500000, 0.500000, 0, 0, -0.500000, 0, 0.500000, 0, 0, 0, \
-0.250000, 1.25000, 0, 0.250000, 1.25000, -0.500000, 0.250000, \
1.25000, 0, 0.250000, 0.750000, 0, -0.250000, 0.750000, 0.500000, \
-0.250000, 0.750000, -0.500000, 0.500000, 0, 0, -0.500000, 0, \
0.500000, 0, 0, 0.250000, -0.250000, 1.00000, 0.250000, 0.250000, \
1.00000, -0.250000, 0.250000, 1.00000, -0.250000, 0.250000, 1.00000, \
-0.250000, -0.250000, 1.00000, 0.250000, -0.250000, 1.00000, \
-0.500000, 0.500000, 0, 0, -0.500000, 0, 0.500000, 0, 0
};
try{
DynRankViewHost ConstructWithLabel(wedgeNodesHost, 12, 3);
wedgeNodesHost(0,0) = 0.0; wedgeNodesHost(0,1) = 0.0; wedgeNodesHost(0,2) = -1.0;
wedgeNodesHost(1,0) = 1.0; wedgeNodesHost(1,1) = 0.0; wedgeNodesHost(1,2) = -1.0;
wedgeNodesHost(2,0) = 0.0; wedgeNodesHost(2,1) = 1.0; wedgeNodesHost(2,2) = -1.0;
wedgeNodesHost(3,0) = 0.0; wedgeNodesHost(3,1) = 0.0; wedgeNodesHost(3,2) = 1.0;
wedgeNodesHost(4,0) = 1.0; wedgeNodesHost(4,1) = 0.0; wedgeNodesHost(4,2) = 1.0;
wedgeNodesHost(5,0) = 0.0; wedgeNodesHost(5,1) = 1.0; wedgeNodesHost(5,2) = 1.0;
wedgeNodesHost(6,0) = 0.25; wedgeNodesHost(6,1) = 0.5; wedgeNodesHost(6,2) = -1.0;
wedgeNodesHost(7,0) = 0.5; wedgeNodesHost(7,1) = 0.25; wedgeNodesHost(7,2) = 0.0;
wedgeNodesHost(8,0) = 0.25; wedgeNodesHost(8,1) = 0.25; wedgeNodesHost(8,2) = 1.0;
wedgeNodesHost(9,0) = 0.25; wedgeNodesHost(9,1) = 0.0; wedgeNodesHost(9,2) = 0.75;
wedgeNodesHost(10,0)= 0.0; wedgeNodesHost(10,1)= 0.5; wedgeNodesHost(10,2)= -0.25;
wedgeNodesHost(11,0)= 0.5; wedgeNodesHost(11,1)= 0.5; wedgeNodesHost(11,2)= 0.0;
const auto wedgeNodes = Kokkos::create_mirror_view(typename DeviceSpaceType::memory_space(), wedgeNodesHost);
Kokkos::deep_copy(wedgeNodes, wedgeNodesHost);
// Dimensions for the output arrays:
const ordinal_type numFields = wedgeBasis.getCardinality();
const ordinal_type numPoints = wedgeNodes.dimension(0);
const ordinal_type spaceDim = wedgeBasis.getBaseCellTopology().getDimension();
{
// Check VALUE of basis functions: resize vals to rank-3 container:
DynRankView ConstructWithLabel(vals, numFields, numPoints, spaceDim);
wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_VALUE);
auto vals_host = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), vals);
Kokkos::deep_copy(vals_host, vals);
for (ordinal_type i = 0; i < numFields; ++i) {
for (ordinal_type j = 0; j < numPoints; ++j) {
for (ordinal_type k = 0; k < spaceDim; ++k) {
// compute offset for (P,F,D) data layout: indices are P->j, F->i, D->k
const ordinal_type l = k + i * spaceDim + j * spaceDim * numFields;
if (std::abs(vals_host(i,j,k) - basisValues[l]) > tol) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed value: " << vals_host(i,j,k)
<< " but reference value: " << basisValues[l] << "\n";
}
}
}
}
}
{
// Check CURL of basis function: resize vals to rank-3 container
DynRankView ConstructWithLabel(vals, numFields, numPoints, spaceDim);
wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_CURL);
auto vals_host = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), vals);
Kokkos::deep_copy(vals_host, vals);
for (ordinal_type i = 0; i < numFields; ++i) {
for (ordinal_type j = 0; j < numPoints; ++j) {
for (ordinal_type k = 0; k < spaceDim; ++k) {
// compute offset for (P,F,D) data layout: indices are P->j, F->i, D->k
const ordinal_type l = k + i * spaceDim + j * spaceDim * numFields;
if (std::abs(vals_host(i,j,k) - basisCurls[l]) > tol) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed curl component: " << vals_host(i,j,k)
<< " but reference curl component: " << basisCurls[l] << "\n";
}
}
}
}
}
}
// Catch unexpected errors
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
int Orientation_Test05(const bool verbose) {
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (verbose)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
typedef typename
Kokkos::Impl::is_space<DeviceSpaceType>::host_mirror_space::execution_space HostSpaceType ;
*outStream << "DeviceSpace:: "; DeviceSpaceType::print_configuration(*outStream, false);
*outStream << "HostSpace:: "; HostSpaceType::print_configuration(*outStream, false);
*outStream << "\n";
*outStream
<< "===============================================================================\n"
<< "| |\n"
<< "| Unit Test (OrientationTools, getModifiedHcurl_I1_Basis) |\n"
<< "| |\n"
<< "===============================================================================\n";
int errorFlag = 0;
const double tol = tolerence();
typedef OrientationTools<DeviceSpaceType> ots;
try {
{
*outStream << "\n -- Testing Quadrilateral \n\n";
Basis_HCURL_QUAD_I1_FEM<DeviceSpaceType> cellBasis;
const auto cellTopo = cellBasis.getBaseCellTopology();
const ordinal_type ndofBasis = cellBasis.getCardinality();
//
// 9 12 13 16
// 4 3 11 15
// 5 2 8 14
// 1 6 7 10
ordinal_type refMesh[9][4] = { { 1, 6, 2, 5 },
{ 6, 7, 8, 2 },
{ 7,10,14, 8 },
{ 5, 2, 3, 4 },
{ 2, 8,11, 3 },
{ 8,14,15,11 },
{ 4, 3,12, 9 },
{ 3,11,13,12 },
{11,15,16,13 } };
const ordinal_type numCells = 9, numVerts = 4, numEdges = 4;
// view to import refMesh from host
Kokkos::DynRankView<ordinal_type,Kokkos::LayoutRight,HostSpaceType>
elemNodesHost(&refMesh[0][0], numCells, numVerts);
auto elemNodes = Kokkos::create_mirror_view(typename DeviceSpaceType::memory_space(), elemNodesHost);
Kokkos::deep_copy(elemNodes, elemNodesHost);
// compute orientations for cells (one time computation)
Kokkos::DynRankView<Orientation,DeviceSpaceType> elemOrts("elemOrts", numCells);
ots::getOrientation(elemOrts, elemNodes, cellTopo);
auto elemOrtsHost = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), elemOrts);
Kokkos::deep_copy(elemOrtsHost, elemOrts);
// cell specific modified basis
Kokkos::DynRankView<double,DeviceSpaceType> outValues("outValues", numCells, ndofBasis);
Kokkos::DynRankView<double,DeviceSpaceType> refValues("refValues", numCells, ndofBasis);
auto refValuesHost = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), refValues);
for (auto cell=0;cell<numCells;++cell)
for (auto bf=0;bf<ndofBasis;++bf)
refValuesHost(cell, bf) = bf;
Kokkos::deep_copy(refValues, refValuesHost);
// modify refValues accounting for orientations
ots::modifyBasisByOrientation(outValues,
refValues,
elemOrts,
&cellBasis);
auto outValuesHost = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), outValues);
Kokkos::deep_copy(outValuesHost, outValues);
for (auto cell=0;cell<numCells;++cell) {
int flag = 0 ;
std::stringstream s1, s2;
ordinal_type orts[numEdges];
elemOrtsHost(cell).getEdgeOrientation(orts, numEdges);
const double ortVal[2] = { 1.0 , - 1.0 };
s1 << " :: edge(0000) = " ;
s2 << " :: edge(" << orts[0] << orts[1] << orts[2] << orts[3] << ") = ";
for (auto edgeId=0;edgeId<numEdges;++edgeId) {
const auto ndof = cellBasis.getDofTag(cellBasis.getDofOrdinal(1, edgeId, 0))(3);
for (auto i=0;i<ndof;++i) {
const auto refOrd = cellBasis.getDofOrdinal(1, edgeId, i);
const auto outOrd = cellBasis.getDofOrdinal(1, edgeId, i);
s1 << std::setw(4) << refValuesHost(cell, outOrd);
s2 << std::setw(4) << outValuesHost(cell, outOrd);
flag += (std::abs(ortVal[orts[edgeId]]*outValuesHost(cell, outOrd) - refValuesHost(cell, refOrd)) > tol);
}
s1 << " // ";
s2 << " // ";
}
*outStream << "\n cell = " << cell << "\n"
<< " - refValues = " << s1.str() << "\n"
<< " - outValues = " << s2.str() << "\n";
if (flag) {
*outStream << " ^^^^^^^^^^^^ FAILURE\n";
errorFlag += flag;
}
}
ots::clearCoeffMatrix();
}
} catch (std::exception err) {
std::cout << " Exeption\n";
*outStream << err.what() << "\n\n";
errorFlag = -1000;
}
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED = " << errorFlag << "\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
int HGRAD_TET_C2_FEM_Test01(const bool verbose) {
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (verbose)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
typedef typename
Kokkos::Impl::is_space<DeviceSpaceType>::host_mirror_space::execution_space HostSpaceType ;
*outStream << "DeviceSpace:: "; DeviceSpaceType::print_configuration(*outStream, false);
*outStream << "HostSpace:: "; HostSpaceType::print_configuration(*outStream, false);
*outStream
<< "\n"
<< "===============================================================================\n"
<< "| |\n"
<< "| Unit Test (Basis_HGRAD_TET_C2_FEM) |\n"
<< "| |\n"
<< "| 1) Conversion of Dof tags into Dof ordinals and back |\n"
<< "| 2) Basis values for VALUE, GRAD, and Dk operators |\n"
<< "| |\n"
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n"
<< "| Denis Ridzal ([email protected]), |\n"
<< "| Kara Peterson ([email protected]). |\n"
<< "| Kyungjoo Kim ([email protected]). |\n"
<< "| |\n"
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n"
<< "| Trilinos website: http://trilinos.sandia.gov |\n"
<< "| |\n"
<< "===============================================================================\n";
typedef Kokkos::DynRankView<ValueType,DeviceSpaceType> DynRankView;
typedef Kokkos::DynRankView<ValueType,HostSpaceType> DynRankViewHost;
#define ConstructWithLabel(obj, ...) obj(#obj, __VA_ARGS__)
const ValueType tol = tolerence();
int errorFlag = 0;
// for virtual function, value and point types are declared in the class
typedef ValueType outputValueType;
typedef ValueType pointValueType;
Basis_HGRAD_TET_C2_FEM<DeviceSpaceType,outputValueType,pointValueType> tetBasis;
*outStream
<< "\n"
<< "===============================================================================\n"
<< "| TEST 1: Basis creation, exception testing |\n"
<< "===============================================================================\n";
try{
ordinal_type nthrow = 0, ncatch = 0;
#ifdef HAVE_INTREPID2_DEBUG
DynRankView ConstructWithLabel(tetNodes, 10, 3);
const auto numFields = tetBasis.getCardinality();
const auto numPoints = tetNodes.dimension(0);
const auto spaceDim = tetBasis.getBaseCellTopology().getDimension();
DynRankView ConstructWithLabel(vals, numFields, numPoints);
DynRankView ConstructWithLabel(vals_vec, numFields, numPoints, 4);
{
// exception #1: CURL cannot be applied to scalar functions
// resize vals to rank-3 container with dimensions (num. points, num. basis functions, arbitrary)
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getValues(vals_vec, tetNodes, OPERATOR_CURL) );
}
{
// exception #2: DIV cannot be applied to scalar functions
// resize vals to rank-2 container with dimensions (num. points, num. basis functions)
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getValues(vals, tetNodes, OPERATOR_DIV) );
}
// Exceptions 3-7: all bf tags/bf Ids below are wrong and should cause getDofOrdinal() and
// getDofTag() to access invalid array elements thereby causing bounds check exception
{
// exception #3
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getDofOrdinal(3,0,0) );
// exception #4
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getDofOrdinal(1,1,1) );
// exception #5
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getDofOrdinal(0,4,0) );
// exception #6
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getDofTag(10) );
// exception #7
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getDofTag(-1) );
}
// Exceptions 8-18 test exception handling with incorrectly dimensioned input/output arrays
{
// exception #8: input points array must be of rank-2
DynRankView ConstructWithLabel(badPoints1, 4, 5, 3);
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getValues(vals, badPoints1, OPERATOR_VALUE) );
}
{
// exception #9 dimension 1 in the input point array must equal space dimension of the cell
DynRankView ConstructWithLabel(badPoints2, 4, spaceDim - 1);
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getValues(vals, badPoints2, OPERATOR_VALUE) );
}
{
// exception #10 output values must be of rank-2 for OPERATOR_VALUE
DynRankView ConstructWithLabel(badVals1, 4, 3, 1);
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getValues(badVals1, tetNodes, OPERATOR_VALUE) );
}
{
// exception #11 output values must be of rank-3 for OPERATOR_GRAD
DynRankView ConstructWithLabel(badVals2, 4, 3);
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getValues(badVals2, tetNodes, OPERATOR_GRAD) );
// exception #12 output values must be of rank-3 for OPERATOR_D1
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getValues(badVals2, tetNodes, OPERATOR_D1) );
// exception #13 output values must be of rank-3 for OPERATOR_D2
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getValues(badVals2, tetNodes, OPERATOR_D2) );
}
{
// exception #14 incorrect 0th dimension of output array (must equal number of basis functions)
DynRankView ConstructWithLabel(badVals3, numFields + 1, numPoints);
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getValues(badVals3, tetNodes, OPERATOR_VALUE) );
}
{
// exception #15 incorrect 1st dimension of output array (must equal number of points)
DynRankView ConstructWithLabel(badVals4, numFields, numPoints + 1);
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getValues(badVals4, tetNodes, OPERATOR_VALUE) );
}
{
// exception #16: incorrect 2nd dimension of output array (must equal the space dimension)
DynRankView ConstructWithLabel(badVals5, numFields, numPoints, spaceDim + 1);
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getValues(badVals5, tetNodes, OPERATOR_GRAD) );
}
{
// exception #17: incorrect 2nd dimension of output array (must equal D2 cardinality in 2D)
DynRankView ConstructWithLabel(badVals6, numFields, numPoints, 40);
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getValues(badVals6, tetNodes, OPERATOR_D1) );
// exception #18: incorrect 2nd dimension of output array (must equal D3 cardinality in 2D)
INTREPID2_TEST_ERROR_EXPECTED( tetBasis.getValues(badVals6, tetNodes, OPERATOR_D2) );
}
#endif
// Check if number of thrown exceptions matches the one we expect
if (nthrow != ncatch) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << "# of catch ("<< ncatch << ") is different from # of throw (" << nthrow << ")\n";
}
} catch (std::logic_error err) {
*outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
*outStream << err.what() << '\n';
*outStream << "-------------------------------------------------------------------------------" << "\n\n";
errorFlag = -1000;
};
*outStream
<< "\n"
<< "===============================================================================\n"
<< "| TEST 2: correctness of tag to enum and enum to tag lookups |\n"
<< "===============================================================================\n";
try{
const auto numFields = tetBasis.getCardinality();
const auto allTags = tetBasis.getAllDofTags();
// Loop over all tags, lookup the associated dof enumeration and then lookup the tag again
const auto dofTagSize = allTags.dimension(0);
for (auto i = 0; i < dofTagSize; ++i) {
const auto bfOrd = tetBasis.getDofOrdinal(allTags(i,0), allTags(i,1), allTags(i,2));
const auto myTag = tetBasis.getDofTag(bfOrd);
if( !( (myTag(0) == allTags(i,0)) &&
(myTag(1) == allTags(i,1)) &&
(myTag(2) == allTags(i,2)) &&
(myTag(3) == allTags(i,3)) ) ) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " getDofOrdinal( {"
<< allTags(i,0) << ", "
<< allTags(i,1) << ", "
<< allTags(i,2) << ", "
<< allTags(i,3) << "}) = " << bfOrd <<" but \n";
*outStream << " getDofTag(" << bfOrd << ") = { "
<< myTag(0) << ", "
<< myTag(1) << ", "
<< myTag(2) << ", "
<< myTag(3) << "}\n";
}
}
// Now do the same but loop over basis functions
for( auto bfOrd = 0; bfOrd < numFields; bfOrd++) {
const auto myTag = tetBasis.getDofTag(bfOrd);
const auto myBfOrd = tetBasis.getDofOrdinal(myTag(0), myTag(1), myTag(2));
if( bfOrd != myBfOrd) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " getDofTag(" << bfOrd << ") = { "
<< myTag(0) << ", "
<< myTag(1) << ", "
<< myTag(2) << ", "
<< myTag(3) << "} but getDofOrdinal({"
<< myTag(0) << ", "
<< myTag(1) << ", "
<< myTag(2) << ", "
<< myTag(3) << "} ) = " << myBfOrd << "\n";
}
}
}
catch (std::logic_error err){
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
*outStream
<< "\n"
<< "===============================================================================\n"
<< "| TEST 3: correctness of basis function values |\n"
<< "===============================================================================\n";
outStream -> precision(20);
// VALUE: in (F,P) format
const ValueType basisValues[] = {
1.00000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00000, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 1.00000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00000, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 1.00000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00000, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
1.00000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00000, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 1.00000 };
// GRAD and D1: in (F,P,D) format
const ValueType basisGrads[] = {
-3.00000, -3.00000, -3.00000, 1.00000, 1.00000, 1.00000, 1.00000, \
1.00000, 1.00000, 1.00000, 1.00000, 1.00000, -1.00000, -1.00000, \
-1.00000, 1.00000, 1.00000, 1.00000, -1.00000, -1.00000, -1.00000, \
-1.00000, -1.00000, -1.00000, 1.00000, 1.00000, 1.00000, 1.00000, \
1.00000, 1.00000, -1.00000, 0, 0, 3.00000, 0, 0, -1.00000, 0, 0, \
-1.00000, 0, 0, 1.00000, 0, 0, 1.00000, 0, 0, -1.00000, 0, 0, \
-1.00000, 0, 0, 1.00000, 0, 0, -1.00000, 0, 0, 0, -1.00000, 0, 0, \
-1.00000, 0, 0, 3.00000, 0, 0, -1.00000, 0, 0, -1.00000, 0, 0, \
1.00000, 0, 0, 1.00000, 0, 0, -1.00000, 0, 0, -1.00000, 0, 0, \
1.00000, 0, 0, 0, -1.00000, 0, 0, -1.00000, 0, 0, -1.00000, 0, 0, \
3.00000, 0, 0, -1.00000, 0, 0, -1.00000, 0, 0, -1.00000, 0, 0, \
1.00000, 0, 0, 1.00000, 0, 0, 1.00000, 4.00000, 0, 0, -4.00000, \
-4.00000, -4.00000, 0, 0, 0, 0, 0, 0, 0, -2.00000, -2.00000, \
-2.00000, -2.00000, -2.00000, 2.00000, 0, 0, 2.00000, 0, 0, -2.00000, \
-2.00000, -2.00000, 0, 0, 0, 0, 0, 0, 0, 4.00000, 0, 4.00000, 0, 0, \
0, 0, 0, 0, 2.00000, 0, 2.00000, 2.00000, 0, 2.00000, 0, 0, 0, 0, 0, \
0, 2.00000, 0, 2.00000, 0, 0, 0, 4.00000, 0, 0, 0, 0, -4.00000, \
-4.00000, -4.00000, 0, 0, 0, 0, 2.00000, 0, -2.00000, -2.00000, \
-2.00000, -2.00000, 0, -2.00000, 0, 2.00000, 0, 0, 0, 0, -2.00000, \
-2.00000, -2.00000, 0, 0, 4.00000, 0, 0, 0, 0, 0, 0, -4.00000, \
-4.00000, -4.00000, 0, 0, 2.00000, 0, 0, 0, 0, 0, 2.00000, -2.00000, \
-2.00000, 0, -2.00000, -2.00000, -2.00000, -2.00000, -2.00000, \
-2.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 4.00000, 0, 0, 0, 0, \
2.00000, 0, 0, 2.00000, 0, 0, 0, 2.00000, 0, 0, 2.00000, 0, 2.00000, \
2.00000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4.00000, 0, 4.00000, 0, 0, 0, \
0, 0, 0, 2.00000, 0, 0, 2.00000, 0, 2.00000, 0, 0, 2.00000, 0, 0, \
2.00000, 2.00000};
// D2 values in (F,P, Dk) format
const ValueType basisD2[]={
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 0, 0, 0, 0, 0, 4.00000, \
0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, \
4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, \
0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, \
0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, \
4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, \
0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, \
0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 0, 0, 4.00000, \
0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, \
4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, \
0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, \
0, 0, 4.00000, -8.00000, -4.00000, -4.00000, 0, 0, 0, -8.00000, \
-4.00000, -4.00000, 0, 0, 0, -8.00000, -4.00000, -4.00000, 0, 0, 0, \
-8.00000, -4.00000, -4.00000, 0, 0, 0, -8.00000, -4.00000, -4.00000, \
0, 0, 0, -8.00000, -4.00000, -4.00000, 0, 0, 0, -8.00000, -4.00000, \
-4.00000, 0, 0, 0, -8.00000, -4.00000, -4.00000, 0, 0, 0, -8.00000, \
-4.00000, -4.00000, 0, 0, 0, -8.00000, -4.00000, -4.00000, 0, 0, 0, \
0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, \
0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, \
0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, \
0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, -4.00000, 0, -8.00000, -4.00000, \
0, 0, -4.00000, 0, -8.00000, -4.00000, 0, 0, -4.00000, 0, -8.00000, \
-4.00000, 0, 0, -4.00000, 0, -8.00000, -4.00000, 0, 0, -4.00000, 0, \
-8.00000, -4.00000, 0, 0, -4.00000, 0, -8.00000, -4.00000, 0, 0, \
-4.00000, 0, -8.00000, -4.00000, 0, 0, -4.00000, 0, -8.00000, \
-4.00000, 0, 0, -4.00000, 0, -8.00000, -4.00000, 0, 0, -4.00000, 0, \
-8.00000, -4.00000, 0, 0, 0, -4.00000, 0, -4.00000, -8.00000, 0, 0, \
-4.00000, 0, -4.00000, -8.00000, 0, 0, -4.00000, 0, -4.00000, \
-8.00000, 0, 0, -4.00000, 0, -4.00000, -8.00000, 0, 0, -4.00000, 0, \
-4.00000, -8.00000, 0, 0, -4.00000, 0, -4.00000, -8.00000, 0, 0, \
-4.00000, 0, -4.00000, -8.00000, 0, 0, -4.00000, 0, -4.00000, \
-8.00000, 0, 0, -4.00000, 0, -4.00000, -8.00000, 0, 0, -4.00000, 0, \
-4.00000, -8.00000, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, \
0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, \
0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, \
0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 0, 0, \
4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, \
0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, \
0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, \
0, 0, 0, 4.00000, 0
};
try{
ordinal_type nthrow = 0, ncatch = 0;
DynRankViewHost ConstructWithLabel(tetNodesHost, 10, 3);
tetNodesHost(0,0) = 0.0; tetNodesHost(0,1) = 0.0; tetNodesHost(0,2) = 0.0;
tetNodesHost(1,0) = 1.0; tetNodesHost(1,1) = 0.0; tetNodesHost(1,2) = 0.0;
tetNodesHost(2,0) = 0.0; tetNodesHost(2,1) = 1.0; tetNodesHost(2,2) = 0.0;
tetNodesHost(3,0) = 0.0; tetNodesHost(3,1) = 0.0; tetNodesHost(3,2) = 1.0;
tetNodesHost(4,0) = 0.5; tetNodesHost(4,1) = 0.0; tetNodesHost(4,2) = 0.0;
tetNodesHost(5,0) = 0.5; tetNodesHost(5,1) = 0.5; tetNodesHost(5,2) = 0.0;
tetNodesHost(6,0) = 0.0; tetNodesHost(6,1) = 0.5; tetNodesHost(6,2) = 0.0;
tetNodesHost(7,0) = 0.0; tetNodesHost(7,1) = 0.0; tetNodesHost(7,2) = 0.5;
tetNodesHost(8,0) = 0.5; tetNodesHost(8,1) = 0.0; tetNodesHost(8,2) = 0.5;
tetNodesHost(9,0) = 0.0; tetNodesHost(9,1) = 0.5; tetNodesHost(9,2) = 0.5;
auto tetNodes = Kokkos::create_mirror_view(typename DeviceSpaceType::memory_space(), tetNodesHost);
Kokkos::deep_copy(tetNodes, tetNodesHost);
// Dimensions for the output arrays:
const auto numFields = tetBasis.getCardinality();
const auto numPoints = tetNodes.dimension(0);
const auto spaceDim = tetBasis.getBaseCellTopology().getDimension();
const auto D2cardinality = getDkCardinality(OPERATOR_D2, spaceDim);
{
// Check VALUE of basis functions: resize vals to rank-2 container:
DynRankView ConstructWithLabel(vals, numFields, numPoints);
tetBasis.getValues(vals, tetNodes, OPERATOR_VALUE);
auto vals_host = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), vals);
Kokkos::deep_copy(vals_host, vals);
for (auto i = 0; i < numFields; ++i) {
for (auto j = 0; j < numPoints; ++j) {
const auto l = i + j * numFields;
if (std::abs(vals_host(i,j) - basisValues[l]) > tol) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";
*outStream << "} computed value: " << vals_host(i,j)
<< " but reference value: " << basisValues[l] << "\n";
}
}
}
}
{
// Check GRAD of basis function: resize vals to rank-3 container
DynRankView ConstructWithLabel(vals, numFields, numPoints, spaceDim);
tetBasis.getValues(vals, tetNodes, OPERATOR_GRAD);
auto vals_host = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), vals);
Kokkos::deep_copy(vals_host, vals);
for (auto i = 0; i < numFields; ++i) {
for (auto j = 0; j < numPoints; ++j) {
for (auto k = 0; k < spaceDim; ++k) {
// basisGrads is (F,P,D), compute offset:
const auto l = k + j * spaceDim + i * spaceDim * numPoints;
if (std::abs(vals_host(i,j,k) - basisGrads[l]) > tol) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed grad component: " << vals_host(i,j,k)
<< " but reference grad component: " << basisGrads[l] << "\n";
}
}
}
}
// Check D1 of basis function (do not resize vals because it has the correct size: D1 = GRAD)
tetBasis.getValues(vals, tetNodes, OPERATOR_D1);
Kokkos::deep_copy(vals_host, vals);
for (auto i = 0; i < numFields; ++i) {
for (auto j = 0; j < numPoints; ++j) {
for (auto k = 0; k < spaceDim; ++k) {
// basisGrads is (F,P,D), compute offset:
const auto l = k + j * spaceDim + i * spaceDim * numPoints;
if (std::abs(vals_host(i,j,k) - basisGrads[l]) > tol) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed D1 component: " << vals_host(i,j,k)
<< " but reference D1 component: " << basisGrads[l] << "\n";
}
}
}
}
}
{
// Check D2 of basis function
DynRankView ConstructWithLabel(vals, numFields, numPoints, D2cardinality);
tetBasis.getValues(vals, tetNodes, OPERATOR_D2);
auto vals_host = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), vals);
Kokkos::deep_copy(vals_host, vals);
for (auto i = 0; i < numFields; ++i) {
for (auto j = 0; j < numPoints; ++j) {
for (auto k = 0; k < D2cardinality; ++k) {
// basisD2 is (F,P,Dk), compute offset:
const auto l = k + j * D2cardinality + i * D2cardinality * numPoints;
if (std::abs(vals_host(i,j,k) - basisD2[l]) > tol) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed D2 component: " << vals_host(i,j,k)
<< " but reference D2 component: " << basisD2[l] << "\n";
}
}
}
}
}
{
// Check all higher derivatives - must be zero.
const EOperator ops[] = { OPERATOR_D3,
OPERATOR_D4,
OPERATOR_D5,
OPERATOR_D6,
OPERATOR_D7,
OPERATOR_D8,
OPERATOR_D9,
OPERATOR_D10,
OPERATOR_MAX };
for (auto h=0;ops[h]!=OPERATOR_MAX;++h) {
const auto op = ops[h];
// The last dimension is the number of kth derivatives and needs to be resized for every Dk
const auto DkCardin = getDkCardinality(op, spaceDim);
DynRankView vals("vals", numFields, numPoints, DkCardin);
tetBasis.getValues(vals, tetNodes, op);
auto vals_host = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), vals);
Kokkos::deep_copy(vals_host, vals);
for (auto i1 = 0; i1 < numFields; ++i1)
for (auto i2 = 0; i2 < numPoints; ++i2)
for (auto i3 = 0; i3 < DkCardin; ++i3) {
if (std::abs(vals_host(i1,i2,i3)) > tol) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Get the multi-index of the value where the error is and the operator order
int ord = Intrepid2::getOperatorOrder(op);
*outStream << " At multi-index { "<<i1<<" "<<i2 <<" "<<i3;
*outStream << "} computed D"<< ord <<" component: " << vals_host(i1,i2,i3)
<< " but reference D" << ord << " component: 0 \n";
}
}
}
}
} catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
Kokkos::initialize();
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (Basis_HGRAD_TET_Cn_FEM) |\n" \
<< "| |\n" \
<< "| 1) Patch test involving mass and stiffness matrices, |\n" \
<< "| for the Neumann problem on a tetrahedral patch |\n" \
<< "| Omega with boundary Gamma. |\n" \
<< "| |\n" \
<< "| - div (grad u) + u = f in Omega, (grad u) . n = g on Gamma |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n"\
<< "| TEST 1: Patch test |\n"\
<< "===============================================================================\n";
int errorFlag = 0;
outStream -> precision(16);
try {
int max_order = 5; // max total order of polynomial solution
DefaultCubatureFactory<double> cubFactory; // create factory
shards::CellTopology cell(shards::getCellTopologyData< shards::Tetrahedron<> >()); // create parent cell topology
shards::CellTopology side(shards::getCellTopologyData< shards::Triangle<> >()); // create relevant subcell (side) topology
int cellDim = cell.getDimension();
int sideDim = side.getDimension();
// Define array containing points at which the solution is evaluated, on the reference tet.
int numIntervals = 10;
int numInterpPoints = ((numIntervals + 1)*(numIntervals + 2)*(numIntervals + 3))/6;
FieldContainer<double> interp_points_ref(numInterpPoints, 3);
int counter = 0;
for (int k=0; k<=numIntervals; k++) {
for (int j=0; j<=numIntervals; j++) {
for (int i=0; i<=numIntervals; i++) {
if (i+j+k <= numIntervals) {
interp_points_ref(counter,0) = i*(1.0/numIntervals);
interp_points_ref(counter,1) = j*(1.0/numIntervals);
interp_points_ref(counter,2) = k*(1.0/numIntervals);
counter++;
}
}
}
}
/* Definition of parent cell. */
FieldContainer<double> cell_nodes(1, 4, cellDim);
// funky tet
cell_nodes(0, 0, 0) = -1.0;
cell_nodes(0, 0, 1) = -2.0;
cell_nodes(0, 0, 2) = 0.0;
cell_nodes(0, 1, 0) = 6.0;
cell_nodes(0, 1, 1) = 2.0;
cell_nodes(0, 1, 2) = 0.0;
cell_nodes(0, 2, 0) = -5.0;
cell_nodes(0, 2, 1) = 1.0;
cell_nodes(0, 2, 2) = 0.0;
cell_nodes(0, 3, 0) = -4.0;
cell_nodes(0, 3, 1) = -1.0;
cell_nodes(0, 3, 2) = 3.0;
// perturbed reference tet
/*cell_nodes(0, 0, 0) = 0.1;
cell_nodes(0, 0, 1) = -0.1;
cell_nodes(0, 0, 2) = 0.2;
cell_nodes(0, 1, 0) = 1.2;
cell_nodes(0, 1, 1) = -0.1;
cell_nodes(0, 1, 2) = 0.05;
cell_nodes(0, 2, 0) = 0.0;
cell_nodes(0, 2, 1) = 0.9;
cell_nodes(0, 2, 2) = 0.1;
cell_nodes(0, 3, 0) = 0.1;
cell_nodes(0, 3, 1) = -0.1;
cell_nodes(0, 3, 2) = 1.1;*/
// reference tet
/*cell_nodes(0, 0, 0) = 0.0;
cell_nodes(0, 0, 1) = 0.0;
cell_nodes(0, 0, 2) = 0.0;
cell_nodes(0, 1, 0) = 1.0;
cell_nodes(0, 1, 1) = 0.0;
cell_nodes(0, 1, 2) = 0.0;
cell_nodes(0, 2, 0) = 0.0;
cell_nodes(0, 2, 1) = 1.0;
cell_nodes(0, 2, 2) = 0.0;
cell_nodes(0, 3, 0) = 0.0;
cell_nodes(0, 3, 1) = 0.0;
cell_nodes(0, 3, 2) = 1.0;*/
FieldContainer<double> interp_points(1, numInterpPoints, cellDim);
CellTools<double>::mapToPhysicalFrame(interp_points, interp_points_ref, cell_nodes, cell);
interp_points.resize(numInterpPoints, cellDim);
// we test two types of bases
EPointType pointtype[] = {POINTTYPE_EQUISPACED, POINTTYPE_WARPBLEND};
for (int ptype=0; ptype < 2; ptype++) {
*outStream << "\nTesting bases with " << EPointTypeToString(pointtype[ptype]) << ":\n";
for (int x_order=0; x_order <= max_order; x_order++) {
for (int y_order=0; y_order <= max_order-x_order; y_order++) {
for (int z_order=0; z_order <= max_order-x_order-y_order; z_order++) {
// evaluate exact solution
FieldContainer<double> exact_solution(1, numInterpPoints);
u_exact(exact_solution, interp_points, x_order, y_order, z_order);
int total_order = std::max(x_order + y_order + z_order, 1);
for (int basis_order=total_order; basis_order <= max_order; basis_order++) {
// set test tolerance;
double zero = basis_order*basis_order*basis_order*100*INTREPID_TOL;
//create basis
Teuchos::RCP<Basis<double,FieldContainer<double> > > basis =
Teuchos::rcp(new Basis_HGRAD_TET_Cn_FEM<double,FieldContainer<double> >(basis_order, pointtype[ptype]) );
int numFields = basis->getCardinality();
// create cubatures
Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*basis_order);
Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*basis_order);
int numCubPointsCell = cellCub->getNumPoints();
int numCubPointsSide = sideCub->getNumPoints();
/* Computational arrays. */
/* Section 1: Related to parent cell integration. */
FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim);
FieldContainer<double> cub_points_cell_physical(1, numCubPointsCell, cellDim);
FieldContainer<double> cub_weights_cell(numCubPointsCell);
FieldContainer<double> jacobian_cell(1, numCubPointsCell, cellDim, cellDim);
FieldContainer<double> jacobian_inv_cell(1, numCubPointsCell, cellDim, cellDim);
FieldContainer<double> jacobian_det_cell(1, numCubPointsCell);
FieldContainer<double> weighted_measure_cell(1, numCubPointsCell);
FieldContainer<double> value_of_basis_at_cub_points_cell(numFields, numCubPointsCell);
FieldContainer<double> transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell);
FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell);
FieldContainer<double> grad_of_basis_at_cub_points_cell(numFields, numCubPointsCell, cellDim);
FieldContainer<double> transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
FieldContainer<double> weighted_transformed_grad_of_basis_at_cub_points_cell(1, numFields, numCubPointsCell, cellDim);
FieldContainer<double> fe_matrix(1, numFields, numFields);
FieldContainer<double> rhs_at_cub_points_cell_physical(1, numCubPointsCell);
FieldContainer<double> rhs_and_soln_vector(1, numFields);
/* Section 2: Related to subcell (side) integration. */
unsigned numSides = 4;
FieldContainer<double> cub_points_side(numCubPointsSide, sideDim);
FieldContainer<double> cub_weights_side(numCubPointsSide);
FieldContainer<double> cub_points_side_refcell(numCubPointsSide, cellDim);
FieldContainer<double> cub_points_side_physical(1, numCubPointsSide, cellDim);
FieldContainer<double> jacobian_side_refcell(1, numCubPointsSide, cellDim, cellDim);
FieldContainer<double> jacobian_det_side_refcell(1, numCubPointsSide);
FieldContainer<double> weighted_measure_side_refcell(1, numCubPointsSide);
FieldContainer<double> value_of_basis_at_cub_points_side_refcell(numFields, numCubPointsSide);
FieldContainer<double> transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide);
FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points_side_refcell(1, numFields, numCubPointsSide);
FieldContainer<double> neumann_data_at_cub_points_side_physical(1, numCubPointsSide);
FieldContainer<double> neumann_fields_per_side(1, numFields);
/* Section 3: Related to global interpolant. */
FieldContainer<double> value_of_basis_at_interp_points_ref(numFields, numInterpPoints);
FieldContainer<double> transformed_value_of_basis_at_interp_points_ref(1, numFields, numInterpPoints);
FieldContainer<double> interpolant(1, numInterpPoints);
FieldContainer<int> ipiv(numFields);
/******************* START COMPUTATION ***********************/
// get cubature points and weights
cellCub->getCubature(cub_points_cell, cub_weights_cell);
// compute geometric cell information
CellTools<double>::setJacobian(jacobian_cell, cub_points_cell, cell_nodes, cell);
CellTools<double>::setJacobianInv(jacobian_inv_cell, jacobian_cell);
CellTools<double>::setJacobianDet(jacobian_det_cell, jacobian_cell);
// compute weighted measure
FunctionSpaceTools::computeCellMeasure<double>(weighted_measure_cell, jacobian_det_cell, cub_weights_cell);
///////////////////////////
// Computing mass matrices:
// tabulate values of basis functions at (reference) cubature points
basis->getValues(value_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_VALUE);
// transform values of basis functions
FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_cell,
value_of_basis_at_cub_points_cell);
// multiply with weighted measure
FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_cell,
weighted_measure_cell,
transformed_value_of_basis_at_cub_points_cell);
// compute mass matrices
FunctionSpaceTools::integrate<double>(fe_matrix,
transformed_value_of_basis_at_cub_points_cell,
weighted_transformed_value_of_basis_at_cub_points_cell,
COMP_BLAS);
///////////////////////////
////////////////////////////////
// Computing stiffness matrices:
// tabulate gradients of basis functions at (reference) cubature points
basis->getValues(grad_of_basis_at_cub_points_cell, cub_points_cell, OPERATOR_GRAD);
// transform gradients of basis functions
FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points_cell,
jacobian_inv_cell,
grad_of_basis_at_cub_points_cell);
// multiply with weighted measure
FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points_cell,
weighted_measure_cell,
transformed_grad_of_basis_at_cub_points_cell);
// compute stiffness matrices and sum into fe_matrix
FunctionSpaceTools::integrate<double>(fe_matrix,
transformed_grad_of_basis_at_cub_points_cell,
weighted_transformed_grad_of_basis_at_cub_points_cell,
COMP_BLAS,
true);
////////////////////////////////
///////////////////////////////
// Computing RHS contributions:
// map cell (reference) cubature points to physical space
CellTools<double>::mapToPhysicalFrame(cub_points_cell_physical, cub_points_cell, cell_nodes, cell);
// evaluate rhs function
rhsFunc(rhs_at_cub_points_cell_physical, cub_points_cell_physical, x_order, y_order, z_order);
// compute rhs
FunctionSpaceTools::integrate<double>(rhs_and_soln_vector,
rhs_at_cub_points_cell_physical,
weighted_transformed_value_of_basis_at_cub_points_cell,
COMP_BLAS);
// compute neumann b.c. contributions and adjust rhs
sideCub->getCubature(cub_points_side, cub_weights_side);
for (unsigned i=0; i<numSides; i++) {
// compute geometric cell information
CellTools<double>::mapToReferenceSubcell(cub_points_side_refcell, cub_points_side, sideDim, (int)i, cell);
CellTools<double>::setJacobian(jacobian_side_refcell, cub_points_side_refcell, cell_nodes, cell);
CellTools<double>::setJacobianDet(jacobian_det_side_refcell, jacobian_side_refcell);
// compute weighted face measure
FunctionSpaceTools::computeFaceMeasure<double>(weighted_measure_side_refcell,
jacobian_side_refcell,
cub_weights_side,
i,
cell);
// tabulate values of basis functions at side cubature points, in the reference parent cell domain
basis->getValues(value_of_basis_at_cub_points_side_refcell, cub_points_side_refcell, OPERATOR_VALUE);
// transform
FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points_side_refcell,
value_of_basis_at_cub_points_side_refcell);
// multiply with weighted measure
FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points_side_refcell,
weighted_measure_side_refcell,
transformed_value_of_basis_at_cub_points_side_refcell);
// compute Neumann data
// map side cubature points in reference parent cell domain to physical space
CellTools<double>::mapToPhysicalFrame(cub_points_side_physical, cub_points_side_refcell, cell_nodes, cell);
// now compute data
neumann(neumann_data_at_cub_points_side_physical, cub_points_side_physical, jacobian_side_refcell,
cell, (int)i, x_order, y_order, z_order);
FunctionSpaceTools::integrate<double>(neumann_fields_per_side,
neumann_data_at_cub_points_side_physical,
weighted_transformed_value_of_basis_at_cub_points_side_refcell,
COMP_BLAS);
// adjust RHS
RealSpaceTools<double>::add(rhs_and_soln_vector, neumann_fields_per_side);;
}
///////////////////////////////
/////////////////////////////
// Solution of linear system:
int info = 0;
Teuchos::LAPACK<int, double> solver;
solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info);
/////////////////////////////
////////////////////////
// Building interpolant:
// evaluate basis at interpolation points
basis->getValues(value_of_basis_at_interp_points_ref, interp_points_ref, OPERATOR_VALUE);
// transform values of basis functions
FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points_ref,
value_of_basis_at_interp_points_ref);
FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points_ref);
////////////////////////
/******************* END COMPUTATION ***********************/
RealSpaceTools<double>::subtract(interpolant, exact_solution);
*outStream << "\nRelative norm-2 error between exact solution polynomial of order ("
<< x_order << ", " << y_order << ", " << z_order
<< ") and finite element interpolant of order " << basis_order << ": "
<< RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) /
RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) << "\n";
if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) /
RealSpaceTools<double>::vectorNorm(&exact_solution[0], exact_solution.dimension(1), NORM_TWO) > zero) {
*outStream << "\n\nPatch test failed for solution polynomial order ("
<< x_order << ", " << y_order << ", " << z_order << ") and basis order " << basis_order << "\n\n";
errorFlag++;
}
} // end for basis_order
} // end for z_order
} // end for y_order
} // end for x_order
} // end for ptype
}
// Catch unexpected errors
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return errorFlag;
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (Basis_HGRAD_WEDGE_C2_FEM) |\n" \
<< "| |\n" \
<< "| 1) Conversion of Dof tags into Dof ordinals and back |\n" \
<< "| 2) Basis values for VALUE, GRAD, and Dk operators |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n"\
<< "| TEST 1: Basis creation, exception testing |\n"\
<< "===============================================================================\n";
// Define basis and error flag
Basis_HGRAD_WEDGE_C2_FEM<double, FieldContainer<double> > wedgeBasis;
int errorFlag = 0;
// Initialize throw counter for exception testing
int nException = 0;
int throwCounter = 0;
// Nodes of Wedde<18>: vertices, edge midpoints, Quadrilateral face centers
FieldContainer<double> wedgeNodes(18, 3);
wedgeNodes(0,0) = 0.0; wedgeNodes(0,1) = 0.0; wedgeNodes(0,2) = -1.0;
wedgeNodes(1,0) = 1.0; wedgeNodes(1,1) = 0.0; wedgeNodes(1,2) = -1.0;
wedgeNodes(2,0) = 0.0; wedgeNodes(2,1) = 1.0; wedgeNodes(2,2) = -1.0;
wedgeNodes(3,0) = 0.0; wedgeNodes(3,1) = 0.0; wedgeNodes(3,2) = 1.0;
wedgeNodes(4,0) = 1.0; wedgeNodes(4,1) = 0.0; wedgeNodes(4,2) = 1.0;
wedgeNodes(5,0) = 0.0; wedgeNodes(5,1) = 1.0; wedgeNodes(5,2) = 1.0;
wedgeNodes(6,0) = 0.5; wedgeNodes(6,1) = 0.0; wedgeNodes(6,2) = -1.0;
wedgeNodes(7,0) = 0.5; wedgeNodes(7,1) = 0.5; wedgeNodes(7,2) = -1.0;
wedgeNodes(8,0) = 0.0; wedgeNodes(8,1) = 0.5; wedgeNodes(8,2) = -1.0;
wedgeNodes(9,0) = 0.0; wedgeNodes(9,1) = 0.0; wedgeNodes(9,2) = 0.0;
wedgeNodes(10,0)= 1.0; wedgeNodes(10,1)= 0.0; wedgeNodes(10,2)= 0.0;
wedgeNodes(11,0)= 0.0; wedgeNodes(11,1)= 1.0; wedgeNodes(11,2)= 0.0;
wedgeNodes(12,0)= 0.5; wedgeNodes(12,1)= 0.0; wedgeNodes(12,2)= 1.0;
wedgeNodes(13,0)= 0.5; wedgeNodes(13,1)= 0.5; wedgeNodes(13,2)= 1.0;
wedgeNodes(14,0)= 0.0; wedgeNodes(14,1)= 0.5; wedgeNodes(14,2)= 1.0;
wedgeNodes(15,0)= 0.5; wedgeNodes(15,1)= 0.0; wedgeNodes(15,2)= 0.0;
wedgeNodes(16,0)= 0.5; wedgeNodes(16,1)= 0.5; wedgeNodes(16,2)= 0.0;
wedgeNodes(17,0)= 0.0; wedgeNodes(17,1)= 0.5; wedgeNodes(17,2)= 0.0;
// Generic array for the output values; needs to be properly resized depending on the operator type
FieldContainer<double> vals;
try{
// exception #1: CURL cannot be applied to scalar functions
// resize vals to rank-3 container with dimensions (num. points, num. basis functions)
vals.resize(wedgeBasis.getCardinality(), wedgeNodes.dimension(0), 3 );
INTREPID_TEST_COMMAND( wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_DIV), throwCounter, nException );
// exception #2: DIV cannot be applied to scalar functions
// resize vals to rank-2 container with dimensions (num. points, num. basis functions)
vals.resize(wedgeBasis.getCardinality(), wedgeNodes.dimension(0) );
INTREPID_TEST_COMMAND( wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_DIV), throwCounter, nException );
// Exceptions 3-7: all bf tags/bf Ids below are wrong and should cause getDofOrdinal() and
// getDofTag() to access invalid array elements thereby causing bounds check exception
// exception #3
INTREPID_TEST_COMMAND( wedgeBasis.getDofOrdinal(3,0,0), throwCounter, nException );
// exception #4
INTREPID_TEST_COMMAND( wedgeBasis.getDofOrdinal(1,1,1), throwCounter, nException );
// exception #5
INTREPID_TEST_COMMAND( wedgeBasis.getDofOrdinal(0,9,0), throwCounter, nException );
// exception #6
INTREPID_TEST_COMMAND( wedgeBasis.getDofTag(18), throwCounter, nException );
// exception #7
INTREPID_TEST_COMMAND( wedgeBasis.getDofTag(-1), throwCounter, nException );
#ifdef HAVE_INTREPID_DEBUG
// Exceptions 8-18 test exception handling with incorrectly dimensioned input/output arrays
// exception #8: input points array must be of rank-2
FieldContainer<double> badPoints1(4, 5, 3);
INTREPID_TEST_COMMAND( wedgeBasis.getValues(vals, badPoints1, OPERATOR_VALUE), throwCounter, nException );
// exception #9 dimension 1 in the input point array must equal space dimension of the cell
FieldContainer<double> badPoints2(4, wedgeBasis.getBaseCellTopology().getDimension() + 1);
INTREPID_TEST_COMMAND( wedgeBasis.getValues(vals, badPoints2, OPERATOR_VALUE), throwCounter, nException );
// exception #10 output values must be of rank-2 for OPERATOR_VALUE
FieldContainer<double> badVals1(4, 3, 1);
INTREPID_TEST_COMMAND( wedgeBasis.getValues(badVals1, wedgeNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #11 output values must be of rank-3 for OPERATOR_GRAD
FieldContainer<double> badVals2(4, 3);
INTREPID_TEST_COMMAND( wedgeBasis.getValues(badVals2, wedgeNodes, OPERATOR_GRAD), throwCounter, nException );
// exception #12 output values must be of rank-3 for OPERATOR_D1
INTREPID_TEST_COMMAND( wedgeBasis.getValues(badVals2, wedgeNodes, OPERATOR_D1), throwCounter, nException );
// exception #13 output values must be of rank-3 for OPERATOR_D2
INTREPID_TEST_COMMAND( wedgeBasis.getValues(badVals2, wedgeNodes, OPERATOR_D2), throwCounter, nException );
// exception #14 incorrect 0th dimension of output array (must equal number of basis functions)
FieldContainer<double> badVals3(wedgeBasis.getCardinality() + 1, wedgeNodes.dimension(0));
INTREPID_TEST_COMMAND( wedgeBasis.getValues(badVals3, wedgeNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #15 incorrect 1st dimension of output array (must equal number of points)
FieldContainer<double> badVals4(wedgeBasis.getCardinality(), wedgeNodes.dimension(0) + 1);
INTREPID_TEST_COMMAND( wedgeBasis.getValues(badVals4, wedgeNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #16: incorrect 2nd dimension of output array (must equal the space dimension)
FieldContainer<double> badVals5(wedgeBasis.getCardinality(), wedgeNodes.dimension(0), wedgeBasis.getBaseCellTopology().getDimension() - 1);
INTREPID_TEST_COMMAND( wedgeBasis.getValues(badVals5, wedgeNodes, OPERATOR_GRAD), throwCounter, nException );
// exception #17: incorrect 2nd dimension of output array (must equal D2 cardinality in 3D)
FieldContainer<double> badVals6(wedgeBasis.getCardinality(), wedgeNodes.dimension(0), 40);
INTREPID_TEST_COMMAND( wedgeBasis.getValues(badVals6, wedgeNodes, OPERATOR_D2), throwCounter, nException );
// exception #18: incorrect 2nd dimension of output array (must equal D3 cardinality in 3D)
INTREPID_TEST_COMMAND( wedgeBasis.getValues(badVals6, wedgeNodes, OPERATOR_D3), throwCounter, nException );
#endif
}
catch (std::logic_error err) {
*outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
*outStream << err.what() << '\n';
*outStream << "-------------------------------------------------------------------------------" << "\n\n";
errorFlag = -1000;
};
// Check if number of thrown exceptions matches the one we expect - 18
if (throwCounter != nException) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
}
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 2: correctness of tag to enum and enum to tag lookups |\n"\
<< "===============================================================================\n";
try{
std::vector<std::vector<int> > allTags = wedgeBasis.getAllDofTags();
// Loop over all tags, lookup the associated dof enumeration and then lookup the tag again
for (unsigned i = 0; i < allTags.size(); i++) {
int bfOrd = wedgeBasis.getDofOrdinal(allTags[i][0], allTags[i][1], allTags[i][2]);
std::vector<int> myTag = wedgeBasis.getDofTag(bfOrd);
if( !( (myTag[0] == allTags[i][0]) &&
(myTag[1] == allTags[i][1]) &&
(myTag[2] == allTags[i][2]) &&
(myTag[3] == allTags[i][3]) ) ) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " getDofOrdinal( {"
<< allTags[i][0] << ", "
<< allTags[i][1] << ", "
<< allTags[i][2] << ", "
<< allTags[i][3] << "}) = " << bfOrd <<" but \n";
*outStream << " getDofTag(" << bfOrd << ") = { "
<< myTag[0] << ", "
<< myTag[1] << ", "
<< myTag[2] << ", "
<< myTag[3] << "}\n";
}
}
// Now do the same but loop over basis functions
for( int bfOrd = 0; bfOrd < wedgeBasis.getCardinality(); bfOrd++) {
std::vector<int> myTag = wedgeBasis.getDofTag(bfOrd);
int myBfOrd = wedgeBasis.getDofOrdinal(myTag[0], myTag[1], myTag[2]);
if( bfOrd != myBfOrd) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " getDofTag(" << bfOrd << ") = { "
<< myTag[0] << ", "
<< myTag[1] << ", "
<< myTag[2] << ", "
<< myTag[3] << "} but getDofOrdinal({"
<< myTag[0] << ", "
<< myTag[1] << ", "
<< myTag[2] << ", "
<< myTag[3] << "} ) = " << myBfOrd << "\n";
}
}
}
catch (std::logic_error err){
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 3: correctness of basis function values |\n"\
<< "===============================================================================\n";
outStream -> precision(20);
// VALUE: correct basis function values in (F,P) format
double basisValues[] = {
1.00, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 1.00, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 1.00, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 1.00, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
1.00, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 1.00, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 1.00, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 1.00, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
1.00, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00 };
// GRAD, D1, D2, D3 and D4 test values are stored in files due to their large size
std::string fileName;
std::ifstream dataFile;
// GRAD and D1 values are stored in (F,P,D) format in a data file. Read file and do the test
std::vector<double> basisGrads; // Flat array for the gradient values.
fileName = "./testdata/WEDGE_C2_GradVals.dat";
dataFile.open(fileName.c_str());
TEST_FOR_EXCEPTION( !dataFile.good(), std::logic_error,
">>> ERROR (HGRAD_WEDGE_C2/test01): could not open GRAD values data file, test aborted.");
while (!dataFile.eof() ){
double temp;
string line; // string for one line of input file
std::getline(dataFile, line); // get next line from file
stringstream data_line(line); // convert to stringstream
while(data_line >> temp){ // extract value from line
basisGrads.push_back(temp); // push into vector
}
}
// It turns out that just closing and then opening the ifstream variable does not reset it
// and subsequent open() command fails. One fix is to explicitely clear the ifstream, or
// scope the variables.
dataFile.close();
dataFile.clear();
//D2: flat array with the values of D2 applied to basis functions. Multi-index is (F,P,D2cardinality)
std::vector<double> basisD2;
fileName = "./testdata/WEDGE_C2_D2Vals.dat";
dataFile.open(fileName.c_str());
TEST_FOR_EXCEPTION( !dataFile.good(), std::logic_error,
">>> ERROR (HGRAD_WEDGE_C2/test01): could not open D2 values data file, test aborted.");
while (!dataFile.eof() ){
double temp;
string line; // string for one line of input file
std::getline(dataFile, line); // get next line from file
stringstream data_line(line); // convert to stringstream
while(data_line >> temp){ // extract value from line
basisD2.push_back(temp); // push into vector
}
}
dataFile.close();
dataFile.clear();
//D3: flat array with the values of D3 applied to basis functions. Multi-index is (F,P,D3cardinality)
std::vector<double> basisD3;
fileName = "./testdata/WEDGE_C2_D3Vals.dat";
dataFile.open(fileName.c_str());
TEST_FOR_EXCEPTION( !dataFile.good(), std::logic_error,
">>> ERROR (HGRAD_WEDGE_C2/test01): could not open D3 values data file, test aborted.");
while (!dataFile.eof() ){
double temp;
string line; // string for one line of input file
std::getline(dataFile, line); // get next line from file
stringstream data_line(line); // convert to stringstream
while(data_line >> temp){ // extract value from line
basisD3.push_back(temp); // push into vector
}
}
dataFile.close();
dataFile.clear();
//D4: flat array with the values of D3 applied to basis functions. Multi-index is (F,P,D4cardinality)
std::vector<double> basisD4;
fileName = "./testdata/WEDGE_C2_D4Vals.dat";
dataFile.open(fileName.c_str());
TEST_FOR_EXCEPTION( !dataFile.good(), std::logic_error,
">>> ERROR (HGRAD_WEDGE_C2/test01): could not open D4 values data file, test aborted.");
while (!dataFile.eof() ){
double temp;
string line; // string for one line of input file
std::getline(dataFile, line); // get next line from file
stringstream data_line(line); // convert to stringstream
while(data_line >> temp){ // extract value from line
basisD4.push_back(temp); // push into vector
}
}
dataFile.close();
dataFile.clear();
try{
// Dimensions for the output arrays:
int numFields = wedgeBasis.getCardinality();
int numPoints = wedgeNodes.dimension(0);
int spaceDim = wedgeBasis.getBaseCellTopology().getDimension();
// Generic array for values, grads, curls, etc. that will be properly sized before each call
FieldContainer<double> vals;
// Check VALUE of basis functions: resize vals to rank-2 container:
vals.resize(numFields, numPoints);
wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_VALUE);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
int l = i + j * numFields;
if (std::abs(vals(i,j) - basisValues[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";
*outStream << "} computed value: " << vals(i,j)
<< " but reference value: " << basisValues[l] << "\n";
}
}
}
// Check GRAD of basis function: resize vals to rank-3 container
vals.resize(numFields, numPoints, spaceDim);
wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_GRAD);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
for (int k = 0; k < spaceDim; k++) {
// basisGrads is (F,P,D), compute offset:
int l = k + j * spaceDim + i * spaceDim * numPoints;
if (std::abs(vals(i,j,k) - basisGrads[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed grad component: " << vals(i,j,k)
<< " but reference grad component: " << basisGrads[l] << "\n";
}
}
}
}
// Check D1 of basis function (do not resize vals because it has the correct size: D1 = GRAD)
wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_D1);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
for (int k = 0; k < spaceDim; k++) {
// basisGrads is (F,P,D), compute offset:
int l = k + j * spaceDim + i * spaceDim * numPoints;
if (std::abs(vals(i,j,k) - basisGrads[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed D1 component: " << vals(i,j,k)
<< " but reference D1 component: " << basisGrads[l] << "\n";
}
}
}
}
// Check D2 of basis function
int D2cardinality = Intrepid::getDkCardinality(OPERATOR_D2, spaceDim);
vals.resize(numFields, numPoints, D2cardinality);
wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_D2);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
for (int k = 0; k < D2cardinality; k++) {
// basisD2 is (F,P,Dk), compute offset:
int l = k + j * D2cardinality + i * D2cardinality * numPoints;
if (std::abs(vals(i,j,k) - basisD2[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed D2 component: " << vals(i,j,k)
<< " but reference D2 component: " << basisD2[l] << "\n";
}
}
}
}
// Check D3 of basis function
int D3cardinality = Intrepid::getDkCardinality(OPERATOR_D3, spaceDim);
vals.resize(numFields, numPoints, D3cardinality);
wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_D3);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
for (int k = 0; k < D3cardinality; k++) {
// basisD3 is (F,P,Dk), compute offset:
int l = k + j * D3cardinality + i * D3cardinality * numPoints;
if (std::abs(vals(i,j,k) - basisD3[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed D3 component: " << vals(i,j,k)
<< " but reference D3 component: " << basisD3[l] << "\n";
}
}
}
}
// Check D4 of basis function
int D4cardinality = Intrepid::getDkCardinality(OPERATOR_D4, spaceDim);
vals.resize(numFields, numPoints, D4cardinality);
wedgeBasis.getValues(vals, wedgeNodes, OPERATOR_D4);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
for (int k = 0; k < D4cardinality; k++) {
// basisD4 is (F,P,Dk), compute offset:
int l = k + j * D4cardinality + i * D4cardinality * numPoints;
if (std::abs(vals(i,j,k) - basisD4[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed D4 component: " << vals(i,j,k)
<< " but reference D4 component: " << basisD2[l] << "\n";
}
}
}
}
// Check all higher derivatives - must be zero.
for(EOperator op = OPERATOR_D5; op < OPERATOR_MAX; op++) {
// The last dimension is the number of kth derivatives and needs to be resized for every Dk
int DkCardin = Intrepid::getDkCardinality(op, spaceDim);
vals.resize(numFields, numPoints, DkCardin);
wedgeBasis.getValues(vals, wedgeNodes, op);
for (int i = 0; i < vals.size(); i++) {
if (std::abs(vals[i]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Get the multi-index of the value where the error is and the operator order
std::vector<int> myIndex;
vals.getMultiIndex(myIndex,i);
int ord = Intrepid::getOperatorOrder(op);
*outStream << " At multi-index { ";
for(int j = 0; j < vals.rank(); j++) {
*outStream << myIndex[j] << " ";
}
*outStream << "} computed D"<< ord <<" component: " << vals[i]
<< " but reference D" << ord << " component: 0 \n";
}
}
}
}
// Catch unexpected errors
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (Basis_HGRAD_LINE_Cn_FEM_JACOBI) |\n" \
<< "| |\n" \
<< "| 1) Conversion of Dof tags into Dof ordinals and back |\n" \
<< "| 2) Basis values for VALUE, GRAD, CURL, and Dk operators |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n"\
<< "| TEST 1: Basis creation, exception testing |\n"\
<< "===============================================================================\n";
// Define basis and error flag
double alpha = 0.0, beta = 0.0;
Basis_HGRAD_LINE_Cn_FEM_JACOBI<double, FieldContainer<double> > lineBasis(5, alpha, beta);
int errorFlag = 0;
// Initialize throw counter for exception testing
int nException = 0;
int throwCounter = 0;
// Define array containing vertices of the reference Line and a few other points
int numIntervals = 100;
FieldContainer<double> lineNodes(numIntervals+1, 1);
for (int i=0; i<numIntervals+1; i++) {
lineNodes(i,0) = -1.0+(2.0*(double)i)/(double)numIntervals;
}
// Generic array for the output values; needs to be properly resized depending on the operator type
FieldContainer<double> vals;
try{
// Exceptions 1-5: all bf tags/bf Ids below are wrong and should cause getDofOrdinal() and
// getDofTag() to access invalid array elements thereby causing bounds check exception
// exception #1
INTREPID_TEST_COMMAND( lineBasis.getDofOrdinal(2,0,0), throwCounter, nException );
// exception #2
INTREPID_TEST_COMMAND( lineBasis.getDofOrdinal(1,1,1), throwCounter, nException );
// exception #3
INTREPID_TEST_COMMAND( lineBasis.getDofOrdinal(1,0,7), throwCounter, nException );
// not an exception
INTREPID_TEST_COMMAND( lineBasis.getDofOrdinal(1,0,5), throwCounter, nException ); --nException;
// exception #4
INTREPID_TEST_COMMAND( lineBasis.getDofTag(6), throwCounter, nException );
// exception #5
INTREPID_TEST_COMMAND( lineBasis.getDofTag(-1), throwCounter, nException );
// not an exception
INTREPID_TEST_COMMAND( lineBasis.getDofTag(5), throwCounter, nException ); --nException;
#ifdef HAVE_INTREPID_DEBUG
// Exceptions 6-16 test exception handling with incorrectly dimensioned input/output arrays
// exception #6: input points array must be of rank-2
FieldContainer<double> badPoints1(4, 5, 3);
INTREPID_TEST_COMMAND( lineBasis.getValues(vals, badPoints1, OPERATOR_VALUE), throwCounter, nException );
// exception #7: dimension 1 in the input point array must equal space dimension of the cell
FieldContainer<double> badPoints2(4, 3);
INTREPID_TEST_COMMAND( lineBasis.getValues(vals, badPoints2, OPERATOR_VALUE), throwCounter, nException );
// exception #8: output values must be of rank-2 for OPERATOR_VALUE
FieldContainer<double> badVals1(4, 3, 1);
INTREPID_TEST_COMMAND( lineBasis.getValues(badVals1, lineNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #9: output values must be of rank-3 for OPERATOR_GRAD
FieldContainer<double> badVals2(4, 3);
INTREPID_TEST_COMMAND( lineBasis.getValues(badVals2, lineNodes, OPERATOR_GRAD), throwCounter, nException );
// exception #10: output values must be of rank-3 for OPERATOR_CURL
INTREPID_TEST_COMMAND( lineBasis.getValues(badVals2, lineNodes, OPERATOR_CURL), throwCounter, nException );
// exception #11: output values must be of rank-2 for OPERATOR_DIV
INTREPID_TEST_COMMAND( lineBasis.getValues(badVals2, lineNodes, OPERATOR_DIV), throwCounter, nException );
// exception #12: output values must be of rank-2 for OPERATOR_D1
INTREPID_TEST_COMMAND( lineBasis.getValues(badVals2, lineNodes, OPERATOR_D1), throwCounter, nException );
// exception #13: incorrect 0th dimension of output array (must equal number of basis functions)
FieldContainer<double> badVals3(lineBasis.getCardinality() + 1, lineNodes.dimension(0));
INTREPID_TEST_COMMAND( lineBasis.getValues(badVals3, lineNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #14: incorrect 1st dimension of output array (must equal number of points)
FieldContainer<double> badVals4(lineBasis.getCardinality(), lineNodes.dimension(0) + 1);
INTREPID_TEST_COMMAND( lineBasis.getValues(badVals4, lineNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #15: incorrect 2nd dimension of output array (must equal spatial dimension)
FieldContainer<double> badVals5(lineBasis.getCardinality(), lineNodes.dimension(0), 2);
INTREPID_TEST_COMMAND( lineBasis.getValues(badVals5, lineNodes, OPERATOR_GRAD), throwCounter, nException );
// not an exception
FieldContainer<double> goodVals2(lineBasis.getCardinality(), lineNodes.dimension(0));
INTREPID_TEST_COMMAND( lineBasis.getValues(goodVals2, lineNodes, OPERATOR_VALUE), throwCounter, nException ); --nException;
#endif
}
catch (std::logic_error err) {
*outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
*outStream << err.what() << '\n';
*outStream << "-------------------------------------------------------------------------------" << "\n\n";
errorFlag = -1000;
};
// Check if number of thrown exceptions matches the one we expect
if (throwCounter != nException) {
errorFlag++;
*outStream << std::setw(70) << "FAILURE! Incorrect number of exceptions." << "\n";
}
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 3: orthogonality of basis functions |\n"\
<< "===============================================================================\n";
outStream -> precision(20);
try {
// Check orthogonality property for Legendre polynomials.
int maxorder = 10;
DefaultCubatureFactory<double> cubFactory; // create factory
shards::CellTopology line(shards::getCellTopologyData< shards::Line<> >()); // create cell topology
for (int ordi=0; ordi < maxorder; ordi++) {
//create left basis
Teuchos::RCP<Basis<double,FieldContainer<double> > > lineBasisLeft =
Teuchos::rcp(new Basis_HGRAD_LINE_Cn_FEM_JACOBI<double,FieldContainer<double> >(ordi) );
for (int ordj=0; ordj < maxorder; ordj++) {
//create right basis
Teuchos::RCP<Basis<double,FieldContainer<double> > > lineBasisRight =
Teuchos::rcp(new Basis_HGRAD_LINE_Cn_FEM_JACOBI<double,FieldContainer<double> >(ordj) );
// get cubature points and weights
Teuchos::RCP<Cubature<double> > lineCub = cubFactory.create(line, ordi+ordj);
int numPoints = lineCub->getNumPoints();
FieldContainer<double> cubPoints (numPoints, lineCub->getDimension());
FieldContainer<double> cubWeights(numPoints);
FieldContainer<double> cubWeightsC(1, numPoints);
lineCub->getCubature(cubPoints, cubWeights);
// "reshape" weights
for (int i=0; i<numPoints; i++) { cubWeightsC(0,i) = cubWeights(i); }
// get basis values
int numFieldsLeft = lineBasisLeft ->getCardinality();
int numFieldsRight = lineBasisRight->getCardinality();
FieldContainer<double> valsLeft(numFieldsLeft,numPoints),
valsRight(numFieldsRight,numPoints);
lineBasisLeft ->getValues(valsLeft, cubPoints, OPERATOR_VALUE);
lineBasisRight->getValues(valsRight, cubPoints, OPERATOR_VALUE);
// reshape by cloning and integrate
FieldContainer<double> valsLeftC(1, numFieldsLeft,numPoints),
valsRightC(1, numFieldsRight,numPoints),
massMatrix(1, numFieldsLeft, numFieldsRight);
ArrayTools::cloneFields<double>(valsLeftC, valsLeft);
ArrayTools::cloneFields<double>(valsRightC, valsRight);
ArrayTools::scalarMultiplyDataField<double>(valsRightC, cubWeightsC, valsRightC);
FunctionSpaceTools::integrate<double>(massMatrix, valsLeftC, valsRightC, COMP_CPP);
// check orthogonality property
for (int i=0; i<numFieldsLeft; i++) {
for (int j=0; j<numFieldsRight; j++) {
if (i==j) {
if ( std::abs(massMatrix(0,i,j)-(double)(2.0/(2.0*j+1.0))) > INTREPID_TOL ) {
*outStream << "Incorrect ii (\"diagonal\") value for i=" << i << ", j=" << j << ": "
<< massMatrix(0,i,j) << " != " << "2/(2*" << j << "+1)\n\n";
errorFlag++;
}
}
else {
if ( std::abs(massMatrix(0,i,j)) > INTREPID_TOL ) {
*outStream << "Incorrect ij (\"off-diagonal\") value for i=" << i << ", j=" << j << ": "
<< massMatrix(0,i,j) << " != " << "0\n\n";
errorFlag++;
}
}
}
}
}
}
}
// Catch unexpected errors
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 4: correctness of basis function derivatives |\n"\
<< "===============================================================================\n";
outStream -> precision(20);
// function values stored by bf, then pt
double basisValues[] = {
1.000000000000000, 1.000000000000000, 1.000000000000000, \
1.000000000000000, -1.000000000000000, -0.3333333333333333, \
0.3333333333333333, 1.000000000000000, 1.000000000000000, \
-0.3333333333333333, -0.3333333333333333, 1.000000000000000, \
-1.000000000000000, 0.4074074074074074, -0.4074074074074074, \
1.000000000000000};
double basisD1Values[] =
{0, 0, 0, 0, 1.000000000000000, 1.000000000000000, 1.000000000000000, \
1.000000000000000, -3.000000000000000, -1.000000000000000, \
1.000000000000000, 3.000000000000000, 6.000000000000000, \
-0.6666666666666667, -0.6666666666666667, 6.000000000000000};
double basisD2Values[] =
{0, 0, 0, 0, 0, 0, 0, 0, 3.000000000000000, 3.000000000000000, \
3.000000000000000, 3.000000000000000, -15.00000000000000, \
-5.000000000000000, 5.000000000000000, 15.00000000000000};
double basisD3Values[] =
{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15.00000000000000, \
15.00000000000000, 15.00000000000000, 15.00000000000000};
try {
Basis_HGRAD_LINE_Cn_FEM_JACOBI<double, FieldContainer<double> > lineBasis3(3, alpha, beta);
int numIntervals = 3;
FieldContainer<double> lineNodes3(numIntervals+1, 1);
FieldContainer<double> vals;
for (int i=0; i<numIntervals+1; i++) {
lineNodes3(i,0) = -1.0+(2.0*(double)i)/(double)numIntervals;
}
int numFields = lineBasis3.getCardinality();
int numPoints = lineNodes3.dimension(0);
// test basis values
vals.resize(numFields, numPoints);
lineBasis3.getValues(vals,lineNodes3,OPERATOR_VALUE);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
// Compute offset for (F,P) container
int l = j + i * numPoints;
if (std::abs(vals(i,j) - basisValues[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";
*outStream << "} computed value: " << vals(i,j)
<< " but reference value: " << basisValues[l] << "\n";
}
}
}
// test basis derivatives
vals.resize(numFields, numPoints,1);
lineBasis3.getValues(vals,lineNodes3,OPERATOR_D1);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
// Compute offset for (F,P) container
int l = j + i * numPoints;
if (std::abs(vals(i,j,0) - basisD1Values[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";
*outStream << "} computed value: " << vals(i,j,0)
<< " but reference value: " << basisD1Values[l] << "\n";
}
}
}
vals.resize(numFields, numPoints,1);
lineBasis3.getValues(vals,lineNodes3,OPERATOR_D2);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
// Compute offset for (F,P) container
int l = j + i * numPoints;
if (std::abs(vals(i,j,0) - basisD2Values[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";
*outStream << "} computed value: " << vals(i,j,0)
<< " but reference value: " << basisD2Values[l] << "\n";
}
}
}
vals.resize(numFields, numPoints,1);
lineBasis3.getValues(vals,lineNodes3,OPERATOR_D3);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
// Compute offset for (F,P) container
int l = j + i * numPoints;
if (std::abs(vals(i,j,0) - basisD3Values[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";
*outStream << "} computed value: " << vals(i,j,0)
<< " but reference value: " << basisD3Values[l] << "\n";
}
}
}
}
// Catch unexpected errors
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
Kokkos::initialize();
typedef CellTools<double> CellTools;
typedef shards::CellTopology CellTopology;
// This little trick lets us print to std::cout only if a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test CellTools |\n" \
<< "| |\n" \
<< "| 1) Edge parametrizations |\n" \
<< "| 2) Face parametrizations |\n" \
<< "| 3) Edge tangents |\n" \
<< "| 4) Face tangents and normals |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]) |\n" \
<< "| Denis Ridzal ([email protected]), or |\n" \
<< "| Kara Peterson ([email protected]) |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n";
int errorFlag = 0;
// Vertices of the parametrization domain for 1-subcells: standard 1-cube [-1,1]
FieldContainer<double> cube_1(2, 1);
cube_1(0,0) = -1.0;
cube_1(1,0) = 1.0;
// Vertices of the parametrization domain for triangular faces: the standard 2-simplex
FieldContainer<double> simplex_2(3, 2);
simplex_2(0, 0) = 0.0; simplex_2(0, 1) = 0.0;
simplex_2(1, 0) = 1.0; simplex_2(1, 1) = 0.0;
simplex_2(2, 0) = 0.0; simplex_2(2, 1) = 1.0;
// Vertices of the parametrization domain for quadrilateral faces: the standard 2-cube
FieldContainer<double> cube_2(4, 2);
cube_2(0, 0) = -1.0; cube_2(0, 1) = -1.0;
cube_2(1, 0) = 1.0; cube_2(1, 1) = -1.0;
cube_2(2, 0) = 1.0; cube_2(2, 1) = 1.0;
cube_2(3, 0) = -1.0; cube_2(3, 1) = 1.0;
// Pull all available topologies from Shards
std::vector<shards::CellTopology> allTopologies;
shards::getTopologies(allTopologies);
// Set to 1 for edge and 2 for face tests
int subcDim;
try{
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| Test 1: edge parametrizations: |\n"\
<< "===============================================================================\n\n";
subcDim = 1;
// Loop over the cell topologies
for(int topoOrd = 0; topoOrd < (int)allTopologies.size(); topoOrd++){
// Test only 2D and 3D topologies that have reference cells, e.g., exclude Line, Pentagon, etc.
if(allTopologies[topoOrd].getDimension() > 1 && CellTools::hasReferenceCell(allTopologies[topoOrd]) ){
*outStream << " Testing edge parametrization for " << allTopologies[topoOrd].getName() <<"\n";
testSubcellParametrizations(errorFlag,
allTopologies[topoOrd],
cube_1,
cube_1,
subcDim,
outStream);
}
}
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| Test 2: face parametrizations: |\n"\
<< "===============================================================================\n\n";
subcDim = 2;
// Loop over the cell topologies
for(int topoOrd = 0; topoOrd < (int)allTopologies.size(); topoOrd++){
// Test only 3D topologies that have reference cells
if(allTopologies[topoOrd].getDimension() > 2 && CellTools::hasReferenceCell(allTopologies[topoOrd]) ){
*outStream << " Testing face parametrization for cell topology " << allTopologies[topoOrd].getName() <<"\n";
testSubcellParametrizations(errorFlag,
allTopologies[topoOrd],
simplex_2,
cube_2,
subcDim,
outStream);
}
}
/***********************************************************************************************
*
* Common for test 3 and 4: edge tangents and face normals for standard cells with base topo
*
**********************************************************************************************/
// Allocate storage and extract all standard cells with base topologies
std::vector<shards::CellTopology> standardBaseTopologies;
shards::getTopologies(standardBaseTopologies, 4, shards::STANDARD_CELL, shards::BASE_TOPOLOGY);
// Define topologies for the edge and face parametrization domains. (faces are Tri or Quad)
CellTopology paramEdge (shards::getCellTopologyData<shards::Line<2> >() );
CellTopology paramTriFace (shards::getCellTopologyData<shards::Triangle<3> >() );
CellTopology paramQuadFace(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
// Define CubatureFactory:
DefaultCubatureFactory<double> cubFactory;
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| Test 3: edge tangents/normals for stand. cells with base topologies: |\n"\
<< "===============================================================================\n\n";
// This test loops over standard cells with base topologies, creates a set of nodes and tests tangents/normals
std::vector<shards::CellTopology>::iterator cti;
// Define cubature on the edge parametrization domain:
Teuchos::RCP<Cubature<double> > edgeCubature = cubFactory.create(paramEdge, 6);
int cubDim = edgeCubature -> getDimension();
int numCubPoints = edgeCubature -> getNumPoints();
// Allocate storage for cubature points and weights on edge parameter domain and fill with points:
FieldContainer<double> paramEdgePoints(numCubPoints, cubDim);
FieldContainer<double> paramEdgeWeights(numCubPoints);
edgeCubature -> getCubature(paramEdgePoints, paramEdgeWeights);
// Loop over admissible topologies
for(cti = standardBaseTopologies.begin(); cti !=standardBaseTopologies.end(); ++cti){
// Exclude 0D (node), 1D (Line) and Pyramid<5> cells
if( ( (*cti).getDimension() >= 2) && ( (*cti).getKey() != shards::Pyramid<5>::key) ){
int cellDim = (*cti).getDimension();
int vCount = (*cti).getVertexCount();
FieldContainer<double> refCellVertices(vCount, cellDim);
CellTools::getReferenceSubcellVertices(refCellVertices, cellDim, 0, (*cti) );
*outStream << " Testing edge tangents";
if(cellDim == 2) { *outStream << " and normals"; }
*outStream <<" for cell topology " << (*cti).getName() <<"\n";
// Array for physical cell vertices ( must have rank 3 for setJacobians)
FieldContainer<double> physCellVertices(1, vCount, cellDim);
// Randomize reference cell vertices by moving them up to +/- (1/8) units along their
// coordinate axis. Guaranteed to be non-degenerate for standard cells with base topology
for(int v = 0; v < vCount; v++){
for(int d = 0; d < cellDim; d++){
double delta = Teuchos::ScalarTraits<double>::random()/8.0;
physCellVertices(0, v, d) = refCellVertices(v, d) + delta;
} //for d
}// for v
// Allocate storage for cub. points on a ref. edge; Jacobians, phys. edge tangents/normals
FieldContainer<double> refEdgePoints(numCubPoints, cellDim);
FieldContainer<double> edgePointsJacobians(1, numCubPoints, cellDim, cellDim);
FieldContainer<double> edgePointTangents(1, numCubPoints, cellDim);
FieldContainer<double> edgePointNormals(1, numCubPoints, cellDim);
// Loop over edges:
for(int edgeOrd = 0; edgeOrd < (int)(*cti).getEdgeCount(); edgeOrd++){
/*
* Compute tangents on the specified physical edge using CellTools:
* 1. Map points from edge parametrization domain to ref. edge with specified ordinal
* 2. Compute parent cell Jacobians at ref. edge points
* 3. Compute physical edge tangents
*/
CellTools::mapToReferenceSubcell(refEdgePoints, paramEdgePoints, 1, edgeOrd, (*cti) );
CellTools::setJacobian(edgePointsJacobians, refEdgePoints, physCellVertices, (*cti) );
CellTools::getPhysicalEdgeTangents(edgePointTangents, edgePointsJacobians, edgeOrd, (*cti));
/*
* Compute tangents directly using parametrization of phys. edge and compare with CellTools tangents.
* 1. Get edge vertices
* 2. For affine edges tangent coordinates are given by F'(t) = (V1-V0)/2
* (for now we only test affine edges, but later we will test edges for cells
* with extended topologies.)
*/
int v0ord = (*cti).getNodeMap(1, edgeOrd, 0);
int v1ord = (*cti).getNodeMap(1, edgeOrd, 1);
for(int pt = 0; pt < numCubPoints; pt++){
// Temp storage for directly computed edge tangents
FieldContainer<double> edgeBenchmarkTangents(3);
for(int d = 0; d < cellDim; d++){
edgeBenchmarkTangents(d) = (physCellVertices(0, v1ord, d) - physCellVertices(0, v0ord, d))/2.0;
// Compare with d-component of edge tangent by CellTools
if( abs(edgeBenchmarkTangents(d) - edgePointTangents(0, pt, d)) > INTREPID2_THRESHOLD ){
errorFlag++;
*outStream
<< std::setw(70) << "^^^^----FAILURE!" << "\n"
<< " Edge tangent computation by CellTools failed for: \n"
<< " Cell Topology = " << (*cti).getName() << "\n"
<< " Edge ordinal = " << edgeOrd << "\n"
<< " Edge point number = " << pt << "\n"
<< " Tangent coordinate = " << d << "\n"
<< " CellTools value = " << edgePointTangents(0, pt, d) << "\n"
<< " Benchmark value = " << edgeBenchmarkTangents(d) << "\n\n";
}
} // for d
// Test side normals for 2D cells only: edge normal has coordinates (t1, -t0)
if(cellDim == 2) {
CellTools::getPhysicalSideNormals(edgePointNormals, edgePointsJacobians, edgeOrd, (*cti));
if( abs(edgeBenchmarkTangents(1) - edgePointNormals(0, pt, 0)) > INTREPID2_THRESHOLD ){
errorFlag++;
*outStream
<< std::setw(70) << "^^^^----FAILURE!" << "\n"
<< " Edge Normal computation by CellTools failed for: \n"
<< " Cell Topology = " << (*cti).getName() << "\n"
<< " Edge ordinal = " << edgeOrd << "\n"
<< " Edge point number = " << pt << "\n"
<< " Normal coordinate = " << 0 << "\n"
<< " CellTools value = " << edgePointNormals(0, pt, 0) << "\n"
<< " Benchmark value = " << edgeBenchmarkTangents(1) << "\n\n";
}
if( abs(edgeBenchmarkTangents(0) + edgePointNormals(0, pt, 1)) > INTREPID2_THRESHOLD ){
errorFlag++;
*outStream
<< std::setw(70) << "^^^^----FAILURE!" << "\n"
<< " Edge Normal computation by CellTools failed for: \n"
<< " Cell Topology = " << (*cti).getName() << "\n"
<< " Edge ordinal = " << edgeOrd << "\n"
<< " Edge point number = " << pt << "\n"
<< " Normal coordinate = " << 1 << "\n"
<< " CellTools value = " << edgePointNormals(0, pt, 1) << "\n"
<< " Benchmark value = " << -edgeBenchmarkTangents(0) << "\n\n";
}
} // edge normals
} // for pt
}// for edgeOrd
}// if admissible cell
}// for cti
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| Test 4: face/side normals for stand. 3D cells with base topologies: | |\n"\
<< "===============================================================================\n\n";
// This test loops over standard 3D cells with base topologies, creates a set of nodes and tests normals
// Define cubature on the edge parametrization domain:
Teuchos::RCP<Cubature<double> > triFaceCubature = cubFactory.create(paramTriFace, 6);
Teuchos::RCP<Cubature<double> > quadFaceCubature = cubFactory.create(paramQuadFace, 6);
int faceCubDim = triFaceCubature -> getDimension();
int numTriFaceCubPoints = triFaceCubature -> getNumPoints();
int numQuadFaceCubPoints = quadFaceCubature -> getNumPoints();
// Allocate storage for cubature points and weights on face parameter domain and fill with points:
FieldContainer<double> paramTriFacePoints(numTriFaceCubPoints, faceCubDim);
FieldContainer<double> paramTriFaceWeights(numTriFaceCubPoints);
FieldContainer<double> paramQuadFacePoints(numQuadFaceCubPoints, faceCubDim);
FieldContainer<double> paramQuadFaceWeights(numQuadFaceCubPoints);
triFaceCubature -> getCubature(paramTriFacePoints, paramTriFaceWeights);
quadFaceCubature -> getCubature(paramQuadFacePoints, paramQuadFaceWeights);
// Loop over admissible topologies
for(cti = standardBaseTopologies.begin(); cti !=standardBaseTopologies.end(); ++cti){
// Exclude 2D and Pyramid<5> cells
if( ( (*cti).getDimension() == 3) && ( (*cti).getKey() != shards::Pyramid<5>::key) ){
int cellDim = (*cti).getDimension();
int vCount = (*cti).getVertexCount();
FieldContainer<double> refCellVertices(vCount, cellDim);
CellTools::getReferenceSubcellVertices(refCellVertices, cellDim, 0, (*cti) );
*outStream << " Testing face/side normals for cell topology " << (*cti).getName() <<"\n";
// Array for physical cell vertices ( must have rank 3 for setJacobians)
FieldContainer<double> physCellVertices(1, vCount, cellDim);
// Randomize reference cell vertices by moving them up to +/- (1/8) units along their
// coordinate axis. Guaranteed to be non-degenerate for standard cells with base topology
for(int v = 0; v < vCount; v++){
for(int d = 0; d < cellDim; d++){
double delta = Teuchos::ScalarTraits<double>::random()/8.0;
physCellVertices(0, v, d) = refCellVertices(v, d) + delta;
} //for d
}// for v
// Allocate storage for cub. points on a ref. face; Jacobians, phys. face normals and
// benchmark normals.
FieldContainer<double> refTriFacePoints(numTriFaceCubPoints, cellDim);
FieldContainer<double> refQuadFacePoints(numQuadFaceCubPoints, cellDim);
FieldContainer<double> triFacePointsJacobians(1, numTriFaceCubPoints, cellDim, cellDim);
FieldContainer<double> quadFacePointsJacobians(1, numQuadFaceCubPoints, cellDim, cellDim);
FieldContainer<double> triFacePointNormals(1, numTriFaceCubPoints, cellDim);
FieldContainer<double> triSidePointNormals(1, numTriFaceCubPoints, cellDim);
FieldContainer<double> quadFacePointNormals(1, numQuadFaceCubPoints, cellDim);
FieldContainer<double> quadSidePointNormals(1, numQuadFaceCubPoints, cellDim);
// Loop over faces:
for(int faceOrd = 0; faceOrd < (int)(*cti).getSideCount(); faceOrd++){
// This test presently includes only Triangle<3> and Quadrilateral<4> faces. Once we support
// cells with extended topologies we will add their faces as well.
switch( (*cti).getCellTopologyData(2, faceOrd) -> key ) {
case shards::Triangle<3>::key:
{
// Compute face normals using CellTools
CellTools::mapToReferenceSubcell(refTriFacePoints, paramTriFacePoints, 2, faceOrd, (*cti) );
CellTools::setJacobian(triFacePointsJacobians, refTriFacePoints, physCellVertices, (*cti) );
CellTools::getPhysicalFaceNormals(triFacePointNormals, triFacePointsJacobians, faceOrd, (*cti));
CellTools::getPhysicalSideNormals(triSidePointNormals, triFacePointsJacobians, faceOrd, (*cti));
/*
* Compute face normals using direct linear parametrization of the face: the map from
* standard 2-simplex to physical Triangle<3> face in 3D is
* F(x,y) = V0 + (V1-V0)x + (V2-V0)*y
* Face normal is vector product Tx X Ty where Tx = (V1-V0); Ty = (V2-V0)
*/
int v0ord = (*cti).getNodeMap(2, faceOrd, 0);
int v1ord = (*cti).getNodeMap(2, faceOrd, 1);
int v2ord = (*cti).getNodeMap(2, faceOrd, 2);
// Loop over face points: redundant for affine faces, but CellTools gives one vector
// per point so need to check all points anyways.
for(int pt = 0; pt < numTriFaceCubPoints; pt++){
FieldContainer<double> tanX(3), tanY(3), faceNormal(3);
for(int d = 0; d < cellDim; d++){
tanX(d) = (physCellVertices(0, v1ord, d) - physCellVertices(0, v0ord, d));
tanY(d) = (physCellVertices(0, v2ord, d) - physCellVertices(0, v0ord, d));
}// for d
RealSpaceTools<double>::vecprod(faceNormal, tanX, tanY);
// Compare direct normal with d-component of the face/side normal by CellTools
for(int d = 0; d < cellDim; d++){
// face normal method
if( abs(faceNormal(d) - triFacePointNormals(0, pt, d)) > INTREPID2_THRESHOLD ){
errorFlag++;
*outStream
<< std::setw(70) << "^^^^----FAILURE!" << "\n"
<< " Face normal computation by CellTools failed for: \n"
<< " Cell Topology = " << (*cti).getName() << "\n"
<< " Face Topology = " << (*cti).getCellTopologyData(2, faceOrd) -> name << "\n"
<< " Face ordinal = " << faceOrd << "\n"
<< " Face point number = " << pt << "\n"
<< " Normal coordinate = " << d << "\n"
<< " CellTools value = " << triFacePointNormals(0, pt, d)
<< " Benchmark value = " << faceNormal(d) << "\n\n";
}
//side normal method
if( abs(faceNormal(d) - triSidePointNormals(0, pt, d)) > INTREPID2_THRESHOLD ){
errorFlag++;
*outStream
<< std::setw(70) << "^^^^----FAILURE!" << "\n"
<< " Side normal computation by CellTools failed for: \n"
<< " Cell Topology = " << (*cti).getName() << "\n"
<< " Side Topology = " << (*cti).getCellTopologyData(2, faceOrd) -> name << "\n"
<< " Side ordinal = " << faceOrd << "\n"
<< " Side point number = " << pt << "\n"
<< " Normal coordinate = " << d << "\n"
<< " CellTools value = " << triSidePointNormals(0, pt, d)
<< " Benchmark value = " << faceNormal(d) << "\n\n";
}
} // for d
} // for pt
}
break;
case shards::Quadrilateral<4>::key:
{
// Compute face normals using CellTools
CellTools::mapToReferenceSubcell(refQuadFacePoints, paramQuadFacePoints, 2, faceOrd, (*cti) );
CellTools::setJacobian(quadFacePointsJacobians, refQuadFacePoints, physCellVertices, (*cti) );
CellTools::getPhysicalFaceNormals(quadFacePointNormals, quadFacePointsJacobians, faceOrd, (*cti));
CellTools::getPhysicalSideNormals(quadSidePointNormals, quadFacePointsJacobians, faceOrd, (*cti));
/*
* Compute face normals using direct bilinear parametrization of the face: the map from
* [-1,1]^2 to physical Quadrilateral<4> face in 3D is
* F(x,y) = ((V0+V1+V2+V3) + (-V0+V1+V2-V3)*X + (-V0-V1+V2+V3)*Y + (V0-V1+V2-V3)*X*Y)/4
* Face normal is vector product Tx X Ty where
* Tx = ((-V0+V1+V2-V3) + (V0-V1+V2-V3)*Y)/4
* Ty = ((-V0-V1+V2+V3) + (V0-V1+V2-V3)*X)/4
*/
int v0ord = (*cti).getNodeMap(2, faceOrd, 0);
int v1ord = (*cti).getNodeMap(2, faceOrd, 1);
int v2ord = (*cti).getNodeMap(2, faceOrd, 2);
int v3ord = (*cti).getNodeMap(2, faceOrd, 3);
// Loop over face points (redundant for affine faces, but needed for later when we handle non-affine ones)
for(int pt = 0; pt < numTriFaceCubPoints; pt++){
FieldContainer<double> tanX(3), tanY(3), faceNormal(3);
for(int d = 0; d < cellDim; d++){
tanX(d) = (physCellVertices(0, v0ord, d)*(-1.0 + paramQuadFacePoints(pt,1) ) +
physCellVertices(0, v1ord, d)*( 1.0 - paramQuadFacePoints(pt,1) ) +
physCellVertices(0, v2ord, d)*( 1.0 + paramQuadFacePoints(pt,1) ) +
physCellVertices(0, v3ord, d)*(-1.0 - paramQuadFacePoints(pt,1) ) )/4.0;
tanY(d) = (physCellVertices(0, v0ord, d)*(-1.0 + paramQuadFacePoints(pt,0) ) +
physCellVertices(0, v1ord, d)*(-1.0 - paramQuadFacePoints(pt,0) ) +
physCellVertices(0, v2ord, d)*( 1.0 + paramQuadFacePoints(pt,0) ) +
physCellVertices(0, v3ord, d)*( 1.0 - paramQuadFacePoints(pt,0) ) )/4.0;
}// for d
RealSpaceTools<double>::vecprod(faceNormal, tanX, tanY);
// Compare direct normal with d-component of the face/side normal by CellTools
for(int d = 0; d < cellDim; d++){
// face normal method
if( abs(faceNormal(d) - quadFacePointNormals(0, pt, d)) > INTREPID2_THRESHOLD ){
errorFlag++;
*outStream
<< std::setw(70) << "^^^^----FAILURE!" << "\n"
<< " Face normal computation by CellTools failed for: \n"
<< " Cell Topology = " << (*cti).getName() << "\n"
<< " Face Topology = " << (*cti).getCellTopologyData(2, faceOrd) -> name << "\n"
<< " Face ordinal = " << faceOrd << "\n"
<< " Face point number = " << pt << "\n"
<< " Normal coordinate = " << d << "\n"
<< " CellTools value = " << quadFacePointNormals(0, pt, d)
<< " Benchmark value = " << faceNormal(d) << "\n\n";
}
//side normal method
if( abs(faceNormal(d) - quadSidePointNormals(0, pt, d)) > INTREPID2_THRESHOLD ){
errorFlag++;
*outStream
<< std::setw(70) << "^^^^----FAILURE!" << "\n"
<< " Side normal computation by CellTools failed for: \n"
<< " Cell Topology = " << (*cti).getName() << "\n"
<< " Side Topology = " << (*cti).getCellTopologyData(2, faceOrd) -> name << "\n"
<< " Side ordinal = " << faceOrd << "\n"
<< " Side point number = " << pt << "\n"
<< " Normal coordinate = " << d << "\n"
<< " CellTools value = " << quadSidePointNormals(0, pt, d)
<< " Benchmark value = " << faceNormal(d) << "\n\n";
}
} // for d
}// for pt
}// case Quad
break;
default:
errorFlag++;
*outStream << " Face normals test failure: face topology not supported \n\n";
} // switch
}// for faceOrd
}// if admissible
}// for cti
}// try
//============================================================================================//
// Wrap up test: check if the test broke down unexpectedly due to an exception //
//============================================================================================//
catch (std::logic_error err) {
*outStream << err.what() << "\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return errorFlag;
}
int Orientation_Test01(const bool verbose) {
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (verbose)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
typedef typename
Kokkos::Impl::is_space<DeviceSpaceType>::host_mirror_space::execution_space HostSpaceType ;
*outStream << "DeviceSpace:: "; DeviceSpaceType::print_configuration(*outStream, false);
*outStream << "HostSpace:: "; HostSpaceType::print_configuration(*outStream, false);
*outStream << "\n";
*outStream
<< "===============================================================================\n"
<< "| |\n"
<< "| Unit Test (Orientation) |\n"
<< "| |\n"
<< "===============================================================================\n";
int errorFlag = 0;
try {
ordinal_type nthrow = 0, ncatch = 0;
{
Orientation ort;
INTREPID2_TEST_ERROR_EXPECTED( if (ort.isAlignedToReference()) \
throw std::logic_error("Default Orientation is not zero"); );
}
if (nthrow != ncatch) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << "# of catch ("<< ncatch << ") is different from # of throw (" << nthrow << ")\n";
}
{
*outStream << "\n -- Testing Triangle \n\n";
const auto cellTopo = shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() );
const ordinal_type elemNodes[6][3] = { { 1, 2, 3 },
{ 1, 3, 2 },
{ 2, 1, 3 },
{ 2, 3, 1 },
{ 3, 1, 2 },
{ 3, 2, 1 } };
const ordinal_type refEdgeOrts[6][3] = { { 0, 0, 1 },
{ 0, 1, 1 },
{ 1, 0, 1 },
{ 0, 1, 0 },
{ 1, 0, 0 },
{ 1, 1, 0 } };
for (auto i=0;i<6;++i) {
// find orientation
const auto nodes = Kokkos::View<const ordinal_type[3],HostSpaceType>(elemNodes[i]);
const auto ort = Orientation::getOrientation(cellTopo, nodes);
// decode orientation
ordinal_type edgeOrt[3] = {};
for (auto edgeId=0;edgeId<3;++edgeId)
ort.getEdgeOrientation(edgeOrt, 3);
*outStream << " elemNodes = "
<< elemNodes[i][0] << " "
<< elemNodes[i][1] << " "
<< elemNodes[i][2] << " :: "
<< " computed edgeOrts = "
<< edgeOrt[0] << " "
<< edgeOrt[1] << " "
<< edgeOrt[2] << " :: "
<< " reference edgeOrts = "
<< refEdgeOrts[i][0] << " "
<< refEdgeOrts[i][1] << " "
<< refEdgeOrts[i][2] << " ::\n";
if (edgeOrt[0] != refEdgeOrts[i][0] ||
edgeOrt[1] != refEdgeOrts[i][1] ||
edgeOrt[2] != refEdgeOrts[i][2]) {
*outStream << " ^^^^^^^^^^^^^^^^ FAILURE\n";
++errorFlag;
}
}
}
{
*outStream << "\n -- Testing Quadrilateral \n\n";
const auto cellTopo = shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
const ordinal_type elemNodes[24][4] = { { 1 , 2 , 3 , 4 },
{ 2 , 1 , 3 , 4 },
{ 1 , 3 , 2 , 4 },
{ 2 , 3 , 1 , 4 },
{ 3 , 1 , 2 , 4 },
{ 3 , 2 , 1 , 4 },
{ 1 , 2 , 4 , 3 },
{ 2 , 1 , 4 , 3 },
{ 1 , 3 , 4 , 2 },
{ 2 , 3 , 4 , 1 },
{ 3 , 1 , 4 , 2 },
{ 3 , 2 , 4 , 1 },
{ 1 , 4 , 2 , 3 },
{ 2 , 4 , 1 , 3 },
{ 1 , 4 , 3 , 2 },
{ 2 , 4 , 3 , 1 },
{ 3 , 4 , 1 , 2 },
{ 3 , 4 , 2 , 1 },
{ 4 , 1 , 2 , 3 },
{ 4 , 2 , 1 , 3 },
{ 4 , 1 , 3 , 2 },
{ 4 , 2 , 3 , 1 },
{ 4 , 3 , 1 , 2 },
{ 4 , 3 , 2 , 1 } };
const ordinal_type refEdgeOrts[24][4] = { { 0, 0, 0, 1 },
{ 1, 0, 0, 1 },
{ 0, 1, 0, 1 },
{ 0, 1, 0, 1 },
{ 1, 0, 0, 1 },
{ 1, 1, 0, 1 },
{ 0, 0, 1, 1 },
{ 1, 0, 1, 1 },
{ 0, 0, 1, 1 },
{ 0, 0, 1, 0 },
{ 1, 0, 1, 0 },
{ 1, 0, 1, 0 },
{ 0, 1, 0, 1 },
{ 0, 1, 0, 1 },
{ 0, 1, 1, 1 },
{ 0, 1, 1, 0 },
{ 0, 1, 0, 0 },
{ 0, 1, 1, 0 },
{ 1, 0, 0, 0 },
{ 1, 1, 0, 0 },
{ 1, 0, 1, 0 },
{ 1, 0, 1, 0 },
{ 1, 1, 0, 0 },
{ 1, 1, 1, 0 } };
for (auto i=0;i<24;++i) {
// find orientation
const auto nodes = Kokkos::View<const ordinal_type[4],HostSpaceType>(elemNodes[i]);
const auto ort = Orientation::getOrientation(cellTopo, nodes);
// decode orientation
ordinal_type edgeOrt[4] = {};
for (auto edgeId=0;edgeId<4;++edgeId)
ort.getEdgeOrientation(edgeOrt, 4);
*outStream << " elemNodes = "
<< elemNodes[i][0] << " "
<< elemNodes[i][1] << " "
<< elemNodes[i][2] << " "
<< elemNodes[i][3] << " :: "
<< " computed edgeOrts = "
<< edgeOrt[0] << " "
<< edgeOrt[1] << " "
<< edgeOrt[2] << " "
<< edgeOrt[3] << " :: "
<< " reference edgeOrts = "
<< refEdgeOrts[i][0] << " "
<< refEdgeOrts[i][1] << " "
<< refEdgeOrts[i][2] << " "
<< refEdgeOrts[i][3] << " ::\n";
if (edgeOrt[0] != refEdgeOrts[i][0] ||
edgeOrt[1] != refEdgeOrts[i][1] ||
edgeOrt[2] != refEdgeOrts[i][2] ||
edgeOrt[3] != refEdgeOrts[i][3]) {
*outStream << " ^^^^^^^^^^^^^^^^ FAILURE\n";
++errorFlag;
}
}
}
} catch (std::exception err) {
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (FunctionSpaceTools) |\n" \
<< "| |\n" \
<< "| 1) basic operator transformations and integration in HGRAD |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]) or |\n" \
<< "| Denis Ridzal ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n";
int errorFlag = 0;
#ifdef HAVE_INTREPID_DEBUG
int beginThrowNumber = Teuchos::TestForException_getThrowNumber();
int endThrowNumber = beginThrowNumber + 28;
#endif
typedef FunctionSpaceTools fst;
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 1: exceptions |\n"\
<< "===============================================================================\n";
try{
#ifdef HAVE_INTREPID_DEBUG
FieldContainer<double, 1> a_2(2);
FieldContainer<double, 2> a_2_2(2, 2);
FieldContainer<double, 3> a_2_3(2, 3);
FieldContainer<double, 4> a_3_2(3, 2);
FieldContainer<double, 5> a_2_2_3(2, 2, 3);
FieldContainer<double, 6> a_2_2_3_3(2, 2, 3, 3);
FieldContainer<double, 7> a_2_2_2(2, 2, 2);
FieldContainer<double, 8> a_2_2_2_3_3(2, 2, 2, 3, 3);
FieldContainer<double, 9> a_2_2_2_2_2(2, 2, 2, 2, 2);
FieldContainer<double, 10> a_2_2_2_2(2, 2, 2, 2);
FieldContainer<double, 11> a_3_2_2_2(3, 2, 2, 2);
FieldContainer<double, 12> a_2_3_2_2(2, 3, 2, 2);
FieldContainer<double, 13> a_2_2_3_2(2, 2, 3, 2);
FieldContainer<double, 14> a_2_2_2_3(2, 2, 2, 3);
*outStream << "\n >>>>> TESTING computeCellMeasure:\n";
INTREPID_TEST_COMMAND( fst::computeCellMeasure<double>(a_2_2, a_2, a_2) );
INTREPID_TEST_COMMAND( fst::computeCellMeasure<double>(a_2_2, a_2_2, a_2) );
*outStream << "\n >>>>> TESTING computeFaceMeasure:\n";
INTREPID_TEST_COMMAND( fst::computeFaceMeasure<double>(a_2_2, a_2, a_2, 0, shards::getCellTopologyData< shards::Tetrahedron<> >()) );
INTREPID_TEST_COMMAND( fst::computeFaceMeasure<double>(a_2_2, a_2_2_3_3, a_2, 0, shards::getCellTopologyData< shards::Tetrahedron<> >()) );
*outStream << "\n >>>>> TESTING computeEdgeMeasure:\n";
INTREPID_TEST_COMMAND( fst::computeEdgeMeasure<double>(a_2_2, a_2, a_2, 0, shards::getCellTopologyData< shards::Triangle<> >()) );
INTREPID_TEST_COMMAND( fst::computeEdgeMeasure<double>(a_2_2, a_2_2_2_2, a_2, 0, shards::getCellTopologyData< shards::Triangle<> >()) );
*outStream << "\n >>>>> TESTING integrate:\n";
INTREPID_TEST_COMMAND( fst::integrate<double>(a_2_2_2_2, a_2_2_2, a_2_2_2, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::integrate<double>(a_2, a_2_2, a_2_2, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::integrate<double>(a_2, a_2_2_3, a_2_2_3, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::integrate<double>(a_2, a_2_2_3_3, a_2_2_3_3, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::integrate<double>(a_2_2, a_2_2, a_2_2_2, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::integrate<double>(a_2_2, a_2_2_3, a_2_2_2_3, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::integrate<double>(a_2_2, a_2_2_3_3, a_2_2_2_3_3, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::integrate<double>(a_2_2_2, a_2_2_2, a_2_2_2, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::integrate<double>(a_2_2_2, a_2_2_2_3, a_2_2_2_3, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::integrate<double>(a_2_2_2, a_2_2_2_3_3, a_2_2_2_3_3, COMP_CPP) );
*outStream << "\n >>>>> TESTING operatorIntegral:\n";
INTREPID_TEST_COMMAND( fst::operatorIntegral<double>(a_2_2_2, a_2_2, a_2_2_2, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::operatorIntegral<double>(a_2_2_2, a_2_2_2, a_2_2_2, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::operatorIntegral<double>(a_2_2_2, a_2_2_2_3, a_2_2_2_3, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::operatorIntegral<double>(a_2_2_2, a_2_2_2_3_3, a_2_2_2_3_3, COMP_CPP) );
*outStream << "\n >>>>> TESTING functionalIntegral:\n";
INTREPID_TEST_COMMAND( fst::functionalIntegral<double>(a_2_2, a_2_2_2_3_3, a_2_2_2, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::functionalIntegral<double>(a_2_2, a_2_2, a_2_2_2, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::functionalIntegral<double>(a_2_2, a_2_2_3, a_2_2_2_3, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::functionalIntegral<double>(a_2_2, a_2_2_3_3, a_2_2_2_3_3, COMP_CPP) );
*outStream << "\n >>>>> TESTING dataIntegral:\n";
INTREPID_TEST_COMMAND( fst::dataIntegral<double>(a_2, a_2, a_2_2_2, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::dataIntegral<double>(a_2, a_2_2, a_2_2, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::dataIntegral<double>(a_2, a_2_2_3, a_2_2_3, COMP_CPP) );
INTREPID_TEST_COMMAND( fst::dataIntegral<double>(a_2, a_2_2_3_3, a_2_2_3_3, COMP_CPP) );
*outStream << "\n >>>>> TESTING applyLeftFieldSigns:\n";
INTREPID_TEST_COMMAND( fst::applyLeftFieldSigns<double>(a_2, a_2) );
INTREPID_TEST_COMMAND( fst::applyLeftFieldSigns<double>(a_2_2_2, a_2) );
INTREPID_TEST_COMMAND( fst::applyLeftFieldSigns<double>(a_2_2_2, a_3_2) );
INTREPID_TEST_COMMAND( fst::applyLeftFieldSigns<double>(a_2_2_2, a_2_3) );
INTREPID_TEST_COMMAND( fst::applyLeftFieldSigns<double>(a_2_2_2, a_2_2) );
*outStream << "\n >>>>> TESTING applyRightFieldSigns:\n";
INTREPID_TEST_COMMAND( fst::applyRightFieldSigns<double>(a_2, a_2) );
INTREPID_TEST_COMMAND( fst::applyRightFieldSigns<double>(a_2_2_2, a_2) );
INTREPID_TEST_COMMAND( fst::applyRightFieldSigns<double>(a_2_2_2, a_3_2) );
INTREPID_TEST_COMMAND( fst::applyRightFieldSigns<double>(a_2_2_2, a_2_3) );
INTREPID_TEST_COMMAND( fst::applyRightFieldSigns<double>(a_2_2_2, a_2_2) );
*outStream << "\n >>>>> TESTING applyFieldSigns:\n";
INTREPID_TEST_COMMAND( fst::applyFieldSigns<double>(a_2, a_2) );
INTREPID_TEST_COMMAND( fst::applyFieldSigns<double>(a_2_2, a_2) );
INTREPID_TEST_COMMAND( fst::applyFieldSigns<double>(a_2_2, a_3_2) );
INTREPID_TEST_COMMAND( fst::applyFieldSigns<double>(a_2_2, a_2_3) );
INTREPID_TEST_COMMAND( fst::applyFieldSigns<double>(a_2_2_2_3_3, a_2_2) );
*outStream << "\n >>>>> TESTING evaluate:\n";
INTREPID_TEST_COMMAND( fst::evaluate<double>(a_2, a_2, a_2_2) );
INTREPID_TEST_COMMAND( fst::evaluate<double>(a_2, a_2, a_2_2_2_3_3) );
INTREPID_TEST_COMMAND( fst::evaluate<double>(a_2, a_2_2, a_2_2_2_3_3) );
INTREPID_TEST_COMMAND( fst::evaluate<double>(a_2_2_3_3, a_3_2, a_2_2_2_3_3) );
INTREPID_TEST_COMMAND( fst::evaluate<double>(a_2_2_3_3, a_2_3, a_2_2_2_3_3) );
INTREPID_TEST_COMMAND( fst::evaluate<double>(a_3_2_2_2, a_2_2, a_2_2_2_2_2) );
INTREPID_TEST_COMMAND( fst::evaluate<double>(a_2_3_2_2, a_2_2, a_2_2_2_2_2) );
INTREPID_TEST_COMMAND( fst::evaluate<double>(a_2_2_3_2, a_2_2, a_2_2_2_2_2) );
INTREPID_TEST_COMMAND( fst::evaluate<double>(a_2_2_2_3, a_2_2, a_2_2_2_2_2) );
INTREPID_TEST_COMMAND( fst::evaluate<double>(a_2_2_2_2, a_2_2, a_2_2_2_2_2) );
#endif
}
catch (std::logic_error err) {
*outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
*outStream << err.what() << '\n';
*outStream << "-------------------------------------------------------------------------------" << "\n\n";
errorFlag = -1000;
};
#ifdef HAVE_INTREPID_DEBUG
if (Teuchos::TestForException_getThrowNumber() != endThrowNumber)
errorFlag++;
#endif
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 2: correctness of math operations |\n"\
<< "===============================================================================\n";
outStream->precision(20);
try {
// cell type: tet
shards::CellTopology cellType = shards::getCellTopologyData< shards::Tetrahedron<> >();
/* Related to cubature. */
// create cubature factory
DefaultCubatureFactory<double, FieldContainer<double, 1>, FieldContainer<double, 2> > cubFactory;
// cubature degree
int cubDegree = 2;
// create default cubature
Teuchos::RCP<Cubature<double, FieldContainer<double, 1>, FieldContainer<double, 2> > > myCub = cubFactory.create(cellType, cubDegree);
// get spatial dimension
int spaceDim = myCub->getDimension();
// get number of cubature points
int numCubPoints = myCub->getNumPoints();
/* Related to basis. */
// create tet basis
Basis_HGRAD_TET_C1_FEM<double, FieldContainer<double, 1> > tetBasis;
// get basis cardinality
int numFields = tetBasis.getCardinality();
/* Cell geometries. */
int numCells = 4;
int numNodes = 4;
int numCellData = numCells*numNodes*spaceDim;
double tetnodes[] = {
// tet 0
0.0, 0.0, 0.0,
1.0, 0.0, 0.0,
0.0, 1.0, 0.0,
0.0, 0.0, 1.0,
// tet 1
4.0, 5.0, 1.0,
-6.0, 2.0, 0.0,
4.0, -3.0, -1.0,
0.0, 2.0, 5.0,
// tet 2
-6.0, -3.0, 1.0,
9.0, 2.0, 1.0,
8.9, 2.1, 0.9,
8.9, 2.1, 1.1,
// tet 3
-6.0, -3.0, 1.0,
12.0, 3.0, 1.0,
2.9, 0.1, 0.9,
2.9, 0.1, 1.1
};
/* Computational arrays. */
FieldContainer<double, 1> cub_points(numCubPoints, spaceDim);
FieldContainer<double, 2> cub_weights(numCubPoints);
FieldContainer<double, 3> cell_nodes(numCells, numNodes, spaceDim);
FieldContainer<double, 4> jacobian(numCells, numCubPoints, spaceDim, spaceDim);
FieldContainer<double, 5> jacobian_inv(numCells, numCubPoints, spaceDim, spaceDim);
FieldContainer<double, 6> jacobian_det(numCells, numCubPoints);
FieldContainer<double, 7> weighted_measure(numCells, numCubPoints);
FieldContainer<double, 1> grad_of_basis_at_cub_points(numFields, numCubPoints, spaceDim);
FieldContainer<double, 9> transformed_grad_of_basis_at_cub_points(numCells, numFields, numCubPoints, spaceDim);
FieldContainer<double, 10> weighted_transformed_grad_of_basis_at_cub_points(numCells, numFields, numCubPoints, spaceDim);
FieldContainer<double, 11> stiffness_matrices(numCells, numFields, numFields);
FieldContainer<double, 1> value_of_basis_at_cub_points(numFields, numCubPoints);
FieldContainer<double, 13> transformed_value_of_basis_at_cub_points(numCells, numFields, numCubPoints);
FieldContainer<double, 14> weighted_transformed_value_of_basis_at_cub_points(numCells, numFields, numCubPoints);
FieldContainer<double, 15> mass_matrices(numCells, numFields, numFields);
/******************* START COMPUTATION ***********************/
// get cubature points and weights
myCub->getCubature(cub_points, cub_weights);
// fill cell vertex array
cell_nodes.setValues(tetnodes, numCellData);
// compute geometric cell information
CellTools<double>::setJacobian(jacobian, cub_points, cell_nodes, cellType);
CellTools<double>::setJacobianInv(jacobian_inv, jacobian);
CellTools<double>::setJacobianDet(jacobian_det, jacobian);
// compute weighted measure
fst::computeCellMeasure<double>(weighted_measure, jacobian_det, cub_weights);
// Computing stiffness matrices:
// tabulate gradients of basis functions at (reference) cubature points
tetBasis.getValues(grad_of_basis_at_cub_points, cub_points, OPERATOR_GRAD);
// transform gradients of basis functions
fst::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points,
jacobian_inv,
grad_of_basis_at_cub_points);
// multiply with weighted measure
fst::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points,
weighted_measure,
transformed_grad_of_basis_at_cub_points);
// compute stiffness matrices
fst::integrate<double>(stiffness_matrices,
transformed_grad_of_basis_at_cub_points,
weighted_transformed_grad_of_basis_at_cub_points,
COMP_CPP);
// Computing mass matrices:
// tabulate values of basis functions at (reference) cubature points
tetBasis.getValues(value_of_basis_at_cub_points, cub_points, OPERATOR_VALUE);
// transform values of basis functions
fst::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points,
value_of_basis_at_cub_points);
// multiply with weighted measure
fst::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points,
weighted_measure,
transformed_value_of_basis_at_cub_points);
// compute mass matrices
fst::integrate<double>(mass_matrices,
transformed_value_of_basis_at_cub_points,
weighted_transformed_value_of_basis_at_cub_points,
COMP_CPP);
/******************* STOP COMPUTATION ***********************/
/******************* START COMPARISON ***********************/
string basedir = "./testdata";
for (int cell_id = 0; cell_id < numCells; cell_id++) {
stringstream namestream;
string filename;
namestream << basedir << "/mass_TET_FEM_P1" << "_" << "0" << cell_id+1 << ".dat";
namestream >> filename;
ifstream massfile(&filename[0]);
if (massfile.is_open()) {
if (compareToAnalytic<double>(&mass_matrices(cell_id, 0, 0), massfile, 1e-10, 0) > 0)
errorFlag++;
massfile.close();
}
else {
errorFlag = -1;
std::cout << "End Result: TEST FAILED\n";
return errorFlag;
}
namestream.clear();
namestream << basedir << "/stiff_TET_FEM_P1" << "_" << "0" << cell_id+1 << ".dat";
namestream >> filename;
ifstream stifffile(&filename[0]);
if (stifffile.is_open())
{
if (compareToAnalytic<double>(&stiffness_matrices(cell_id, 0, 0), stifffile, 1e-10, 0) > 0)
errorFlag++;
stifffile.close();
}
else {
errorFlag = -1;
std::cout << "End Result: TEST FAILED\n";
return errorFlag;
}
}
/******************* STOP COMPARISON ***********************/
*outStream << "\n";
}
catch (std::logic_error err) {
*outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
*outStream << err.what() << '\n';
*outStream << "-------------------------------------------------------------------------------" << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (Basis_HGRAD_TRI_C1_FEM) |\n" \
<< "| |\n" \
<< "| 1) Conversion of Dof tags into Dof ordinals and back |\n" \
<< "| 2) Basis values for VALUE, GRAD, CURL, and Dk operators |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n"\
<< "| TEST 1: Basis creation, exception testing |\n"\
<< "===============================================================================\n";
// Define basis and error flag
Basis_HGRAD_TRI_C1_FEM<double, FieldContainer<double> > triBasis;
int errorFlag = 0;
// Initialize throw counter for exception testing
int nException = 0;
int throwCounter = 0;
// Define array containing the 3 vertices of the reference Triangle, its center and another point
FieldContainer<double> triNodes(5, 2);
triNodes(0,0) = 0.0; triNodes(0,1) = 0.0;
triNodes(1,0) = 1.0; triNodes(1,1) = 0.0;
triNodes(2,0) = 0.0; triNodes(2,1) = 1.0;
triNodes(3,0) = 0.5; triNodes(3,1) = 0.5;
triNodes(4,0) = 0.0; triNodes(4,1) = 0.75;
// Generic array for the output values; needs to be properly resized depending on the operator type
FieldContainer<double> vals;
try{
// exception #1: DIV cannot be applied to scalar functions
// resize vals to rank-2 container with dimensions (num. points, num. basis functions)
vals.resize(triBasis.getCardinality(), triNodes.dimension(0) );
INTREPID_TEST_COMMAND( triBasis.getValues(vals, triNodes, OPERATOR_DIV), throwCounter, nException );
// Exceptions 2-6: all bf tags/bf Ids below are wrong and should cause getDofOrdinal() and
// getDofTag() to access invalid array elements thereby causing bounds check exception
// exception #2
INTREPID_TEST_COMMAND( triBasis.getDofOrdinal(2,0,0), throwCounter, nException );
// exception #3
INTREPID_TEST_COMMAND( triBasis.getDofOrdinal(1,1,1), throwCounter, nException );
// exception #4
INTREPID_TEST_COMMAND( triBasis.getDofOrdinal(0,4,0), throwCounter, nException );
// exception #5
INTREPID_TEST_COMMAND( triBasis.getDofTag(5), throwCounter, nException );
// exception #6
INTREPID_TEST_COMMAND( triBasis.getDofTag(-1), throwCounter, nException );
#ifdef HAVE_INTREPID_DEBUG
// Exceptions 7-17 test exception handling with incorrectly dimensioned input/output arrays
// exception #7: input points array must be of rank-2
FieldContainer<double> badPoints1(4, 5, 3);
INTREPID_TEST_COMMAND( triBasis.getValues(vals, badPoints1, OPERATOR_VALUE), throwCounter, nException );
// exception #8 dimension 1 in the input point array must equal space dimension of the cell
FieldContainer<double> badPoints2(4, 3);
INTREPID_TEST_COMMAND( triBasis.getValues(vals, badPoints2, OPERATOR_VALUE), throwCounter, nException );
// exception #9 output values must be of rank-2 for OPERATOR_VALUE
FieldContainer<double> badVals1(4, 3, 1);
INTREPID_TEST_COMMAND( triBasis.getValues(badVals1, triNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #10 output values must be of rank-3 for OPERATOR_GRAD
FieldContainer<double> badVals2(4, 3);
INTREPID_TEST_COMMAND( triBasis.getValues(badVals2, triNodes, OPERATOR_GRAD), throwCounter, nException );
// exception #11 output values must be of rank-3 for OPERATOR_CURL
INTREPID_TEST_COMMAND( triBasis.getValues(badVals2, triNodes, OPERATOR_CURL), throwCounter, nException );
// exception #12 output values must be of rank-3 for OPERATOR_D2
INTREPID_TEST_COMMAND( triBasis.getValues(badVals2, triNodes, OPERATOR_D2), throwCounter, nException );
// exception #13 incorrect 1st dimension of output array (must equal number of basis functions)
FieldContainer<double> badVals3(triBasis.getCardinality() + 1, triNodes.dimension(0));
INTREPID_TEST_COMMAND( triBasis.getValues(badVals3, triNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #14 incorrect 0th dimension of output array (must equal number of points)
FieldContainer<double> badVals4(triBasis.getCardinality(), triNodes.dimension(0) + 1);
INTREPID_TEST_COMMAND( triBasis.getValues(badVals4, triNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #15: incorrect 2nd dimension of output array (must equal the space dimension)
FieldContainer<double> badVals5(triBasis.getCardinality(), triNodes.dimension(0), 4);
INTREPID_TEST_COMMAND( triBasis.getValues(badVals5, triNodes, OPERATOR_GRAD), throwCounter, nException );
// exception #16: incorrect 2nd dimension of output array (must equal D2 cardinality in 2D)
FieldContainer<double> badVals6(triBasis.getCardinality(), triNodes.dimension(0), 40);
INTREPID_TEST_COMMAND( triBasis.getValues(badVals6, triNodes, OPERATOR_D2), throwCounter, nException );
// exception #17: incorrect 2nd dimension of output array (must equal D3 cardinality in 2D)
INTREPID_TEST_COMMAND( triBasis.getValues(badVals6, triNodes, OPERATOR_D3), throwCounter, nException );
#endif
}
catch (std::logic_error err) {
*outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
*outStream << err.what() << '\n';
*outStream << "-------------------------------------------------------------------------------" << "\n\n";
errorFlag = -1000;
};
// Check if number of thrown exceptions matches the one we expect
if (throwCounter != nException) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
}
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 2: correctness of tag to enum and enum to tag lookups |\n"\
<< "===============================================================================\n";
try{
std::vector<std::vector<int> > allTags = triBasis.getAllDofTags();
// Loop over all tags, lookup the associated dof enumeration and then lookup the tag again
for (unsigned i = 0; i < allTags.size(); i++) {
int bfOrd = triBasis.getDofOrdinal(allTags[i][0], allTags[i][1], allTags[i][2]);
std::vector<int> myTag = triBasis.getDofTag(bfOrd);
if( !( (myTag[0] == allTags[i][0]) &&
(myTag[1] == allTags[i][1]) &&
(myTag[2] == allTags[i][2]) &&
(myTag[3] == allTags[i][3]) ) ) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " getDofOrdinal( {"
<< allTags[i][0] << ", "
<< allTags[i][1] << ", "
<< allTags[i][2] << ", "
<< allTags[i][3] << "}) = " << bfOrd <<" but \n";
*outStream << " getDofTag(" << bfOrd << ") = { "
<< myTag[0] << ", "
<< myTag[1] << ", "
<< myTag[2] << ", "
<< myTag[3] << "}\n";
}
}
// Now do the same but loop over basis functions
for( int bfOrd = 0; bfOrd < triBasis.getCardinality(); bfOrd++) {
std::vector<int> myTag = triBasis.getDofTag(bfOrd);
int myBfOrd = triBasis.getDofOrdinal(myTag[0], myTag[1], myTag[2]);
if( bfOrd != myBfOrd) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " getDofTag(" << bfOrd << ") = { "
<< myTag[0] << ", "
<< myTag[1] << ", "
<< myTag[2] << ", "
<< myTag[3] << "} but getDofOrdinal({"
<< myTag[0] << ", "
<< myTag[1] << ", "
<< myTag[2] << ", "
<< myTag[3] << "} ) = " << myBfOrd << "\n";
}
}
}
catch (std::logic_error err){
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 3: correctness of basis function values |\n"\
<< "===============================================================================\n";
outStream -> precision(20);
// VALUE: Each row gives the 3 correct basis set values at an evaluation point
double basisValues[] = {
1.0, 0.0, 0.0,
0.0, 1.0, 0.0,
0.0, 0.0, 1.0,
0.0, 0.5, 0.5,
0.25,0.0, 0.75
};
// GRAD and D1: each row gives the 6 correct values of the gradients of the 3 basis functions
double basisGrads[] = {
-1.0, -1.0, 1.0, 0.0, 0.0, 1.0,
-1.0, -1.0, 1.0, 0.0, 0.0, 1.0,
-1.0, -1.0, 1.0, 0.0, 0.0, 1.0,
-1.0, -1.0, 1.0, 0.0, 0.0, 1.0,
-1.0, -1.0, 1.0, 0.0, 0.0, 1.0,
};
// CURL: each row gives the 6 correct values of the curls of the 3 basis functions
double basisCurls[] = {
-1.0, 1.0, 0.0, -1.0, 1.0, 0.0,
-1.0, 1.0, 0.0, -1.0, 1.0, 0.0,
-1.0, 1.0, 0.0, -1.0, 1.0, 0.0,
-1.0, 1.0, 0.0, -1.0, 1.0, 0.0,
-1.0, 1.0, 0.0, -1.0, 1.0, 0.0
};
try{
// Dimensions for the output arrays:
int numFields = triBasis.getCardinality();
int numPoints = triNodes.dimension(0);
int spaceDim = triBasis.getBaseCellTopology().getDimension();
// Generic array for values, grads, curls, etc. that will be properly sized before each call
FieldContainer<double> vals;
// Check VALUE of basis functions: resize vals to rank-2 container:
vals.resize(numFields, numPoints);
triBasis.getValues(vals, triNodes, OPERATOR_VALUE);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
int l = i + j * numFields;
if (std::abs(vals(i,j) - basisValues[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";
*outStream << "} computed value: " << vals(i,j)
<< " but reference value: " << basisValues[l] << "\n";
}
}
}
// Check GRAD of basis function: resize vals to rank-3 container
vals.resize(numFields, numPoints, spaceDim);
triBasis.getValues(vals, triNodes, OPERATOR_GRAD);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
for (int k = 0; k < spaceDim; k++) {
int l = k + i * spaceDim + j * spaceDim * numFields;
if (std::abs(vals(i,j,k) - basisGrads[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed grad component: " << vals(i,j,k)
<< " but reference grad component: " << basisGrads[l] << "\n";
}
}
}
}
// Check D1 of basis function (do not resize vals because it has the correct size: D1 = GRAD)
triBasis.getValues(vals, triNodes, OPERATOR_D1);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
for (int k = 0; k < spaceDim; k++) {
int l = k + i * spaceDim + j * spaceDim * numFields;
if (std::abs(vals(i,j,k) - basisGrads[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed D1 component: " << vals(i,j,k)
<< " but reference D1 component: " << basisGrads[l] << "\n";
}
}
}
}
// Check CURL of basis function: resize vals just for illustration!
vals.resize(numFields, numPoints, spaceDim);
triBasis.getValues(vals, triNodes, OPERATOR_CURL);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
for (int k = 0; k < spaceDim; k++) {
int l = k + i * spaceDim + j * spaceDim * numFields;
if (std::abs(vals(i,j,k) - basisCurls[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed curl component: " << vals(i,j,k)
<< " but reference curl component: " << basisCurls[l] << "\n";
}
}
}
}
// Check all higher derivatives - must be zero.
for(EOperator op = OPERATOR_D2; op < OPERATOR_MAX; op++) {
// The last dimension is the number of kth derivatives and needs to be resized for every Dk
int DkCardin = Intrepid::getDkCardinality(op, spaceDim);
vals.resize(numFields, numPoints, DkCardin);
triBasis.getValues(vals, triNodes, op);
for (int i = 0; i < vals.size(); i++) {
if (std::abs(vals[i]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Get the multi-index of the value where the error is and the operator order
std::vector<int> myIndex;
vals.getMultiIndex(myIndex,i);
int ord = Intrepid::getOperatorOrder(op);
*outStream << " At multi-index { ";
for(int j = 0; j < vals.rank(); j++) {
*outStream << myIndex[j] << " ";
}
*outStream << "} computed D"<< ord <<" component: " << vals[i]
<< " but reference D" << ord << " component: 0 \n";
}
}
}
}
// Catch unexpected errors
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 4: correctness of DoF locations |\n"\
<< "===============================================================================\n";
try{
Teuchos::RCP<Basis<double, FieldContainer<double> > > basis =
Teuchos::rcp(new Basis_HGRAD_TRI_C1_FEM<double, FieldContainer<double> >);
Teuchos::RCP<DofCoordsInterface<FieldContainer<double> > > coord_iface =
Teuchos::rcp_dynamic_cast<DofCoordsInterface<FieldContainer<double> > >(basis);
FieldContainer<double> cvals;
FieldContainer<double> bvals(basis->getCardinality(), basis->getCardinality());
// Check exceptions.
#ifdef HAVE_INTREPID_DEBUG
cvals.resize(1,2,3);
INTREPID_TEST_COMMAND( coord_iface->getDofCoords(cvals), throwCounter, nException );
cvals.resize(4,2);
INTREPID_TEST_COMMAND( coord_iface->getDofCoords(cvals), throwCounter, nException );
cvals.resize(4,3);
INTREPID_TEST_COMMAND( coord_iface->getDofCoords(cvals), throwCounter, nException );
#endif
cvals.resize(3,2);
INTREPID_TEST_COMMAND( coord_iface->getDofCoords(cvals), throwCounter, nException ); nException--;
// Check if number of thrown exceptions matches the one we expect
if (throwCounter != nException) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
}
// Check mathematical correctness.
basis->getValues(bvals, cvals, OPERATOR_VALUE);
char buffer[120];
for (int i=0; i<bvals.dimension(0); i++) {
for (int j=0; j<bvals.dimension(1); j++) {
if ((i != j) && (std::abs(bvals(i,j) - 0.0) > INTREPID_TOL)) {
errorFlag++;
sprintf(buffer, "\nValue of basis function %d at (%6.4e, %6.4e) is %6.4e but should be %6.4e!\n", i, cvals(i,0), cvals(i,1), bvals(i,j), 0.0);
*outStream << buffer;
}
else if ((i == j) && (std::abs(bvals(i,j) - 1.0) > INTREPID_TOL)) {
errorFlag++;
sprintf(buffer, "\nValue of basis function %d at (%6.4e, %6.4e) is %6.4e but should be %6.4e!\n", i, cvals(i,0), cvals(i,1), bvals(i,j), 1.0);
*outStream << buffer;
}
}
}
}
catch (std::logic_error err){
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
/** \brief outdated tests for orthogonal bases
\param argc [in] - number of command-line arguments
\param argv [in] - command-line arguments
*/
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
// This little trick lets us print to std::cout only if a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test OrthogonalBases |\n" \
<< "| |\n" \
<< "| 1) Tests orthogonality of tetrahedral orthogonal basis |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]) or |\n" \
<< "| Denis Ridzal ([email protected]) or |\n" \
<< "| Robert Kirby ([email protected]) |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n";
int errorFlag = 0;
// First, get a reference quadrature rule
CubatureDirectTetDefault<double,FieldContainer<double> > myCub(20);
FieldContainer<double> cubPts( myCub.getNumPoints() , 3 );
FieldContainer<double> cubWts( myCub.getNumPoints() );
myCub.getCubature( cubPts , cubWts );
// Tabulate the basis functions at the cubature points
const int deg = 10;
const int polydim = (deg+1)*(deg+2)*(deg+3)/6;
FieldContainer<double> basisAtCubPts( polydim , myCub.getNumPoints() );
OrthogonalBases::tabulateTetrahedron<double,FieldContainer<double>,FieldContainer<double> >( cubPts , deg , basisAtCubPts );
// Now let's compute the mass matrix
for (int i=0;i<polydim;i++) {
for (int j=0;j<polydim;j++) {
double cur = 0;
for (int k=0;k<myCub.getNumPoints();k++) {
cur += cubWts(k) * basisAtCubPts( i , k ) * basisAtCubPts( j , k );
}
if (i != j && fabs( cur ) > 20.0 * INTREPID_TOL) {
std::cout << INTREPID_TOL << std::endl;
std::cout << i << " " << j << " " << cur << std::endl;
errorFlag++;
}
else if (i == j && fabs( cur ) < 20.0 * INTREPID_TOL ) {
std::cout << i << " " << j << " " << cur << std::endl;
errorFlag++;
}
}
}
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
int main(int argc, char *argv[]) {
//Check number of arguments
if (argc < 4) {
std::cout <<"\n>>> ERROR: Invalid number of arguments.\n\n";
std::cout <<"Usage:\n\n";
std::cout <<" ./Intrepid_example_Drivers_Example_10.exe deg NX NY NZ verbose\n\n";
std::cout <<" where \n";
std::cout <<" int deg - polynomial degree to be used (assumed >= 1) \n";
std::cout <<" int NX - num intervals in x direction (assumed box domain, 0,1) \n";
std::cout <<" int NY - num intervals in y direction (assumed box domain, 0,1) \n";
std::cout <<" int NZ - num intervals in y direction (assumed box domain, 0,1) \n";
std::cout <<" verbose (optional) - any character, indicates verbose output \n\n";
exit(1);
}
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 2)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Example: Build Stiffness Matrix for |\n" \
<< "| Poisson Equation on Hexahedral Mesh |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n";
// ************************************ GET INPUTS **************************************
int deg = atoi(argv[1]); // polynomial degree to use
int NX = atoi(argv[2]); // num intervals in x direction (assumed box domain, 0,1)
int NY = atoi(argv[3]); // num intervals in y direction (assumed box domain, 0,1)
int NZ = atoi(argv[4]); // num intervals in y direction (assumed box domain, 0,1)
// *********************************** CELL TOPOLOGY **********************************
// Get cell topology for base hexahedron
typedef shards::CellTopology CellTopology;
CellTopology hex_8(shards::getCellTopologyData<shards::Hexahedron<8> >() );
// Get dimensions
int numNodesPerElem = hex_8.getNodeCount();
int spaceDim = hex_8.getDimension();
// *********************************** GENERATE MESH ************************************
*outStream << "Generating mesh ... \n\n";
*outStream << " NX" << " NY" << " NZ\n";
*outStream << std::setw(5) << NX <<
std::setw(5) << NY << std::setw(5) << NZ << "\n\n";
// Print mesh information
int numElems = NX*NY*NZ;
int numNodes = (NX+1)*(NY+1)*(NZ+1);
*outStream << " Number of Elements: " << numElems << " \n";
*outStream << " Number of Nodes: " << numNodes << " \n\n";
// Cube
double leftX = 0.0, rightX = 1.0;
double leftY = 0.0, rightY = 1.0;
double leftZ = 0.0, rightZ = 1.0;
// Mesh spacing
double hx = (rightX-leftX)/((double)NX);
double hy = (rightY-leftY)/((double)NY);
double hz = (rightZ-leftZ)/((double)NZ);
// Get nodal coordinates
FieldContainer<double> nodeCoord(numNodes, spaceDim);
FieldContainer<int> nodeOnBoundary(numNodes);
int inode = 0;
for (int k=0; k<NZ+1; k++)
{
for (int j=0; j<NY+1; j++)
{
for (int i=0; i<NX+1; i++)
{
nodeCoord(inode,0) = leftX + (double)i*hx;
nodeCoord(inode,1) = leftY + (double)j*hy;
nodeCoord(inode,2) = leftZ + (double)k*hz;
if (k==0 || k==NZ || j==0 || i==0 || j==NY || i==NX)
{
nodeOnBoundary(inode)=1;
}
else
{
nodeOnBoundary(inode)=0;
}
inode++;
}
}
}
#define DUMP_DATA
#ifdef DUMP_DATA
// Print nodal coords
ofstream fcoordout("coords.dat");
for (int i=0; i<numNodes; i++) {
fcoordout << nodeCoord(i,0) <<" ";
fcoordout << nodeCoord(i,1) <<" ";
fcoordout << nodeCoord(i,2) <<"\n";
}
fcoordout.close();
#endif
// Element to Node map
// We'll keep it around, but this is only the DOFMap if you are in the lowest order case.
FieldContainer<int> elemToNode(numElems, numNodesPerElem);
int ielem = 0;
for (int k=0; k<NZ; k++)
{
for (int j=0; j<NY; j++)
{
for (int i=0; i<NX; i++)
{
elemToNode(ielem,0) = k * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i;
elemToNode(ielem,1) = k * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i + 1;
elemToNode(ielem,2) = k * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i + 1;
elemToNode(ielem,3) = k * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i;
elemToNode(ielem,4) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i;
elemToNode(ielem,5) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + j * ( NX + 1 ) + i + 1;
elemToNode(ielem,6) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i + 1;
elemToNode(ielem,7) = ( k + 1 ) * ( NX + 1 ) * ( NY + 1 ) + ( j + 1 ) * ( NX + 1 ) + i;
ielem++;
}
}
}
#ifdef DUMP_DATA
// Output connectivity
ofstream fe2nout("elem2node.dat");
for (int k=0;k<NZ;k++)
{
for (int j=0; j<NY; j++)
{
for (int i=0; i<NX; i++)
{
int ielem = i + j * NX + k * NY * NY;
for (int m=0; m<numNodesPerElem; m++)
{
fe2nout << elemToNode(ielem,m) <<" ";
}
fe2nout <<"\n";
}
}
}
fe2nout.close();
#endif
// ************************************ CUBATURE **************************************
*outStream << "Getting cubature ... \n\n";
// Get numerical integration points and weights
DefaultCubatureFactory<double> cubFactory;
int cubDegree = 2*deg;
Teuchos::RCP<Cubature<double> > quadCub = cubFactory.create(hex_8, cubDegree);
int cubDim = quadCub->getDimension();
int numCubPoints = quadCub->getNumPoints();
FieldContainer<double> cubPoints(numCubPoints, cubDim);
FieldContainer<double> cubWeights(numCubPoints);
quadCub->getCubature(cubPoints, cubWeights);
// ************************************** BASIS ***************************************
*outStream << "Getting basis ... \n\n";
// Define basis
Basis_HGRAD_HEX_Cn_FEM<double, FieldContainer<double> > quadHGradBasis(deg,POINTTYPE_SPECTRAL);
int numFieldsG = quadHGradBasis.getCardinality();
FieldContainer<double> quadGVals(numFieldsG, numCubPoints);
FieldContainer<double> quadGrads(numFieldsG, numCubPoints, spaceDim);
// Evaluate basis values and gradients at cubature points
quadHGradBasis.getValues(quadGVals, cubPoints, OPERATOR_VALUE);
quadHGradBasis.getValues(quadGrads, cubPoints, OPERATOR_GRAD);
// create the local-global mapping
FieldContainer<int> ltgMapping(numElems,numFieldsG);
const int numDOF = (NX*deg+1)*(NY*deg+1)*(NZ*deg+1);
ielem=0;
for (int k=0;k<NZ;k++)
{
for (int j=0;j<NY;j++)
{
for (int i=0;i<NX;i++)
{
const int start = k * ( NY * deg + 1 ) * ( NX * deg + 1 ) + j * ( NX * deg + 1 ) + i * deg;
// loop over local dof on this cell
int local_dof_cur=0;
for (int kloc=0;kloc<=deg;kloc++)
{
for (int jloc=0;jloc<=deg;jloc++)
{
for (int iloc=0;iloc<=deg;iloc++)
{
ltgMapping(ielem,local_dof_cur) = start
+ kloc * ( NX * deg + 1 ) * ( NY * deg + 1 )
+ jloc * ( NX * deg + 1 )
+ iloc;
local_dof_cur++;
}
}
}
ielem++;
}
}
}
#ifdef DUMP_DATA
// Output ltg mapping
ielem = 0;
ofstream ltgout("ltg.dat");
for (int k=0;k<NZ;k++)
{
for (int j=0; j<NY; j++)
{
for (int i=0; i<NX; i++)
{
int ielem = i + j * NX + k * NX * NY;
for (int m=0; m<numFieldsG; m++)
{
ltgout << ltgMapping(ielem,m) <<" ";
}
ltgout <<"\n";
}
}
}
ltgout.close();
#endif
// ********** DECLARE GLOBAL OBJECTS *************
Epetra_SerialComm Comm;
Epetra_Map globalMapG(numDOF, 0, Comm);
Epetra_FEVector u(globalMapG); u.Random();
Epetra_FEVector Ku(globalMapG);
// time the instantiation
Epetra_Time instantiateTimer(Comm);
Epetra_FECrsMatrix StiffMatrix(Copy,globalMapG,8*numFieldsG);
const double instantiateTime = instantiateTimer.ElapsedTime();
// ********** CONSTRUCT AND INSERT LOCAL STIFFNESS MATRICES ***********
*outStream << "Building local stiffness matrices...\n\n";
typedef CellTools<double> CellTools;
typedef FunctionSpaceTools fst;
int numCells = numElems;
// vertices
FieldContainer<double> cellVertices(numCells,numNodesPerElem,spaceDim);
// jacobian information
FieldContainer<double> cellJacobian(numCells,numCubPoints,spaceDim,spaceDim);
FieldContainer<double> cellJacobInv(numCells,numCubPoints,spaceDim,spaceDim);
FieldContainer<double> cellJacobDet(numCells,numCubPoints);
// element stiffness matrices and supporting storage space
FieldContainer<double> localStiffMatrices(numCells, numFieldsG, numFieldsG);
FieldContainer<double> transformedBasisGradients(numCells,numFieldsG,numCubPoints,spaceDim);
FieldContainer<double> weightedTransformedBasisGradients(numCells,numFieldsG,numCubPoints,spaceDim);
FieldContainer<double> weightedMeasure(numCells, numCubPoints);
// get vertices of cells (for computing Jacobians)
for (int i=0;i<numElems;i++)
{
for (int j=0;j<numNodesPerElem;j++)
{
const int nodeCur = elemToNode(i,j);
for (int k=0;k<spaceDim;k++)
{
cellVertices(i,j,k) = nodeCoord(nodeCur,k);
}
}
}
Epetra_Time localConstructTimer( Comm );
// jacobian evaluation
CellTools::setJacobian(cellJacobian,cubPoints,cellVertices,hex_8);
CellTools::setJacobianInv(cellJacobInv, cellJacobian );
CellTools::setJacobianDet(cellJacobDet, cellJacobian );
// transform reference element gradients to each cell
fst::HGRADtransformGRAD<double>(transformedBasisGradients, cellJacobInv, quadGrads);
// compute weighted measure
fst::computeCellMeasure<double>(weightedMeasure, cellJacobDet, cubWeights);
// multiply values with weighted measure
fst::multiplyMeasure<double>(weightedTransformedBasisGradients,
weightedMeasure, transformedBasisGradients);
// integrate to compute element stiffness matrix
fst::integrate<double>(localStiffMatrices,
transformedBasisGradients, weightedTransformedBasisGradients , COMP_BLAS);
const double localConstructTime = localConstructTimer.ElapsedTime();
Epetra_Time insertionTimer(Comm);
// *** Element loop ***
for (int k=0; k<numElems; k++)
{
// assemble into global matrix
StiffMatrix.InsertGlobalValues(numFieldsG,<gMapping(k,0),numFieldsG,<gMapping(k,0),&localStiffMatrices(k,0,0));
}
StiffMatrix.GlobalAssemble(); StiffMatrix.FillComplete();
const double insertionTime = insertionTimer.ElapsedTime( );
*outStream << "Time to instantiate global stiffness matrix: " << instantiateTime << "\n";
*outStream << "Time to build local matrices (including Jacobian computation): "<< localConstructTime << "\n";
*outStream << "Time to assemble global matrix from local matrices: " << insertionTime << "\n";
*outStream << "Total construction time: " << instantiateTime + localConstructTime + insertionTime << "\n";
Epetra_Time applyTimer(Comm);
StiffMatrix.Apply(u,Ku);
const double multTime = applyTimer.ElapsedTime();
*outStream << "Time to multiply onto a vector: " << multTime << "\n";
*outStream << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return 0;
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
Kokkos::initialize();
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (CubatureGenSparse) |\n" \
<< "| |\n" \
<< "| 1) Computing integrals of monomials on reference cells in 3D |\n" \
<< "| - using Level 2 BLAS - |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]) or |\n" \
<< "| Matthew Keegan ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n"\
<< "| TEST 1: integrals of monomials in 3D (Level 2 BLAS version) using |\n"\
<< "| Generalized Sparse Grid Construction |\n"\
<< "===============================================================================\n";
// internal variables:
int errorFlag = 0;
int polyCt = 0;
int offset = 0;
Teuchos::Array< Teuchos::Array<double> > testInt;
Teuchos::Array< Teuchos::Array<double> > analyticInt;
Teuchos::Array<double> tmparray(1);
double reltol = 1.0e+04 * INTREPID_TOL;
int maxDeg = 20; // can be as large as INTREPID2_CUBATURE_SPARSE3D_GAUSS_MAX, but runtime is excessive
int maxOffset = INTREPID2_CUBATURE_LINE_GAUSS_MAX;
int numPoly = (maxDeg+1)*(maxDeg+2)*(maxDeg+3)/6;
int numAnalytic = (maxOffset+1)*(maxOffset+2)*(maxOffset+3)/6;
testInt.assign(numPoly, tmparray);
analyticInt.assign(numAnalytic, tmparray);
// get names of files with analytic values
std::string basedir = "./data";
std::stringstream namestream;
std::string filename;
namestream << basedir << "/HEX_integrals" << ".dat";
namestream >> filename;
// format of data files with analytic values
TypeOfExactData dataFormat = INTREPID_UTILS_FRACTION;
// compute and compare integrals
try {
*outStream << "\nIntegrals of monomials:\n";
std::ifstream filecompare(&filename[0]);
// compute integrals
for (int cubDeg=0; cubDeg <= maxDeg; cubDeg++) {
int numMonomials = (cubDeg+1)*(cubDeg+2)*(cubDeg+3)/6;
testInt[cubDeg].resize(numMonomials);
computeIntegral(testInt[cubDeg], cubDeg);
}
// get analytic values
if (filecompare.is_open()) {
getAnalytic(analyticInt, filecompare, dataFormat);
// close file
filecompare.close();
}
// perform comparison
for (int cubDeg=0; cubDeg <= maxDeg; cubDeg++) {
polyCt = 0;
offset = 0;
int oldErrorFlag = errorFlag;
for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
for (int zDeg=0; zDeg <= cubDeg-xDeg-yDeg; zDeg++) {
double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) );
double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]);
if (absdiff > abstol) {
*outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
<< "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg
<< " * z^" << std::setw(2) << zDeg << ":" << " "
<< std::scientific << std::setprecision(16)
<< testInt[cubDeg][polyCt] << " " << analyticInt[polyCt+offset][0] << " "
<< std::setprecision(4) << absdiff << " " << "<?" << " " << abstol << "\n";
errorFlag++;
*outStream << std::right << std::setw(118) << "^^^^---FAILURE!\n";
}
polyCt++;
}
offset = offset + maxOffset - cubDeg;
}
offset = offset + (maxOffset - cubDeg)*(maxOffset - cubDeg + 1)/2;
}
*outStream << "Cubature order " << std::setw(2) << std::left << cubDeg;
if (errorFlag == oldErrorFlag)
*outStream << " passed.\n";
else
*outStream << " failed.\n";
}
*outStream << "\n";
}
catch (std::logic_error err) {
*outStream << err.what() << "\n";
errorFlag = -1;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return errorFlag;
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
Kokkos::initialize();
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (AdaptiveSparseGrid) |\n" \
<< "| |\n" \
<< "| 1) Integrate a sum of Gaussians in 2D (Gerstner and Griebel). |\n" \
<< "| |\n" \
<< "| Questions? Contact Drew Kouri ([email protected]) or |\n" \
<< "| Denis Ridzal ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n"\
<< "| TEST 20: Integrate an anisotropic sum of Gaussians in 2D |\n"\
<< "===============================================================================\n";
// internal variables:
int errorFlag = 0;
long double TOL = INTREPID_TOL;
int dimension = 2;
int maxLevel = 25;
bool isNormalized = true;
std::vector<EIntrepidBurkardt> rule1D(dimension,BURK_CLENSHAWCURTIS);
std::vector<EIntrepidGrowth> growth1D(dimension,GROWTH_FULLEXP);
ASGdata<long double,StdVector<long double> > problem_data(
dimension,rule1D,growth1D,maxLevel,isNormalized);
Teuchos::RCP<std::vector<long double> > integralValue =
Teuchos::rcp(new std::vector<long double>(1,0.0));
StdVector<long double> sol(integralValue); sol.Set(0.0);
problem_data.init(sol);
long double eta = adaptSG(sol,problem_data,TOL);
long double analyticInt = (1.0+10.0)*std::sqrt(M_PI)/2.0*erff(1.0);
long double abstol = 1.0e1*std::sqrt(INTREPID_TOL);
long double absdiff = fabs(analyticInt-sol[0]);
try {
*outStream << "Adaptive Sparse Grid exited with global error "
<< std::scientific << std::setprecision(16) << eta << "\n"
<< "Approx = " << std::scientific << std::setprecision(16) << sol[0]
<< ", Exact = " << std::scientific << std::setprecision(16) << analyticInt << "\n"
<< "Error = " << std::scientific << std::setprecision(16) << absdiff << " "
<< "<?" << " " << abstol << "\n";
if (absdiff > abstol) {
errorFlag++;
*outStream << std::right << std::setw(104) << "^^^^---FAILURE!\n";
}
}
catch (std::logic_error err) {
*outStream << err.what() << "\n";
errorFlag = -1;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return errorFlag;
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
Kokkos::initialize();
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (Basis_HGRAD_LINE_C1_FEM) |\n" \
<< "| |\n" \
<< "| 1) Patch test involving mass and stiffness matrices, |\n" \
<< "| for the Neumann problem on a REFERENCE line: |\n" \
<< "| |\n" \
<< "| - u'' + u = f in (-1,1), u' = g at -1,1 |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n"\
<< "| TEST 1: Patch test |\n"\
<< "===============================================================================\n";
int errorFlag = 0;
double zero = 100*INTREPID_TOL;
outStream -> precision(20);
try {
int max_order = 1; // max total order of polynomial solution
// Define array containing points at which the solution is evaluated
int numIntervals = 100;
int numInterpPoints = numIntervals + 1;
FieldContainer<double> interp_points(numInterpPoints, 1);
for (int i=0; i<numInterpPoints; i++) {
interp_points(i,0) = -1.0+(2.0*(double)i)/(double)numIntervals;
}
DefaultCubatureFactory<double> cubFactory; // create factory
shards::CellTopology line(shards::getCellTopologyData< shards::Line<> >()); // create cell topology
//create basis
Teuchos::RCP<Basis<double,FieldContainer<double> > > lineBasis =
Teuchos::rcp(new Basis_HGRAD_LINE_C1_FEM<double,FieldContainer<double> >() );
int numFields = lineBasis->getCardinality();
int basis_order = lineBasis->getDegree();
// create cubature
Teuchos::RCP<Cubature<double> > lineCub = cubFactory.create(line, 2);
int numCubPoints = lineCub->getNumPoints();
int spaceDim = lineCub->getDimension();
for (int soln_order=0; soln_order <= max_order; soln_order++) {
// evaluate exact solution
FieldContainer<double> exact_solution(1, numInterpPoints);
u_exact(exact_solution, interp_points, soln_order);
/* Computational arrays. */
FieldContainer<double> cub_points(numCubPoints, spaceDim);
FieldContainer<double> cub_points_physical(1, numCubPoints, spaceDim);
FieldContainer<double> cub_weights(numCubPoints);
FieldContainer<double> cell_nodes(1, 2, spaceDim);
FieldContainer<double> jacobian(1, numCubPoints, spaceDim, spaceDim);
FieldContainer<double> jacobian_inv(1, numCubPoints, spaceDim, spaceDim);
FieldContainer<double> jacobian_det(1, numCubPoints);
FieldContainer<double> weighted_measure(1, numCubPoints);
FieldContainer<double> value_of_basis_at_cub_points(numFields, numCubPoints);
FieldContainer<double> transformed_value_of_basis_at_cub_points(1, numFields, numCubPoints);
FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points(1, numFields, numCubPoints);
FieldContainer<double> grad_of_basis_at_cub_points(numFields, numCubPoints, spaceDim);
FieldContainer<double> transformed_grad_of_basis_at_cub_points(1, numFields, numCubPoints, spaceDim);
FieldContainer<double> weighted_transformed_grad_of_basis_at_cub_points(1, numFields, numCubPoints, spaceDim);
FieldContainer<double> fe_matrix(1, numFields, numFields);
FieldContainer<double> rhs_at_cub_points_physical(1, numCubPoints);
FieldContainer<double> rhs_and_soln_vector(1, numFields);
FieldContainer<double> one_point(1, 1);
FieldContainer<double> value_of_basis_at_one(numFields, 1);
FieldContainer<double> value_of_basis_at_minusone(numFields, 1);
FieldContainer<double> bc_neumann(2, numFields);
FieldContainer<double> value_of_basis_at_interp_points(numFields, numInterpPoints);
FieldContainer<double> transformed_value_of_basis_at_interp_points(1, numFields, numInterpPoints);
FieldContainer<double> interpolant(1, numInterpPoints);
FieldContainer<int> ipiv(numFields);
/******************* START COMPUTATION ***********************/
// get cubature points and weights
lineCub->getCubature(cub_points, cub_weights);
// fill cell vertex array
cell_nodes(0, 0, 0) = -1.0;
cell_nodes(0, 1, 0) = 1.0;
// compute geometric cell information
CellTools<double>::setJacobian(jacobian, cub_points, cell_nodes, line);
CellTools<double>::setJacobianInv(jacobian_inv, jacobian);
CellTools<double>::setJacobianDet(jacobian_det, jacobian);
// compute weighted measure
FunctionSpaceTools::computeCellMeasure<double>(weighted_measure, jacobian_det, cub_weights);
///////////////////////////
// Computing mass matrices:
// tabulate values of basis functions at (reference) cubature points
lineBasis->getValues(value_of_basis_at_cub_points, cub_points, OPERATOR_VALUE);
// transform values of basis functions
FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_cub_points,
value_of_basis_at_cub_points);
// multiply with weighted measure
FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_value_of_basis_at_cub_points,
weighted_measure,
transformed_value_of_basis_at_cub_points);
// compute mass matrices
FunctionSpaceTools::integrate<double>(fe_matrix,
transformed_value_of_basis_at_cub_points,
weighted_transformed_value_of_basis_at_cub_points,
COMP_CPP);
///////////////////////////
////////////////////////////////
// Computing stiffness matrices:
// tabulate gradients of basis functions at (reference) cubature points
lineBasis->getValues(grad_of_basis_at_cub_points, cub_points, OPERATOR_GRAD);
// transform gradients of basis functions
FunctionSpaceTools::HGRADtransformGRAD<double>(transformed_grad_of_basis_at_cub_points,
jacobian_inv,
grad_of_basis_at_cub_points);
// multiply with weighted measure
FunctionSpaceTools::multiplyMeasure<double>(weighted_transformed_grad_of_basis_at_cub_points,
weighted_measure,
transformed_grad_of_basis_at_cub_points);
// compute stiffness matrices and sum into fe_matrix
FunctionSpaceTools::integrate<double>(fe_matrix,
transformed_grad_of_basis_at_cub_points,
weighted_transformed_grad_of_basis_at_cub_points,
COMP_CPP,
true);
////////////////////////////////
///////////////////////////////
// Computing RHS contributions:
// map (reference) cubature points to physical space
CellTools<double>::mapToPhysicalFrame(cub_points_physical, cub_points, cell_nodes, line);
// evaluate rhs function
rhsFunc(rhs_at_cub_points_physical, cub_points_physical, soln_order);
// compute rhs
FunctionSpaceTools::integrate<double>(rhs_and_soln_vector,
rhs_at_cub_points_physical,
weighted_transformed_value_of_basis_at_cub_points,
COMP_CPP);
// compute neumann b.c. contributions and adjust rhs
one_point(0,0) = 1.0; lineBasis->getValues(value_of_basis_at_one, one_point, OPERATOR_VALUE);
one_point(0,0) = -1.0; lineBasis->getValues(value_of_basis_at_minusone, one_point, OPERATOR_VALUE);
neumann(bc_neumann, value_of_basis_at_minusone, value_of_basis_at_one, soln_order);
for (int i=0; i<numFields; i++) {
rhs_and_soln_vector(0, i) -= bc_neumann(0, i);
rhs_and_soln_vector(0, i) += bc_neumann(1, i);
}
///////////////////////////////
/////////////////////////////
// Solution of linear system:
int info = 0;
Teuchos::LAPACK<int, double> solver;
//solver.GESV(numRows, 1, &fe_mat(0,0), numRows, &ipiv(0), &fe_vec(0), numRows, &info);
solver.GESV(numFields, 1, &fe_matrix[0], numFields, &ipiv(0), &rhs_and_soln_vector[0], numFields, &info);
/////////////////////////////
////////////////////////
// Building interpolant:
// evaluate basis at interpolation points
lineBasis->getValues(value_of_basis_at_interp_points, interp_points, OPERATOR_VALUE);
// transform values of basis functions
FunctionSpaceTools::HGRADtransformVALUE<double>(transformed_value_of_basis_at_interp_points,
value_of_basis_at_interp_points);
FunctionSpaceTools::evaluate<double>(interpolant, rhs_and_soln_vector, transformed_value_of_basis_at_interp_points);
////////////////////////
/******************* END COMPUTATION ***********************/
RealSpaceTools<double>::subtract(interpolant, exact_solution);
*outStream << "\nNorm-2 difference between exact solution polynomial of order "
<< soln_order << " and finite element interpolant of order " << basis_order << ": "
<< RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) << "\n";
if (RealSpaceTools<double>::vectorNorm(&interpolant[0], interpolant.dimension(1), NORM_TWO) > zero) {
*outStream << "\n\nPatch test failed for solution polynomial order "
<< soln_order << " and basis order " << basis_order << "\n\n";
errorFlag++;
}
} // end for soln_order
}
// Catch unexpected errors
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return errorFlag;
}
int main(int argc, char *argv[]) {
Kokkos::initialize();
//Check number of arguments
if (argc < 4) {
std::cout <<"\n>>> ERROR: Invalid number of arguments.\n\n";
std::cout <<"Usage:\n\n";
std::cout <<" ./Intrepid_example_Drivers_Example_03.exe NX NY NZ verbose\n\n";
std::cout <<" where \n";
std::cout <<" int NX - num intervals in x direction (assumed box domain, 0,1) \n";
std::cout <<" int NY - num intervals in y direction (assumed box domain, 0,1) \n";
std::cout <<" int NZ - num intervals in z direction (assumed box domain, 0,1) \n";
std::cout <<" verbose (optional) - any character, indicates verbose output \n\n";
exit(1);
}
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 3)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Example: Generate Stiffness Matrix and Right Hand Side Vector for |\n" \
<< "| Poisson Equation on Hexahedral Mesh |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n";
// ************************************ GET INPUTS **************************************
int NX = atoi(argv[1]); // num intervals in x direction (assumed box domain, 0,1)
int NY = atoi(argv[2]); // num intervals in y direction (assumed box domain, 0,1)
int NZ = atoi(argv[3]); // num intervals in z direction (assumed box domain, 0,1)
// *********************************** CELL TOPOLOGY **********************************
// Get cell topology for base hexahedron
typedef shards::CellTopology CellTopology;
CellTopology hex_8(shards::getCellTopologyData<shards::Hexahedron<8> >() );
// Get dimensions
int numNodesPerElem = hex_8.getNodeCount();
int spaceDim = hex_8.getDimension();
// *********************************** GENERATE MESH ************************************
*outStream << "Generating mesh ... \n\n";
*outStream << " NX" << " NY" << " NZ\n";
*outStream << std::setw(5) << NX <<
std::setw(5) << NY <<
std::setw(5) << NZ << "\n\n";
// Print mesh information
int numElems = NX*NY*NZ;
int numNodes = (NX+1)*(NY+1)*(NZ+1);
*outStream << " Number of Elements: " << numElems << " \n";
*outStream << " Number of Nodes: " << numNodes << " \n\n";
// Cube
double leftX = 0.0, rightX = 1.0;
double leftY = 0.0, rightY = 1.0;
double leftZ = 0.0, rightZ = 1.0;
// Mesh spacing
double hx = (rightX-leftX)/((double)NX);
double hy = (rightY-leftY)/((double)NY);
double hz = (rightZ-leftZ)/((double)NZ);
// Get nodal coordinates
FieldContainer<double> nodeCoord(numNodes, spaceDim);
FieldContainer<int> nodeOnBoundary(numNodes);
int inode = 0;
for (int k=0; k<NZ+1; k++) {
for (int j=0; j<NY+1; j++) {
for (int i=0; i<NX+1; i++) {
nodeCoord(inode,0) = leftX + (double)i*hx;
nodeCoord(inode,1) = leftY + (double)j*hy;
nodeCoord(inode,2) = leftZ + (double)k*hz;
if (k==0 || j==0 || i==0 || k==NZ || j==NY || i==NX){
nodeOnBoundary(inode)=1;
}
else {
nodeOnBoundary(inode)=0;
}
inode++;
}
}
}
#define DUMP_DATA
#ifdef DUMP_DATA
// Print nodal coords
ofstream fcoordout("coords.dat");
for (int i=0; i<numNodes; i++) {
fcoordout << nodeCoord(i,0) <<" ";
fcoordout << nodeCoord(i,1) <<" ";
fcoordout << nodeCoord(i,2) <<"\n";
}
fcoordout.close();
#endif
// Element to Node map
FieldContainer<int> elemToNode(numElems, numNodesPerElem);
int ielem = 0;
for (int k=0; k<NZ; k++) {
for (int j=0; j<NY; j++) {
for (int i=0; i<NX; i++) {
elemToNode(ielem,0) = (NY + 1)*(NX + 1)*k + (NX + 1)*j + i;
elemToNode(ielem,1) = (NY + 1)*(NX + 1)*k + (NX + 1)*j + i + 1;
elemToNode(ielem,2) = (NY + 1)*(NX + 1)*k + (NX + 1)*(j + 1) + i + 1;
elemToNode(ielem,3) = (NY + 1)*(NX + 1)*k + (NX + 1)*(j + 1) + i;
elemToNode(ielem,4) = (NY + 1)*(NX + 1)*(k + 1) + (NX + 1)*j + i;
elemToNode(ielem,5) = (NY + 1)*(NX + 1)*(k + 1) + (NX + 1)*j + i + 1;
elemToNode(ielem,6) = (NY + 1)*(NX + 1)*(k + 1) + (NX + 1)*(j + 1) + i + 1;
elemToNode(ielem,7) = (NY + 1)*(NX + 1)*(k + 1) + (NX + 1)*(j + 1) + i;
ielem++;
}
}
}
#ifdef DUMP_DATA
// Output connectivity
ofstream fe2nout("elem2node.dat");
for (int k=0; k<NZ; k++) {
for (int j=0; j<NY; j++) {
for (int i=0; i<NX; i++) {
int ielem = i + j * NX + k * NX * NY;
for (int m=0; m<numNodesPerElem; m++){
fe2nout << elemToNode(ielem,m) <<" ";
}
fe2nout <<"\n";
}
}
}
fe2nout.close();
#endif
// ************************************ CUBATURE **************************************
*outStream << "Getting cubature ... \n\n";
// Get numerical integration points and weights
DefaultCubatureFactory<double> cubFactory;
int cubDegree = 2;
Teuchos::RCP<Cubature<double> > hexCub = cubFactory.create(hex_8, cubDegree);
int cubDim = hexCub->getDimension();
int numCubPoints = hexCub->getNumPoints();
FieldContainer<double> cubPoints(numCubPoints, cubDim);
FieldContainer<double> cubWeights(numCubPoints);
hexCub->getCubature(cubPoints, cubWeights);
// ************************************** BASIS ***************************************
*outStream << "Getting basis ... \n\n";
// Define basis
Basis_HGRAD_HEX_C1_FEM<double, FieldContainer<double> > hexHGradBasis;
int numFieldsG = hexHGradBasis.getCardinality();
FieldContainer<double> hexGVals(numFieldsG, numCubPoints);
FieldContainer<double> hexGrads(numFieldsG, numCubPoints, spaceDim);
// Evaluate basis values and gradients at cubature points
hexHGradBasis.getValues(hexGVals, cubPoints, OPERATOR_VALUE);
hexHGradBasis.getValues(hexGrads, cubPoints, OPERATOR_GRAD);
// ******** LOOP OVER ELEMENTS TO CREATE LOCAL STIFFNESS MATRIX *************
*outStream << "Building stiffness matrix and right hand side ... \n\n";
// Settings and data structures for mass and stiffness matrices
typedef CellTools<double> CellTools;
typedef FunctionSpaceTools fst;
int numCells = 1;
// Container for nodes
FieldContainer<double> hexNodes(numCells, numNodesPerElem, spaceDim);
// Containers for Jacobian
FieldContainer<double> hexJacobian(numCells, numCubPoints, spaceDim, spaceDim);
FieldContainer<double> hexJacobInv(numCells, numCubPoints, spaceDim, spaceDim);
FieldContainer<double> hexJacobDet(numCells, numCubPoints);
// Containers for element HGRAD stiffness matrix
FieldContainer<double> localStiffMatrix(numCells, numFieldsG, numFieldsG);
FieldContainer<double> weightedMeasure(numCells, numCubPoints);
FieldContainer<double> hexGradsTransformed(numCells, numFieldsG, numCubPoints, spaceDim);
FieldContainer<double> hexGradsTransformedWeighted(numCells, numFieldsG, numCubPoints, spaceDim);
// Containers for right hand side vectors
FieldContainer<double> rhsData(numCells, numCubPoints);
FieldContainer<double> localRHS(numCells, numFieldsG);
FieldContainer<double> hexGValsTransformed(numCells, numFieldsG, numCubPoints);
FieldContainer<double> hexGValsTransformedWeighted(numCells, numFieldsG, numCubPoints);
// Container for cubature points in physical space
FieldContainer<double> physCubPoints(numCells, numCubPoints, cubDim);
// Global arrays in Epetra format
Epetra_SerialComm Comm;
Epetra_Map globalMapG(numNodes, 0, Comm);
Epetra_FECrsMatrix StiffMatrix(Copy, globalMapG, numFieldsG);
Epetra_FEVector rhs(globalMapG);
// *** Element loop ***
for (int k=0; k<numElems; k++) {
// Physical cell coordinates
for (int i=0; i<numNodesPerElem; i++) {
hexNodes(0,i,0) = nodeCoord(elemToNode(k,i),0);
hexNodes(0,i,1) = nodeCoord(elemToNode(k,i),1);
hexNodes(0,i,2) = nodeCoord(elemToNode(k,i),2);
}
// Compute cell Jacobians, their inverses and their determinants
CellTools::setJacobian(hexJacobian, cubPoints, hexNodes, hex_8);
CellTools::setJacobianInv(hexJacobInv, hexJacobian );
CellTools::setJacobianDet(hexJacobDet, hexJacobian );
// ************************** Compute element HGrad stiffness matrices *******************************
// transform to physical coordinates
fst::HGRADtransformGRAD<double>(hexGradsTransformed, hexJacobInv, hexGrads);
// compute weighted measure
fst::computeCellMeasure<double>(weightedMeasure, hexJacobDet, cubWeights);
// multiply values with weighted measure
fst::multiplyMeasure<double>(hexGradsTransformedWeighted,
weightedMeasure, hexGradsTransformed);
// integrate to compute element stiffness matrix
fst::integrate<double>(localStiffMatrix,
hexGradsTransformed, hexGradsTransformedWeighted, COMP_BLAS);
// assemble into global matrix
for (int row = 0; row < numFieldsG; row++){
for (int col = 0; col < numFieldsG; col++){
int rowIndex = elemToNode(k,row);
int colIndex = elemToNode(k,col);
double val = localStiffMatrix(0,row,col);
StiffMatrix.InsertGlobalValues(1, &rowIndex, 1, &colIndex, &val);
}
}
// ******************************* Build right hand side ************************************
// transform integration points to physical points
CellTools::mapToPhysicalFrame(physCubPoints, cubPoints, hexNodes, hex_8);
// evaluate right hand side function at physical points
for (int nPt = 0; nPt < numCubPoints; nPt++){
double x = physCubPoints(0,nPt,0);
double y = physCubPoints(0,nPt,1);
double z = physCubPoints(0,nPt,2);
rhsData(0,nPt) = evalDivGradu(x, y, z);
}
// transform basis values to physical coordinates
fst::HGRADtransformVALUE<double>(hexGValsTransformed, hexGVals);
// multiply values with weighted measure
fst::multiplyMeasure<double>(hexGValsTransformedWeighted,
weightedMeasure, hexGValsTransformed);
// integrate rhs term
fst::integrate<double>(localRHS, rhsData, hexGValsTransformedWeighted,
COMP_BLAS);
// assemble into global vector
for (int row = 0; row < numFieldsG; row++){
int rowIndex = elemToNode(k,row);
double val = -localRHS(0,row);
rhs.SumIntoGlobalValues(1, &rowIndex, &val);
}
} // *** end element loop ***
// Assemble global matrices
StiffMatrix.GlobalAssemble(); StiffMatrix.FillComplete();
rhs.GlobalAssemble();
// Adjust stiffness matrix and rhs based on boundary conditions
for (int row = 0; row<numNodes; row++){
if (nodeOnBoundary(row)) {
int rowindex = row;
for (int col=0; col<numNodes; col++){
double val = 0.0;
int colindex = col;
StiffMatrix.ReplaceGlobalValues(1, &rowindex, 1, &colindex, &val);
}
double val = 1.0;
StiffMatrix.ReplaceGlobalValues(1, &rowindex, 1, &rowindex, &val);
val = 0.0;
rhs.ReplaceGlobalValues(1, &rowindex, &val);
}
}
#ifdef DUMP_DATA
// Dump matrices to disk
EpetraExt::RowMatrixToMatlabFile("stiff_matrix.dat",StiffMatrix);
EpetraExt::MultiVectorToMatrixMarketFile("rhs_vector.dat",rhs,0,0,false);
#endif
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return 0;
}
/** \brief Tests for Lagrange basis on triangles. Tests Kronecker property of basis and basic execution
of differentiation and dof-tab lookup
\param argc [in] - number of command-line arguments
\param argv [in] - command-line arguments
*/
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
// This little trick lets us print to std::cout only if a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test HGRAD_TRI_Cn_FEM |\n" \
<< "| |\n" \
<< "| 1) Tests triangular Lagrange basis |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]) or |\n" \
<< "| Denis Ridzal ([email protected]) or |\n" \
<< "| Robert Kirby ([email protected]) |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n";
int errorFlag = 0;
// Let's instantiate a basis
try {
const int deg = 10;
Basis_HGRAD_TRI_Cn_FEM<double,FieldContainer<double> > myBasis( deg , POINTTYPE_WARPBLEND );
// Get a lattice
const int np_lattice = PointTools::getLatticeSize( myBasis.getBaseCellTopology() , deg , 0 );
const int nbf = myBasis.getCardinality();
FieldContainer<double> lattice( np_lattice , 2 );
PointTools::getLattice<double,FieldContainer<double> >( lattice ,
myBasis.getBaseCellTopology() ,
deg ,
0 ,
POINTTYPE_WARPBLEND );
FieldContainer<double> vals( nbf , np_lattice );
myBasis.getValues( vals , lattice , OPERATOR_VALUE );
// test for Kronecker property
for (int i=0;i<nbf;i++) {
for (int j=0;j<np_lattice;j++) {
if ( i==j && std::abs( vals(i,j) - 1.0 ) > INTREPID_TOL ) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " Basis function " << i << " does not have unit value at its node\n";
}
if ( i!=j && std::abs( vals(i,j) ) > INTREPID_TOL ) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " Basis function " << i << " does not vanish at node " << j << "\n";
}
}
}
}
catch (std::exception err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
}
try {
const int deg = 3;
Basis_HGRAD_TRI_Cn_FEM<double,FieldContainer<double> > myBasis( deg , POINTTYPE_WARPBLEND );
const std::vector<std::vector<std::vector<int> > >& dofdata = myBasis.getDofOrdinalData();
for (unsigned d=0;d<dofdata.size();d++) {
std::cout << "Dimension " << d << "\n";
for (unsigned f=0;f<dofdata[d].size();f++) {
std::cout << "\tFacet number " << f << "\n";
std::cout << "\t\tDOFS:\n";
for (unsigned n=0;n<dofdata[d][f].size();n++) {
std::cout << "\t\t\t" << dofdata[d][f][n] << "\n";
}
}
}
}
catch (std::exception err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
}
try {
const int deg = 1;
Basis_HGRAD_TRI_Cn_FEM<double,FieldContainer<double> > myBasis( deg , POINTTYPE_WARPBLEND );
// Get a lattice
const int np_lattice = PointTools::getLatticeSize( myBasis.getBaseCellTopology() , deg , 0 );
const int nbf = myBasis.getCardinality();
FieldContainer<double> lattice( np_lattice , 2 );
PointTools::getLattice<double,FieldContainer<double> >( lattice ,
myBasis.getBaseCellTopology() ,
deg ,
0 ,
POINTTYPE_WARPBLEND );
FieldContainer<double> vals( nbf , np_lattice , 2 );
myBasis.getValues( vals , lattice , OPERATOR_CURL );
std::cout << vals << std::endl;
}
catch (std::exception err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
}
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
int FunctionSpaceTools_Test03(const bool verbose) {
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (verbose)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
typedef typename
Kokkos::Impl::is_space<DeviceSpaceType>::host_mirror_space::execution_space HostSpaceType ;
*outStream << "DeviceSpace:: "; DeviceSpaceType::print_configuration(*outStream, false);
*outStream << "HostSpace:: "; HostSpaceType::print_configuration(*outStream, false);
*outStream
<< "===============================================================================\n"
<< "| |\n"
<< "| Unit Test (FunctionSpaceTools) |\n"
<< "| |\n"
<< "| 1) Basic operator transformations and integration in HDIV: |\n"
<< "| |\n"
<< "| Questions? Contact Pavel Bochev ([email protected]) or |\n"
<< "| Denis Ridzal ([email protected]) or |\n"
<< "| Kyungjoo Kim ([email protected]). |\n"
<< "| |\n"
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n"
<< "| Trilinos website: http://trilinos.sandia.gov |\n"
<< "| |\n"
<< "===============================================================================\n";
typedef CellTools<DeviceSpaceType> ct;
typedef FunctionSpaceTools<DeviceSpaceType> fst;
typedef Kokkos::DynRankView<ValueType,DeviceSpaceType> DynRankView;
int errorFlag = 0;
*outStream
<< "\n"
<< "===============================================================================\n"
<< "| TEST 1: correctness of math operations |\n"
<< "===============================================================================\n";
outStream->precision(20);
try {
DefaultCubatureFactory cub_factory;
shards::CellTopology cell_topo = shards::getCellTopologyData< shards::Hexahedron<8> >();
const auto cub_degree = 20;
auto cub = cub_factory.create<DeviceSpaceType,ValueType,ValueType>(cell_topo, cub_degree);
const auto space_dim = cub->getDimension();
const auto num_cub_points = cub->getNumPoints();
Basis_HDIV_HEX_I1_FEM<DeviceSpaceType> basis;
const auto num_fields = basis.getCardinality();
/* Cell geometries and orientations. */
const auto num_cells = 4;
const auto num_nodes = 8;
const ValueType hexnodes[] = {
// hex 0 -- affine
-1.0, -1.0, -1.0,
1.0, -1.0, -1.0,
1.0, 1.0, -1.0,
-1.0, 1.0, -1.0,
-1.0, -1.0, 1.0,
1.0, -1.0, 1.0,
1.0, 1.0, 1.0,
-1.0, 1.0, 1.0,
// hex 1 -- affine
-3.0, -3.0, 1.0,
6.0, 3.0, 1.0,
7.0, 8.0, 0.0,
-2.0, 2.0, 0.0,
-3.0, -3.0, 4.0,
6.0, 3.0, 4.0,
7.0, 8.0, 3.0,
-2.0, 2.0, 3.0,
// hex 2 -- affine
-3.0, -3.0, 0.0,
9.0, 3.0, 0.0,
15.0, 6.1, 0.0,
3.0, 0.1, 0.0,
9.0, 3.0, 0.1,
21.0, 9.0, 0.1,
27.0, 12.1, 0.1,
15.0, 6.1, 0.1,
// hex 3 -- nonaffine
-2.0, -2.0, 0.0,
2.0, -1.0, 0.0,
1.0, 6.0, 0.0,
-1.0, 1.0, 0.0,
0.0, 0.0, 1.0,
1.0, 0.0, 1.0,
1.0, 1.0, 1.0,
0.0, 1.0, 1.0
};
const ValueType facesigns[] = {
1, 1, 1, 1, 1, 1,
1, -1, 1, -1, 1, -1,
-1, -1, 1, 1, -1, 1,
-1, -1, 1, 1, -1, -1
};
/* Computational arrays. */
DynRankView ConstructWithLabel( cub_points, num_cub_points, space_dim);
DynRankView ConstructWithLabel( cub_weights, num_cub_points);
DynRankView ConstructWithLabel( cell_nodes, num_cells, num_nodes, space_dim);
DynRankView ConstructWithLabel( field_signs, num_cells, num_fields);
DynRankView ConstructWithLabel( jacobian, num_cells, num_cub_points, space_dim, space_dim);
DynRankView ConstructWithLabel( jacobian_det, num_cells, num_cub_points);
DynRankView ConstructWithLabel( weighted_measure, num_cells, num_cub_points);
DynRankView ConstructWithLabel( div_of_basis_at_cub_points, num_fields, num_cub_points);
DynRankView ConstructWithLabel( transformed_div_of_basis_at_cub_points, num_cells, num_fields, num_cub_points);
DynRankView ConstructWithLabel( weighted_transformed_div_of_basis_at_cub_points, num_cells, num_fields, num_cub_points);
DynRankView ConstructWithLabel( stiffness_matrices, num_cells, num_fields, num_fields);
DynRankView ConstructWithLabel( value_of_basis_at_cub_points, num_fields, num_cub_points, space_dim);
DynRankView ConstructWithLabel( transformed_value_of_basis_at_cub_points, num_cells, num_fields, num_cub_points, space_dim);
DynRankView ConstructWithLabel( weighted_transformed_value_of_basis_at_cub_points, num_cells, num_fields, num_cub_points, space_dim);
DynRankView ConstructWithLabel( mass_matrices, num_cells, num_fields, num_fields);
/******************* START COMPUTATION ***********************/
// get cubature points and weights
cub->getCubature(cub_points, cub_weights);
const Kokkos::DynRankView<const ValueType,Kokkos::LayoutRight,Kokkos::HostSpace> cell_nodes_host (&hexnodes[0], num_cells, num_nodes, space_dim);
const Kokkos::DynRankView<const ValueType,Kokkos::LayoutRight,Kokkos::HostSpace> field_signs_host(&facesigns[0], num_cells, num_fields);
Kokkos::deep_copy( cell_nodes, cell_nodes_host );
Kokkos::deep_copy( field_signs, field_signs_host );
// compute geometric cell information
ct::setJacobian(jacobian, cub_points, cell_nodes, cell_topo);
ct::setJacobianDet(jacobian_det, jacobian);
// compute weighted measure
fst::computeCellMeasure(weighted_measure, jacobian_det, cub_weights);
// **Computing stiffness matrices:
basis.getValues(div_of_basis_at_cub_points, cub_points, OPERATOR_DIV);
// transform divergences of basis functions
fst::HDIVtransformDIV(transformed_div_of_basis_at_cub_points,
jacobian_det,
div_of_basis_at_cub_points);
// multiply with weighted measure
fst::multiplyMeasure(weighted_transformed_div_of_basis_at_cub_points,
weighted_measure,
transformed_div_of_basis_at_cub_points);
// we can apply the field signs to the basis function arrays, or after the fact, see below
fst::applyFieldSigns(transformed_div_of_basis_at_cub_points, field_signs);
fst::applyFieldSigns(weighted_transformed_div_of_basis_at_cub_points, field_signs);
// compute stiffness matrices
fst::integrate(stiffness_matrices,
transformed_div_of_basis_at_cub_points,
weighted_transformed_div_of_basis_at_cub_points);
// **Computing mass matrices:
basis.getValues(value_of_basis_at_cub_points, cub_points, OPERATOR_VALUE);
// transform values of basis functions
fst::HDIVtransformVALUE(transformed_value_of_basis_at_cub_points,
jacobian,
jacobian_det,
value_of_basis_at_cub_points);
// multiply with weighted measure
fst::multiplyMeasure(weighted_transformed_value_of_basis_at_cub_points,
weighted_measure,
transformed_value_of_basis_at_cub_points);
// compute mass matrices
fst::integrate(mass_matrices,
transformed_value_of_basis_at_cub_points,
weighted_transformed_value_of_basis_at_cub_points);
// apply field signs
fst::applyLeftFieldSigns(mass_matrices, field_signs);
fst::applyRightFieldSigns(mass_matrices, field_signs);
/******************* STOP COMPUTATION ***********************/
/******************* START COMPARISON ***********************/
std::string basedir = "../testdata";
for (auto cid=0;cid<num_cells-1;++cid) {
std::stringstream namestream;
std::string filename;
namestream << basedir << "/mass_HDIV_HEX_I1_FEM" << "_" << "0" << cid+1 << ".dat";
namestream >> filename;
*outStream << "\nCell ID : " << cid << " mass matrix comparing with " << filename << "\n\n";
std::ifstream massfile(&filename[0]);
if (massfile.is_open()) {
const auto mass_matrix_cell = Kokkos::subdynrankview(mass_matrices, cid, Kokkos::ALL(), Kokkos::ALL());
errorFlag += compareToAnalytic(massfile,
mass_matrix_cell,
1e-10,
verbose);
massfile.close();
} else {
errorFlag = -1;
INTREPID2_TEST_FOR_EXCEPTION( true, std::runtime_error,
"Failed to open a file" );
}
namestream.clear();
namestream << basedir << "/stiff_HDIV_HEX_I1_FEM" << "_" << "0" << cid+1 << ".dat";
namestream >> filename;
*outStream << "\nCell ID : " << cid << " stiffness matrix comparing with " << filename << "\n\n";
std::ifstream stifffile(&filename[0]);
if (stifffile.is_open()) {
const auto stiffness_matrix_cell = Kokkos::subdynrankview(stiffness_matrices, cid, Kokkos::ALL(), Kokkos::ALL());
errorFlag += compareToAnalytic(stifffile,
stiffness_matrix_cell,
1e-10,
verbose);
stifffile.close();
} else {
errorFlag = -1;
INTREPID2_TEST_FOR_EXCEPTION( true, std::runtime_error,
"Failed to open a file" );
}
}
for (auto cid=3;cid<num_cells;++cid) {
std::stringstream namestream;
std::string filename;
namestream << basedir << "/mass_fp_HDIV_HEX_I1_FEM" << "_" << "0" << cid+1 << ".dat";
namestream >> filename;
*outStream << "\nCell ID : " << cid << " mass matrix comparing with " << filename << "\n\n";
std::ifstream massfile(&filename[0]);
if (massfile.is_open()) {
const auto mass_matrix_cell = Kokkos::subdynrankview(mass_matrices, cid, Kokkos::ALL(), Kokkos::ALL());
errorFlag += compareToAnalytic(massfile,
mass_matrix_cell,
1e-4,
verbose,
INTREPID2_UTILS_SCALAR);
massfile.close();
} else {
errorFlag = -1;
INTREPID2_TEST_FOR_EXCEPTION( true, std::runtime_error,
"Failed to open a file" );
}
namestream.clear();
namestream << basedir << "/stiff_fp_HDIV_HEX_I1_FEM" << "_" << "0" << cid+1 << ".dat";
namestream >> filename;
*outStream << "\nCell ID : " << cid << " stiffness matrix comparing with " << filename << "\n\n";
std::ifstream stifffile(&filename[0]);
if (stifffile.is_open()) {
const auto stiffness_matrix_cell = Kokkos::subdynrankview(stiffness_matrices, cid, Kokkos::ALL(), Kokkos::ALL());
errorFlag += compareToAnalytic(stifffile,
stiffness_matrix_cell,
1e-4,
verbose,
INTREPID2_UTILS_SCALAR);
stifffile.close();
} else {
errorFlag = -1;
INTREPID2_TEST_FOR_EXCEPTION( true, std::runtime_error,
"Failed to open a file" );
}
}
/******************* STOP COMPARISON ***********************/
*outStream << "\n";
} catch (std::logic_error err) {
*outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
*outStream << err.what() << '\n';
*outStream << "-------------------------------------------------------------------------------" << "\n\n";
errorFlag = -1000;
}
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
/* -------------------------------------------------------------------
This is a routine to test the integration, differentiation and
interpolation routines in the polylib.c.
First, it performs the integral
/1 alpha beta alpha,beta
| (1-x) (1+x) P (x) dx = 0
/-1 n
for all -0.5 <= alpha <= 5 (increments of 0.5)
-0.5 <= beta <= 5 (increments of 0.5)
using np points where
NPLOWER <= np <= NPUPPER
2 <= n <= 2*np - delta
delta = 1 (gauss), 2(radau), 3(lobatto).
The integral is evaluated and if it is larger that EPS then the
value of alpha,beta,np,n and the integral is printed to the screen.
After every alpha value the statement
"finished checking all beta values for alpha = #"
is printed
The routine then evaluates the derivate of
d n n-1
-- x = n x
dx
for all -0.5 <= alpha <= 5 (increments of 0.5)
-0.5 <= beta <= 5 (increments of 0.5)
using np points where
NPLOWER <= np <= NPUPPER
2 <= n <= np - 1
The error is check in a pointwise sense and if it is larger than
EPS then the value of alpha,beta,np,n and the error is printed to
the screen. After every alpha value the statement
"finished checking all beta values for alpha = #"
is printed
Finally the routine evaluates the interpolation of
n n
z to x
where z are the quadrature zeros and x are the equispaced points
2*i
x = ----- - 1.0 (0 <= i <= np-1)
i (np-1)
for all -0.5 <= alpha <= 5 (increments of 0.5)
-0.5 <= beta <= 5 (increments of 0.5)
using np points where
NPLOWER <= np <= NPUPPER
2 <= n <= np - 1
The error is check in a pointwise sense and if it is larger than
EPS then the value of alpha,beta,np,n and the error is printed to
the screen. After every alpha value the statement
"finished checking all beta values for alpha = #"
is printed
The above checks are performed for all the Gauss, Gauss-Radau and
Gauss-Lobatto points. If you want to disable any routine then set
GAUSS_INT, GAUSS_RADAU_INT, GAUSS_LOBATTO_INT = 0
for the integration rouintes
GAUSS_DIFF,GAUSS_RADAU_DIFF, GAUSS_LOBATTO_DIFF = 0
for the differentiation routines
GAUSS_INTERP,GAUSS_RADAU_INTERP, GAUSS_LOBATTO_INTERP = 0
for the interpolation routines.
------------------------------------------------------------------*/
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (IntrepidPolylib) |\n" \
<< "| |\n" \
<< "| 1) the original Polylib tests |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]) or |\n" \
<< "| Denis Ridzal ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n";
int errorFlag = 0;
int beginThrowNumber = TestForException_getThrowNumber();
int endThrowNumber = beginThrowNumber + 1;
typedef IntrepidPolylib ipl;
IntrepidPolylib iplib;
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 1: exceptions |\n"\
<< "===============================================================================\n";
try{
INTREPID_TEST_COMMAND( iplib.gammaF((double)0.33) );
}
catch (std::logic_error err) {
*outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
*outStream << err.what() << '\n';
*outStream << "-------------------------------------------------------------------------------" << "\n\n";
errorFlag = -1000;
};
if (TestForException_getThrowNumber() != endThrowNumber)
errorFlag = -1000;
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 2: correctness of math operations |\n"\
<< "===============================================================================\n";
outStream->precision(20);
try {
{ // start scope
int np,n,i;
double *z,*w,*p,sum=0,alpha,beta,*d;
z = dvector<double>(0,NPUPPER-1);
w = dvector<double>(0,NPUPPER-1);
p = dvector<double>(0,NPUPPER-1);
d = dvector<double>(0,NPUPPER*NPUPPER-1);
#if GAUSS_INT
/* Gauss Integration */
*outStream << "Begin checking Gauss integration\n";
alpha = -0.5;
while(alpha <= 5.0){
beta = -0.5;
while(beta <= 5.0){
for(np = NPLOWER; np <= NPUPPER; ++np){
ipl::zwgj(z,w,np,alpha,beta);
for(n = 2; n < 2*np-1; ++n){
ipl::jacobfd(np,z,p,(double*)0,n,alpha,beta);
sum = ddot(np,w,1,p,1);
if(std::abs(sum)>TEST_EPS) {
errorFlag = -1000;
*outStream << "ERROR: alpha = " << alpha << ", beta = " << beta <<
", np = " << np << ", n = " << n << " integral was " << sum << "\n";
}
}
}
beta += 0.5;
}
*outStream << "finished checking all beta values for alpha = " << alpha << "\n";
alpha += 0.5;
}
*outStream << "Finished checking Gauss Integration\n";
#endif
#if GAUSS_RADAUM_INT
/* Gauss Radau (z = -1) Integration */
*outStream << "Begin checking Gauss-Radau (z = -1) integration\n";
alpha = -0.5;
while(alpha <= 5.0){
beta = -0.5;
while(beta <= 5.0){
for(np = NPLOWER; np <= NPUPPER; ++np){
ipl::zwgrjm(z,w,np,alpha,beta);
for(n = 2; n < 2*np-2; ++n){
ipl::jacobfd(np,z,p,(double*)0,n,alpha,beta);
sum = ddot(np,w,1,p,1);
if(std::abs(sum)>TEST_EPS) {
errorFlag = -1000;
*outStream << "ERROR: alpha = " << alpha << ", beta = " << beta <<
", np = " << np << ", n = " << n << " integral was " << sum << "\n";
}
}
}
beta += 0.5;
}
*outStream << "finished checking all beta values for alpha = " << alpha << "\n";
alpha += 0.5;
}
*outStream << "Finished checking Gauss-Radau (z = -1) Integration\n";
#endif
#if GAUSS_RADAUP_INT
/* Gauss Radau (z = +1) Integration */
*outStream << "Begin checking Gauss-Radau (z = +1) integration\n";
alpha = -0.5;
while(alpha <= 5.0){
beta = -0.5;
while(beta <= 5.0){
for(np = NPLOWER; np <= NPUPPER; ++np){
ipl::zwgrjp(z,w,np,alpha,beta);
for(n = 2; n < 2*np-2; ++n){
ipl::jacobfd(np,z,p,(double*)0,n,alpha,beta);
sum = ddot(np,w,1,p,1);
if(std::abs(sum)>TEST_EPS) {
errorFlag = -1000;
*outStream << "ERROR: alpha = " << alpha << ", beta = " << beta <<
", np = " << np << ", n = " << n << " integral was " << sum << "\n";
}
}
}
beta += 0.5;
}
*outStream << "finished checking all beta values for alpha = " << alpha << "\n";
alpha += 0.5;
}
*outStream << "Finished checking Gauss-Radau (z = +1) Integration\n";
#endif
#if GAUSS_LOBATTO_INT
/* Gauss Lobatto Integration */
*outStream << "Begin checking Gauss-Lobatto integration\n";
alpha = -0.5;
while(alpha <= 5.0){
beta = -0.5;
while(beta <= 5.0){
for(np = NPLOWER; np <= NPUPPER; ++np){
ipl::zwglj(z,w,np,alpha,beta);
for(n = 2; n < 2*np-3; ++n){
ipl::jacobfd(np,z,p,(double*)0,n,alpha,beta);
sum = ddot(np,w,1,p,1);
if(std::abs(sum)>TEST_EPS) {
errorFlag = -1000;
*outStream << "ERROR: alpha = " << alpha << ", beta = " << beta <<
", np = " << np << ", n = " << n << " integral was " << sum << "\n";
}
}
}
beta += 0.5;
}
*outStream << "finished checking all beta values for alpha = " << alpha << "\n";
alpha += 0.5;
}
*outStream << "Finished checking Gauss-Lobatto Integration\n";
#endif
#if GAUSS_DIFF
*outStream << "Begin checking differentiation through Gauss points\n";
alpha = -0.5;
while(alpha <= 5.0){
beta = -0.5;
while(beta <= 5.0){
for(np = NPLOWER; np <= NPUPPER; ++np){
ipl::zwgj(z,w,np,alpha,beta);
for(n = 2; n < np-1; ++n){
ipl::Dgj(d,z,np,alpha,beta);
for(i = 0; i < np; ++i) p[i] = std::pow(z[i],n);
sum = 0;
for(i = 0; i < np; ++i)
sum += std::abs(ddot(np,d+i*np,1,p,1) - n*std::pow(z[i],n-1));
sum /= np;
if(std::abs(sum)>TEST_EPS) {
errorFlag = -1000;
*outStream << "ERROR: alpha = " << alpha << ", beta = " << beta <<
", np = " << np << ", n = " << n << " difference " << sum << "\n";
}
}
}
beta += 0.5;
}
*outStream << "finished checking all beta values for alpha = " << alpha << "\n";
alpha += 0.5;
}
*outStream << "Finished checking Gauss Jacobi differentiation\n";
#endif
#if GAUSS_RADAUM_DIFF
*outStream << "Begin checking differentiation through Gauss-Radau (z=-1) points\n";
alpha = -0.5;
while(alpha <= 5.0){
beta = -0.5;
while(beta <= 5.0){
for(np = NPLOWER; np <= NPUPPER; ++np){
ipl::zwgrjm(z,w,np,alpha,beta);
for(n = 2; n < np-1; ++n){
ipl::Dgrjm(d,z,np,alpha,beta);
for(i = 0; i < np; ++i) p[i] = std::pow(z[i],n);
sum = 0;
for(i = 0; i < np; ++i)
sum += std::abs(ddot(np,d+i*np,1,p,1) - n*std::pow(z[i],n-1));
sum /= np;
if(std::abs(sum)>TEST_EPS) {
errorFlag = -1000;
*outStream << "ERROR: alpha = " << alpha << ", beta = " << beta <<
", np = " << np << ", n = " << n << " difference " << sum << "\n";
}
}
}
beta += 0.5;
}
*outStream << "finished checking all beta values for alpha = " << alpha << "\n";
alpha += 0.5;
}
*outStream << "Finished checking Gauss-Radau (z=-1) differentiation\n";
#endif
#if GAUSS_RADAUP_DIFF
*outStream << "Begin checking differentiation through Gauss-Radau (z=+1) points\n";
alpha = -0.5;
while(alpha <= 5.0){
beta = -0.5;
while(beta <= 5.0){
for(np = NPLOWER; np <= NPUPPER; ++np){
ipl::zwgrjp(z,w,np,alpha,beta);
for(n = 2; n < np-1; ++n){
ipl::Dgrjp(d,z,np,alpha,beta);
for(i = 0; i < np; ++i) p[i] = std::pow(z[i],n);
sum = 0;
for(i = 0; i < np; ++i)
sum += std::abs(ddot(np,d+i*np,1,p,1) - n*std::pow(z[i],n-1));
sum /= np;
if(std::abs(sum)>TEST_EPS) {
errorFlag = -1000;
*outStream << "ERROR: alpha = " << alpha << ", beta = " << beta <<
", np = " << np << ", n = " << n << " difference " << sum << "\n";
}
}
}
beta += 0.5;
}
*outStream << "finished checking all beta values for alpha = " << alpha << "\n";
alpha += 0.5;
}
*outStream << "Finished checking Gauss-Radau (z=+1) differentiation\n";
#endif
#if GAUSS_RADAUP_DIFF
*outStream << "Begin checking differentiation through Gauss-Lobatto (z=+1) points\n";
alpha = -0.5;
while(alpha <= 5.0){
beta = -0.5;
while(beta <= 5.0){
for(np = NPLOWER; np <= NPUPPER; ++np){
ipl::zwglj(z,w,np,alpha,beta);
for(n = 2; n < np-1; ++n){
ipl::Dglj(d,z,np,alpha,beta);
for(i = 0; i < np; ++i) p[i] = std::pow(z[i],n);
sum = 0;
for(i = 0; i < np; ++i)
sum += std::abs(ddot(np,d+i*np,1,p,1) - n*std::pow(z[i],n-1));
sum /= np;
if(std::abs(sum)>TEST_EPS) {
errorFlag = -1000;
*outStream << "ERROR: alpha = " << alpha << ", beta = " << beta <<
", np = " << np << ", n = " << n << " difference " << sum << "\n";
}
}
}
beta += 0.5;
}
*outStream << "finished checking all beta values for alpha = " << alpha << "\n";
alpha += 0.5;
}
*outStream << "Finished checking Gauss-Lobatto differentiation\n";
#endif
#if GAUSS_INTERP
*outStream << "Begin checking interpolation through Gauss points\n";
alpha = -0.5;
while(alpha <= 5.0){
beta = -0.5;
while(beta <= 5.0){
for(np = NPLOWER; np <= NPUPPER; ++np){
ipl::zwgj(z,w,np,alpha,beta);
for(n = 2; n < np-1; ++n){
for(i = 0; i < np; ++i) {
w[i] = 2.0*i/(double)(np-1)-1.0;
p[i] = std::pow(z[i],n);
}
ipl::Imgj(d,z,w,np,np,alpha,beta);
sum = 0;
for(i = 0; i < np; ++i)
sum += std::abs(ddot(np,d+i*np,1,p,1) - std::pow(w[i],n));
sum /= np;
if(std::abs(sum)>TEST_EPS) {
errorFlag = -1000;
*outStream << "ERROR: alpha = " << alpha << ", beta = " << beta <<
", np = " << np << ", n = " << n << " difference " << sum << "\n";
}
}
}
beta += 0.5;
}
*outStream << "finished checking all beta values for alpha = " << alpha << "\n";
alpha += 0.5;
}
*outStream << "Finished checking Gauss Jacobi interpolation\n";
#endif
#if GAUSS_RADAUM_INTERP
*outStream << "Begin checking interpolation through Gauss-Radau (z=-1) points\n";
alpha = -0.5;
while(alpha <= 5.0){
beta = -0.5;
while(beta <= 5.0){
for(np = NPLOWER; np <= NPUPPER; ++np){
ipl::zwgrjm(z,w,np,alpha,beta);
for(n = 2; n < np-1; ++n){
for(i = 0; i < np; ++i) {
w[i] = 2.0*i/(double)(np-1)-1.0;
p[i] = std::pow(z[i],n);
}
ipl::Imgrjm(d,z,w,np,np,alpha,beta);
sum = 0;
for(i = 0; i < np; ++i)
sum += std::abs(ddot(np,d+i*np,1,p,1) - std::pow(w[i],n));
sum /= np;
if(std::abs(sum)>TEST_EPS) {
errorFlag = -1000;
*outStream << "ERROR: alpha = " << alpha << ", beta = " << beta <<
", np = " << np << ", n = " << n << " difference " << sum << "\n";
}
}
}
beta += 0.5;
}
*outStream << "finished checking all beta values for alpha = " << alpha << "\n";
alpha += 0.5;
}
*outStream << "Finished checking Gauss-Radau (z=-1) interpolation\n";
#endif
#if GAUSS_RADAUP_INTERP
*outStream << "Begin checking interpolation through Gauss-Radau (z=+1) points\n";
alpha = -0.5;
while(alpha <= 5.0){
beta = -0.5;
while(beta <= 5.0){
for(np = NPLOWER; np <= NPUPPER; ++np){
ipl::zwgrjp(z,w,np,alpha,beta);
for(n = 2; n < np-1; ++n){
for(i = 0; i < np; ++i) {
w[i] = 2.0*i/(double)(np-1)-1.0;
p[i] = std::pow(z[i],n);
}
ipl::Imgrjp(d,z,w,np,np,alpha,beta);
sum = 0;
for(i = 0; i < np; ++i)
sum += std::abs(ddot(np,d+i*np,1,p,1) - std::pow(w[i],n));
sum /= np;
if(std::abs(sum)>TEST_EPS) {
errorFlag = -1000;
*outStream << "ERROR: alpha = " << alpha << ", beta = " << beta <<
", np = " << np << ", n = " << n << " difference " << sum << "\n";
}
}
}
beta += 0.5;
}
*outStream << "finished checking all beta values for alpha = " << alpha << "\n";
alpha += 0.5;
}
*outStream << "Finished checking Gauss-Radau (z=+1) interpolation\n";
#endif
#if GAUSS_LOBATTO_INTERP
*outStream << "Begin checking interpolation through Gauss-Lobatto points\n";
alpha = -0.5;
while(alpha <= 5.0){
beta = -0.5;
while(beta <= 5.0){
for(np = NPLOWER; np <= NPUPPER; ++np){
ipl::zwglj(z,w,np,alpha,beta);
for(n = 2; n < np-1; ++n){
for(i = 0; i < np; ++i) {
w[i] = 2.0*i/(double)(np-1)-1.0;
p[i] = std::pow(z[i],n);
}
ipl::Imglj(d,z,w,np,np,alpha,beta);
sum = 0;
for(i = 0; i < np; ++i)
sum += std::abs(ddot(np,d+i*np,1,p,1) - std::pow(w[i],n));
sum /= np;
if(std::abs(sum)>TEST_EPS) {
errorFlag = -1000;
*outStream << "ERROR: alpha = " << alpha << ", beta = " << beta <<
", np = " << np << ", n = " << n << " difference " << sum << "\n";
}
}
}
beta += 0.5;
}
*outStream << "finished checking all beta values for alpha = " << alpha << "\n";
alpha += 0.5;
}
*outStream << "Finished checking Gauss-Lobatto interpolation\n";
#endif
free(z); free(w); free(p); free(d);
} // end scope
/******************************************/
*outStream << "\n";
}
catch (std::logic_error err) {
*outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
*outStream << err.what() << '\n';
*outStream << "-------------------------------------------------------------------------------" << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
Kokkos::initialize();
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (Basis_HGRAD_TET_C2_FEM) |\n" \
<< "| |\n" \
<< "| 1) Conversion of Dof tags into Dof ordinals and back |\n" \
<< "| 2) Basis values for VALUE, GRAD, and Dk operators |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n"\
<< "| TEST 1: Basis creation, exception testing |\n"\
<< "===============================================================================\n";
// Define basis and error flag
Basis_HGRAD_TET_C2_FEM<double, FieldContainer<double> > tetBasis;
int errorFlag = 0;
// Initialize throw counter for exception testing
int nException = 0;
int throwCounter = 0;
// Define array containing the 10 nodes of Tetrahedron<10>: 4 vertices + 6 edge midpoints
FieldContainer<double> tetNodes(10, 3);
tetNodes(0,0) = 0.0; tetNodes(0,1) = 0.0; tetNodes(0,2) = 0.0;
tetNodes(1,0) = 1.0; tetNodes(1,1) = 0.0; tetNodes(1,2) = 0.0;
tetNodes(2,0) = 0.0; tetNodes(2,1) = 1.0; tetNodes(2,2) = 0.0;
tetNodes(3,0) = 0.0; tetNodes(3,1) = 0.0; tetNodes(3,2) = 1.0;
tetNodes(4,0) = 0.5; tetNodes(4,1) = 0.0; tetNodes(4,2) = 0.0;
tetNodes(5,0) = 0.5; tetNodes(5,1) = 0.5; tetNodes(5,2) = 0.0;
tetNodes(6,0) = 0.0; tetNodes(6,1) = 0.5; tetNodes(6,2) = 0.0;
tetNodes(7,0) = 0.0; tetNodes(7,1) = 0.0; tetNodes(7,2) = 0.5;
tetNodes(8,0) = 0.5; tetNodes(8,1) = 0.0; tetNodes(8,2) = 0.5;
tetNodes(9,0) = 0.0; tetNodes(9,1) = 0.5; tetNodes(9,2) = 0.5;
// Generic array for the output values; needs to be properly resized depending on the operator type
FieldContainer<double> vals;
try{
// exception #1: CURL cannot be applied to scalar functions
// resize vals to rank-3 container with dimensions (num. points, num. basis functions, arbitrary)
vals.resize(tetBasis.getCardinality(), tetNodes.dimension(0), 4 );
INTREPID_TEST_COMMAND( tetBasis.getValues(vals, tetNodes, OPERATOR_CURL), throwCounter, nException );
// exception #2: DIV cannot be applied to scalar functions
// resize vals to rank-2 container with dimensions (num. points, num. basis functions)
vals.resize(tetBasis.getCardinality(), tetNodes.dimension(0) );
INTREPID_TEST_COMMAND( tetBasis.getValues(vals, tetNodes, OPERATOR_DIV), throwCounter, nException );
// Exceptions 3-7: all bf tags/bf Ids below are wrong and should cause getDofOrdinal() and
// getDofTag() to access invalid array elements thereby causing bounds check exception
// exception #3
INTREPID_TEST_COMMAND( tetBasis.getDofOrdinal(3,0,0), throwCounter, nException );
// exception #4
INTREPID_TEST_COMMAND( tetBasis.getDofOrdinal(1,1,1), throwCounter, nException );
// exception #5
INTREPID_TEST_COMMAND( tetBasis.getDofOrdinal(0,4,0), throwCounter, nException );
// exception #6
INTREPID_TEST_COMMAND( tetBasis.getDofTag(10), throwCounter, nException );
// exception #7
INTREPID_TEST_COMMAND( tetBasis.getDofTag(-1), throwCounter, nException );
#ifdef HAVE_INTREPID2_DEBUG
// Exceptions 8-18 test exception handling with incorrectly dimensioned input/output arrays
// exception #8: input points array must be of rank-2
FieldContainer<double> badPoints1(4, 5, 3);
INTREPID_TEST_COMMAND( tetBasis.getValues(vals, badPoints1, OPERATOR_VALUE), throwCounter, nException );
// exception #9 dimension 1 in the input point array must equal space dimension of the cell
FieldContainer<double> badPoints2(4, tetBasis.getBaseCellTopology().getDimension() - 1);
INTREPID_TEST_COMMAND( tetBasis.getValues(vals, badPoints2, OPERATOR_VALUE), throwCounter, nException );
// exception #10 output values must be of rank-2 for OPERATOR_VALUE
FieldContainer<double> badVals1(4, 3, 1);
INTREPID_TEST_COMMAND( tetBasis.getValues(badVals1, tetNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #11 output values must be of rank-3 for OPERATOR_GRAD
FieldContainer<double> badVals2(4, 3);
INTREPID_TEST_COMMAND( tetBasis.getValues(badVals2, tetNodes, OPERATOR_GRAD), throwCounter, nException );
// exception #12 output values must be of rank-3 for OPERATOR_D1
INTREPID_TEST_COMMAND( tetBasis.getValues(badVals2, tetNodes, OPERATOR_D1), throwCounter, nException );
// exception #13 output values must be of rank-3 for OPERATOR_D2
INTREPID_TEST_COMMAND( tetBasis.getValues(badVals2, tetNodes, OPERATOR_D2), throwCounter, nException );
// exception #14 incorrect 0th dimension of output array (must equal number of basis functions)
FieldContainer<double> badVals3(tetBasis.getCardinality() + 1, tetNodes.dimension(0));
INTREPID_TEST_COMMAND( tetBasis.getValues(badVals3, tetNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #15 incorrect 1st dimension of output array (must equal number of points)
FieldContainer<double> badVals4(tetBasis.getCardinality(), tetNodes.dimension(0) + 1);
INTREPID_TEST_COMMAND( tetBasis.getValues(badVals4, tetNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #16: incorrect 2nd dimension of output array (must equal the space dimension)
FieldContainer<double> badVals5(tetBasis.getCardinality(), tetNodes.dimension(0), tetBasis.getBaseCellTopology().getDimension() + 1);
INTREPID_TEST_COMMAND( tetBasis.getValues(badVals5, tetNodes, OPERATOR_GRAD), throwCounter, nException );
// exception #17: incorrect 2nd dimension of output array (must equal D2 cardinality in 2D)
FieldContainer<double> badVals6(tetBasis.getCardinality(), tetNodes.dimension(0), 40);
INTREPID_TEST_COMMAND( tetBasis.getValues(badVals6, tetNodes, OPERATOR_D1), throwCounter, nException );
// exception #18: incorrect 2nd dimension of output array (must equal D3 cardinality in 2D)
INTREPID_TEST_COMMAND( tetBasis.getValues(badVals6, tetNodes, OPERATOR_D2), throwCounter, nException );
#endif
}
catch (std::logic_error err) {
*outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
*outStream << err.what() << '\n';
*outStream << "-------------------------------------------------------------------------------" << "\n\n";
errorFlag = -1000;
};
// Check if number of thrown exceptions matches the one we expect
if (throwCounter != nException) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
}
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 2: correctness of tag to enum and enum to tag lookups |\n"\
<< "===============================================================================\n";
try{
std::vector<std::vector<int> > allTags = tetBasis.getAllDofTags();
// Loop over all tags, lookup the associated dof enumeration and then lookup the tag again
for (unsigned i = 0; i < allTags.size(); i++) {
int bfOrd = tetBasis.getDofOrdinal(allTags[i][0], allTags[i][1], allTags[i][2]);
std::vector<int> myTag = tetBasis.getDofTag(bfOrd);
if( !( (myTag[0] == allTags[i][0]) &&
(myTag[1] == allTags[i][1]) &&
(myTag[2] == allTags[i][2]) &&
(myTag[3] == allTags[i][3]) ) ) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " getDofOrdinal( {"
<< allTags[i][0] << ", "
<< allTags[i][1] << ", "
<< allTags[i][2] << ", "
<< allTags[i][3] << "}) = " << bfOrd <<" but \n";
*outStream << " getDofTag(" << bfOrd << ") = { "
<< myTag[0] << ", "
<< myTag[1] << ", "
<< myTag[2] << ", "
<< myTag[3] << "}\n";
}
}
// Now do the same but loop over basis functions
for( int bfOrd = 0; bfOrd < tetBasis.getCardinality(); bfOrd++) {
std::vector<int> myTag = tetBasis.getDofTag(bfOrd);
int myBfOrd = tetBasis.getDofOrdinal(myTag[0], myTag[1], myTag[2]);
if( bfOrd != myBfOrd) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " getDofTag(" << bfOrd << ") = { "
<< myTag[0] << ", "
<< myTag[1] << ", "
<< myTag[2] << ", "
<< myTag[3] << "} but getDofOrdinal({"
<< myTag[0] << ", "
<< myTag[1] << ", "
<< myTag[2] << ", "
<< myTag[3] << "} ) = " << myBfOrd << "\n";
}
}
}
catch (std::logic_error err){
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 3: correctness of basis function values |\n"\
<< "===============================================================================\n";
outStream -> precision(20);
// VALUE: in (F,P) format
double basisValues[] = {
1.00000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00000, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 1.00000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00000, 0, 0, 0, 0, \
0, 0, 0, 0, 0, 0, 1.00000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00000, 0, \
0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
1.00000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.00000, 0, 0, 0, 0, 0, 0, 0, \
0, 0, 0, 1.00000 };
// GRAD and D1: in (F,P,D) format
double basisGrads[] = {
-3.00000, -3.00000, -3.00000, 1.00000, 1.00000, 1.00000, 1.00000, \
1.00000, 1.00000, 1.00000, 1.00000, 1.00000, -1.00000, -1.00000, \
-1.00000, 1.00000, 1.00000, 1.00000, -1.00000, -1.00000, -1.00000, \
-1.00000, -1.00000, -1.00000, 1.00000, 1.00000, 1.00000, 1.00000, \
1.00000, 1.00000, -1.00000, 0, 0, 3.00000, 0, 0, -1.00000, 0, 0, \
-1.00000, 0, 0, 1.00000, 0, 0, 1.00000, 0, 0, -1.00000, 0, 0, \
-1.00000, 0, 0, 1.00000, 0, 0, -1.00000, 0, 0, 0, -1.00000, 0, 0, \
-1.00000, 0, 0, 3.00000, 0, 0, -1.00000, 0, 0, -1.00000, 0, 0, \
1.00000, 0, 0, 1.00000, 0, 0, -1.00000, 0, 0, -1.00000, 0, 0, \
1.00000, 0, 0, 0, -1.00000, 0, 0, -1.00000, 0, 0, -1.00000, 0, 0, \
3.00000, 0, 0, -1.00000, 0, 0, -1.00000, 0, 0, -1.00000, 0, 0, \
1.00000, 0, 0, 1.00000, 0, 0, 1.00000, 4.00000, 0, 0, -4.00000, \
-4.00000, -4.00000, 0, 0, 0, 0, 0, 0, 0, -2.00000, -2.00000, \
-2.00000, -2.00000, -2.00000, 2.00000, 0, 0, 2.00000, 0, 0, -2.00000, \
-2.00000, -2.00000, 0, 0, 0, 0, 0, 0, 0, 4.00000, 0, 4.00000, 0, 0, \
0, 0, 0, 0, 2.00000, 0, 2.00000, 2.00000, 0, 2.00000, 0, 0, 0, 0, 0, \
0, 2.00000, 0, 2.00000, 0, 0, 0, 4.00000, 0, 0, 0, 0, -4.00000, \
-4.00000, -4.00000, 0, 0, 0, 0, 2.00000, 0, -2.00000, -2.00000, \
-2.00000, -2.00000, 0, -2.00000, 0, 2.00000, 0, 0, 0, 0, -2.00000, \
-2.00000, -2.00000, 0, 0, 4.00000, 0, 0, 0, 0, 0, 0, -4.00000, \
-4.00000, -4.00000, 0, 0, 2.00000, 0, 0, 0, 0, 0, 2.00000, -2.00000, \
-2.00000, 0, -2.00000, -2.00000, -2.00000, -2.00000, -2.00000, \
-2.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 4.00000, 0, 0, 0, 0, \
2.00000, 0, 0, 2.00000, 0, 0, 0, 2.00000, 0, 0, 2.00000, 0, 2.00000, \
2.00000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4.00000, 0, 4.00000, 0, 0, 0, \
0, 0, 0, 2.00000, 0, 0, 2.00000, 0, 2.00000, 0, 0, 2.00000, 0, 0, \
2.00000, 2.00000};
// D2 values in (F,P, Dk) format
double basisD2[]={
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 4.00000, \
4.00000, 4.00000, 4.00000, 4.00000, 4.00000, 0, 0, 0, 0, 0, 4.00000, \
0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, \
4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, \
0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, \
0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, \
4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, \
0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, \
0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 0, 0, 4.00000, \
0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, \
4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, \
0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, \
0, 0, 4.00000, -8.00000, -4.00000, -4.00000, 0, 0, 0, -8.00000, \
-4.00000, -4.00000, 0, 0, 0, -8.00000, -4.00000, -4.00000, 0, 0, 0, \
-8.00000, -4.00000, -4.00000, 0, 0, 0, -8.00000, -4.00000, -4.00000, \
0, 0, 0, -8.00000, -4.00000, -4.00000, 0, 0, 0, -8.00000, -4.00000, \
-4.00000, 0, 0, 0, -8.00000, -4.00000, -4.00000, 0, 0, 0, -8.00000, \
-4.00000, -4.00000, 0, 0, 0, -8.00000, -4.00000, -4.00000, 0, 0, 0, \
0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, \
0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, \
0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, \
0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, -4.00000, 0, -8.00000, -4.00000, \
0, 0, -4.00000, 0, -8.00000, -4.00000, 0, 0, -4.00000, 0, -8.00000, \
-4.00000, 0, 0, -4.00000, 0, -8.00000, -4.00000, 0, 0, -4.00000, 0, \
-8.00000, -4.00000, 0, 0, -4.00000, 0, -8.00000, -4.00000, 0, 0, \
-4.00000, 0, -8.00000, -4.00000, 0, 0, -4.00000, 0, -8.00000, \
-4.00000, 0, 0, -4.00000, 0, -8.00000, -4.00000, 0, 0, -4.00000, 0, \
-8.00000, -4.00000, 0, 0, 0, -4.00000, 0, -4.00000, -8.00000, 0, 0, \
-4.00000, 0, -4.00000, -8.00000, 0, 0, -4.00000, 0, -4.00000, \
-8.00000, 0, 0, -4.00000, 0, -4.00000, -8.00000, 0, 0, -4.00000, 0, \
-4.00000, -8.00000, 0, 0, -4.00000, 0, -4.00000, -8.00000, 0, 0, \
-4.00000, 0, -4.00000, -8.00000, 0, 0, -4.00000, 0, -4.00000, \
-8.00000, 0, 0, -4.00000, 0, -4.00000, -8.00000, 0, 0, -4.00000, 0, \
-4.00000, -8.00000, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, \
0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, \
0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, \
0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 0, 0, \
4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, \
0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, \
0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, 0, 0, 0, 4.00000, 0, 0, \
0, 0, 0, 4.00000, 0
};
try{
// Dimensions for the output arrays:
int numFields = tetBasis.getCardinality();
int numPoints = tetNodes.dimension(0);
int spaceDim = tetBasis.getBaseCellTopology().getDimension();
// Generic array for values, grads, curls, etc. that will be properly sized before each call
FieldContainer<double> vals;
// Check VALUE of basis functions: resize vals to rank-2 container:
vals.resize(numFields, numPoints);
tetBasis.getValues(vals, tetNodes, OPERATOR_VALUE);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
int l = i + j * numFields;
if (std::abs(vals(i,j) - basisValues[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";
*outStream << "} computed value: " << vals(i,j)
<< " but reference value: " << basisValues[l] << "\n";
}
}
}
// Check GRAD of basis function: resize vals to rank-3 container
vals.resize(numFields, numPoints, spaceDim);
tetBasis.getValues(vals, tetNodes, OPERATOR_GRAD);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
for (int k = 0; k < spaceDim; k++) {
// basisGrads is (F,P,D), compute offset:
int l = k + j * spaceDim + i * spaceDim * numPoints;
if (std::abs(vals(i,j,k) - basisGrads[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed grad component: " << vals(i,j,k)
<< " but reference grad component: " << basisGrads[l] << "\n";
}
}
}
}
// Check D1 of basis function (do not resize vals because it has the correct size: D1 = GRAD)
tetBasis.getValues(vals, tetNodes, OPERATOR_D1);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
for (int k = 0; k < spaceDim; k++) {
// basisGrads is (F,P,D), compute offset:
int l = k + j * spaceDim + i * spaceDim * numPoints;
if (std::abs(vals(i,j,k) - basisGrads[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed D1 component: " << vals(i,j,k)
<< " but reference D1 component: " << basisGrads[l] << "\n";
}
}
}
}
// Check D2 of basis function
int D2cardinality = Intrepid2::getDkCardinality(OPERATOR_D2, spaceDim);
vals.resize(numFields, numPoints, D2cardinality);
tetBasis.getValues(vals, tetNodes, OPERATOR_D2);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
for (int k = 0; k < D2cardinality; k++) {
// basisD2 is (F,P,Dk), compute offset:
int l = k + j * D2cardinality + i * D2cardinality * numPoints;
if (std::abs(vals(i,j,k) - basisD2[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
*outStream << "} computed D2 component: " << vals(i,j,k)
<< " but reference D2 component: " << basisD2[l] << "\n";
}
}
}
}
// Check all higher derivatives - must be zero.
for(EOperator op = OPERATOR_D3; op < OPERATOR_MAX; op++) {
// The last dimension is the number of kth derivatives and needs to be resized for every Dk
int DkCardin = Intrepid2::getDkCardinality(op, spaceDim);
vals.resize(numFields, numPoints, DkCardin);
tetBasis.getValues(vals, tetNodes, op);
for (int i1 = 0; i1 < numFields; i1++)
for (int i2 = 0; i2 < numPoints; i2++)
for (int i3 = 0; i3 < DkCardin; i3++) {
if (std::abs(vals(i1,i2,i3)) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Get the multi-index of the value where the error is and the operator order
int ord = Intrepid2::getOperatorOrder(op);
*outStream << " At multi-index { "<<i1<<" "<<i2 <<" "<<i3;
*outStream << "} computed D"<< ord <<" component: " << vals(i1,i2,i3)
<< " but reference D" << ord << " component: 0 \n";
}
}
}
}
// Catch unexpected errors
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return errorFlag;
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (Basis_HDIV_QUAD_I1_FEM) |\n" \
<< "| |\n" \
<< "| 1) Conversion of Dof tags into Dof ordinals and back |\n" \
<< "| 2) Basis values for VALUE and DIV operators |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n"\
<< "| TEST 1: Basis creation, exception testing |\n"\
<< "===============================================================================\n";
// Define basis and error flag
Basis_HDIV_QUAD_I1_FEM<double, FieldContainer<double> > quadBasis;
int errorFlag = 0;
// Initialize throw counter for exception testing
int nException = 0;
int throwCounter = 0;
// Array with the 4 vertices of the reference Quadrilateral, its center and 4 more points
FieldContainer<double> quadNodes(9, 2);
quadNodes(0,0) = -1.0;
quadNodes(0,1) = -1.0;
quadNodes(1,0) = 1.0;
quadNodes(1,1) = -1.0;
quadNodes(2,0) = 1.0;
quadNodes(2,1) = 1.0;
quadNodes(3,0) = -1.0;
quadNodes(3,1) = 1.0;
quadNodes(4,0) = 0.0;
quadNodes(4,1) = 0.0;
quadNodes(5,0) = 0.0;
quadNodes(5,1) = -0.5;
quadNodes(6,0) = 0.0;
quadNodes(6,1) = 0.5;
quadNodes(7,0) = -0.5;
quadNodes(7,1) = 0.0;
quadNodes(8,0) = 0.5;
quadNodes(8,1) = 0.0;
// Generic array for the output values; needs to be properly resized depending on the operator type
FieldContainer<double> vals;
try {
int spaceDim = quadBasis.getBaseCellTopology().getDimension();
// exception #1: GRAD cannot be applied to HDIV functions
// resize vals to rank-3 container with dimensions (num. basis functions, num. points, arbitrary)
vals.resize(quadBasis.getCardinality(), quadNodes.dimension(0), spaceDim );
INTREPID_TEST_COMMAND( quadBasis.getValues(vals, quadNodes, OPERATOR_GRAD), throwCounter, nException );
// exception #2: CURL cannot be applied to HDIV functions
INTREPID_TEST_COMMAND( quadBasis.getValues(vals, quadNodes, OPERATOR_CURL), throwCounter, nException );
// Exceptions 3-7: all bf tags/bf Ids below are wrong and should cause getDofOrdinal() and
// getDofTag() to access invalid array elements thereby causing bounds check exception
// exception #3
INTREPID_TEST_COMMAND( quadBasis.getDofOrdinal(3,0,0), throwCounter, nException );
// exception #4
INTREPID_TEST_COMMAND( quadBasis.getDofOrdinal(1,1,1), throwCounter, nException );
// exception #5
INTREPID_TEST_COMMAND( quadBasis.getDofOrdinal(0,4,1), throwCounter, nException );
// exception #6
INTREPID_TEST_COMMAND( quadBasis.getDofTag(12), throwCounter, nException );
// exception #7
INTREPID_TEST_COMMAND( quadBasis.getDofTag(-1), throwCounter, nException );
#ifdef HAVE_INTREPID_DEBUG
// Exceptions 8- test exception handling with incorrectly dimensioned input/output arrays
// exception #8: input points array must be of rank-2
FieldContainer<double> badPoints1(4, 5, 3);
INTREPID_TEST_COMMAND( quadBasis.getValues(vals, badPoints1, OPERATOR_VALUE), throwCounter, nException );
// exception #9 dimension 1 in the input point array must equal space dimension of the cell
FieldContainer<double> badPoints2(4, spaceDim + 1);
INTREPID_TEST_COMMAND( quadBasis.getValues(vals, badPoints2, OPERATOR_VALUE), throwCounter, nException );
// exception #10 output values must be of rank-3 for OPERATOR_VALUE
FieldContainer<double> badVals1(4, 5);
INTREPID_TEST_COMMAND( quadBasis.getValues(badVals1, quadNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #11 output values must be of rank-2 for OPERATOR_DIV
FieldContainer<double> badVals2(4, 5, spaceDim);
INTREPID_TEST_COMMAND( quadBasis.getValues(badVals2, quadNodes, OPERATOR_DIV), throwCounter, nException );
// exception #12 incorrect 0th dimension of output array (must equal number of basis functions)
FieldContainer<double> badVals3(quadBasis.getCardinality() + 1, quadNodes.dimension(0), spaceDim);
INTREPID_TEST_COMMAND( quadBasis.getValues(badVals3, quadNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #13 incorrect 0th dimension of output array (must equal number of basis functions)
FieldContainer<double> badVals4(quadBasis.getCardinality() + 1, quadNodes.dimension(0));
INTREPID_TEST_COMMAND( quadBasis.getValues(badVals4, quadNodes, OPERATOR_DIV), throwCounter, nException );
// exception #14 incorrect 1st dimension of output array (must equal number of points)
FieldContainer<double> badVals5(quadBasis.getCardinality(), quadNodes.dimension(0) + 1, spaceDim);
INTREPID_TEST_COMMAND( quadBasis.getValues(badVals5, quadNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #15 incorrect 1st dimension of output array (must equal number of points)
FieldContainer<double> badVals6(quadBasis.getCardinality(), quadNodes.dimension(0) + 1);
INTREPID_TEST_COMMAND( quadBasis.getValues(badVals6, quadNodes, OPERATOR_DIV), throwCounter, nException );
// exception #16: incorrect 2nd dimension of output array (must equal the space dimension)
FieldContainer<double> badVals7(quadBasis.getCardinality(), quadNodes.dimension(0), spaceDim + 1);
INTREPID_TEST_COMMAND( quadBasis.getValues(badVals7, quadNodes, OPERATOR_VALUE), throwCounter, nException );
#endif
}
catch (std::logic_error err) {
*outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
*outStream << err.what() << '\n';
*outStream << "-------------------------------------------------------------------------------" << "\n\n";
errorFlag = -1000;
};
// Check if number of thrown exceptions matches the one we expect
if (throwCounter != nException) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
}
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 2: correctness of tag to enum and enum to tag lookups |\n"\
<< "===============================================================================\n";
try {
std::vector<std::vector<int> > allTags = quadBasis.getAllDofTags();
// Loop over all tags, lookup the associated dof enumeration and then lookup the tag again
for (unsigned i = 0; i < allTags.size(); i++) {
int bfOrd = quadBasis.getDofOrdinal(allTags[i][0], allTags[i][1], allTags[i][2]);
std::vector<int> myTag = quadBasis.getDofTag(bfOrd);
if( !( (myTag[0] == allTags[i][0]) &&
(myTag[1] == allTags[i][1]) &&
(myTag[2] == allTags[i][2]) &&
(myTag[3] == allTags[i][3]) ) ) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " getDofOrdinal( {"
<< allTags[i][0] << ", "
<< allTags[i][1] << ", "
<< allTags[i][2] << ", "
<< allTags[i][3] << "}) = " << bfOrd <<" but \n";
*outStream << " getDofTag(" << bfOrd << ") = { "
<< myTag[0] << ", "
<< myTag[1] << ", "
<< myTag[2] << ", "
<< myTag[3] << "}\n";
}
}
// Now do the same but loop over basis functions
for( int bfOrd = 0; bfOrd < quadBasis.getCardinality(); bfOrd++) {
std::vector<int> myTag = quadBasis.getDofTag(bfOrd);
int myBfOrd = quadBasis.getDofOrdinal(myTag[0], myTag[1], myTag[2]);
if( bfOrd != myBfOrd) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
*outStream << " getDofTag(" << bfOrd << ") = { "
<< myTag[0] << ", "
<< myTag[1] << ", "
<< myTag[2] << ", "
<< myTag[3] << "} but getDofOrdinal({"
<< myTag[0] << ", "
<< myTag[1] << ", "
<< myTag[2] << ", "
<< myTag[3] << "} ) = " << myBfOrd << "\n";
}
}
}
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 3: correctness of basis function values |\n"\
<< "===============================================================================\n";
outStream -> precision(20);
// VALUE: Each row pair gives the 6x3 correct basis set values at an evaluation point: (P,F,D) layout
double basisValues[] = {
0, -0.500000, 0, 0, 0, 0, -0.500000, 0, 0, -0.500000, 0.500000, 0, 0, \
0, 0, 0, 0, 0, 0.500000, 0, 0, 0.500000, 0, 0, 0, 0, 0, 0, 0, \
0.500000, -0.500000, 0, 0, -0.250000, 0.250000, 0, 0, 0.250000, \
-0.250000, 0, 0, -0.375000, 0.250000, 0, 0, 0.125000, -0.250000, 0, \
0, -0.125000, 0.250000, 0, 0, 0.375000, -0.250000, 0, 0, -0.250000, \
0.125000, 0, 0, 0.250000, -0.375000, 0, 0, -0.250000, 0.375000, 0, 0, \
0.250000, -0.125000, 0
};
// DIV: each row gives the 6 correct values of the divergence of the 6 basis functions: (P,F) layout
double basisDivs[] = {
0.25, 0.25, 0.25, 0.25,
0.25, 0.25, 0.25, 0.25,
0.25, 0.25, 0.25, 0.25,
0.25, 0.25, 0.25, 0.25,
0.25, 0.25, 0.25, 0.25,
0.25, 0.25, 0.25, 0.25,
0.25, 0.25, 0.25, 0.25,
0.25, 0.25, 0.25, 0.25,
0.25, 0.25, 0.25, 0.25,
};
try {
// Dimensions for the output arrays:
int numPoints = quadNodes.dimension(0);
int numFields = quadBasis.getCardinality();
int spaceDim = quadBasis.getBaseCellTopology().getDimension();
// Generic array for values and curls that will be properly sized before each call
FieldContainer<double> vals;
// Check VALUE of basis functions: resize vals to rank-3 container:
vals.resize(numFields, numPoints, spaceDim);
quadBasis.getValues(vals, quadNodes, OPERATOR_VALUE);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
for (int k = 0; k < spaceDim; k++) {
// compute offset for (P,F,D) data layout: indices are P->j, F->i, D->k
int l = k + i * spaceDim + j * spaceDim * numFields;
if (std::abs(vals(i,j,k) - basisValues[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";
*outStream << j << " ";
*outStream << k << " ";
*outStream << "} computed value: " << vals(i,j,k)
<< " but reference value: " << basisValues[l] << "\n";
}
}
}
}
// Check DIV of basis function: resize vals to rank-2 container
vals.resize(numFields, numPoints);
quadBasis.getValues(vals, quadNodes, OPERATOR_DIV);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
int l = i + j * numFields;
if (std::abs(vals(i,j) - basisDivs[l]) > INTREPID_TOL) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " ";
*outStream << j << " ";
*outStream << "} computed divergence component: " << vals(i,j)
<< " but reference divergence component: " << basisDivs[l] << "\n";
}
}
}
}
// Catch unexpected errors
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
/** \brief Performs a code-code comparison to FIAT for Raviart-Thomas bases on triangles (values and divs)
\param argc [in] - number of command-line arguments
\param argv [in] - command-line arguments
*/
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
// This little trick lets us print to std::cout only if a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test HDIV_TRI_In_FEM |\n" \
<< "| |\n" \
<< "| 1) Tests triangular Raviart-Thomas basis |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]) or |\n" \
<< "| Denis Ridzal ([email protected]) or |\n" \
<< "| Robert Kirby ([email protected]) |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n";
int errorFlag = 0;
// test for basis values, compare against fiat
try {
const int deg = 2;
Basis_HDIV_TRI_In_FEM<double,FieldContainer<double> > myBasis( deg , POINTTYPE_EQUISPACED );
// Get a lattice
const int np_lattice = PointTools::getLatticeSize( myBasis.getBaseCellTopology() , deg , 0 );
FieldContainer<double> lattice( np_lattice , 2 );
FieldContainer<double> myBasisValues( myBasis.getCardinality() , np_lattice , 2 );
PointTools::getLattice<double,FieldContainer<double> >( lattice ,
myBasis.getBaseCellTopology() ,
deg ,
0 ,
POINTTYPE_EQUISPACED );
myBasis.getValues( myBasisValues , lattice , OPERATOR_VALUE );
const double fiat_vals[] = {
0.000000000000000e+00, -2.000000000000000e+00,
2.500000000000000e-01, -5.000000000000000e-01,
-1.000000000000000e+00, 1.000000000000000e+00,
0.000000000000000e+00, -2.500000000000000e-01,
-5.000000000000000e-01, 5.000000000000000e-01,
0.000000000000000e+00, 0.000000000000000e+00,
0.000000000000000e+00, 1.000000000000000e+00,
2.500000000000000e-01, -5.000000000000000e-01,
2.000000000000000e+00, -2.000000000000000e+00,
0.000000000000000e+00, 5.000000000000000e-01,
2.500000000000000e-01, -2.500000000000000e-01,
0.000000000000000e+00, 0.000000000000000e+00,
0.000000000000000e+00, 0.000000000000000e+00,
2.500000000000000e-01, 0.000000000000000e+00,
2.000000000000000e+00, 0.000000000000000e+00,
0.000000000000000e+00, -5.000000000000000e-01,
2.500000000000000e-01, 2.500000000000000e-01,
0.000000000000000e+00, -1.000000000000000e+00,
0.000000000000000e+00, 0.000000000000000e+00,
-5.000000000000000e-01, 0.000000000000000e+00,
-1.000000000000000e+00, 0.000000000000000e+00,
0.000000000000000e+00, 2.500000000000000e-01,
2.500000000000000e-01, 2.500000000000000e-01,
0.000000000000000e+00, 2.000000000000000e+00,
1.000000000000000e+00, 0.000000000000000e+00,
5.000000000000000e-01, 0.000000000000000e+00,
0.000000000000000e+00, 0.000000000000000e+00,
-5.000000000000000e-01, 2.500000000000000e-01,
-2.500000000000000e-01, 2.500000000000000e-01,
-2.000000000000000e+00, 2.000000000000000e+00,
-2.000000000000000e+00, 0.000000000000000e+00,
-2.500000000000000e-01, 0.000000000000000e+00,
0.000000000000000e+00, 0.000000000000000e+00,
-5.000000000000000e-01, 2.500000000000000e-01,
5.000000000000000e-01, -5.000000000000000e-01,
1.000000000000000e+00, -1.000000000000000e+00,
0.000000000000000e+00, 0.000000000000000e+00,
1.500000000000000e+00, 0.000000000000000e+00,
0.000000000000000e+00, 0.000000000000000e+00,
0.000000000000000e+00, 7.500000000000000e-01,
7.500000000000000e-01, -7.500000000000000e-01,
0.000000000000000e+00, 0.000000000000000e+00,
0.000000000000000e+00, 0.000000000000000e+00,
7.500000000000000e-01, 0.000000000000000e+00,
0.000000000000000e+00, 0.000000000000000e+00,
0.000000000000000e+00, 1.500000000000000e+00,
-7.500000000000000e-01, 7.500000000000000e-01,
0.000000000000000e+00, 0.000000000000000e+00
};
int cur=0;
for (int i=0;i<myBasisValues.dimension(0);i++) {
for (int j=0;j<myBasisValues.dimension(1);j++) {
for (int k=0;k<myBasisValues.dimension(2);k++) {
if (std::abs( myBasisValues(i,j,k) - fiat_vals[cur] ) > INTREPID_TOL ) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " " << j << " " << k;
*outStream << "} computed value: " << myBasisValues(i,j,k)
<< " but correct value: " << fiat_vals[cur] << "\n";
*outStream << "Difference: " << std::abs( myBasisValues(i,j,k) - fiat_vals[cur] ) << "\n";
}
cur++;
}
}
}
}
catch (std::exception err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
}
try {
const int deg = 2;
Basis_HDIV_TRI_In_FEM<double,FieldContainer<double> > myBasis( deg , POINTTYPE_EQUISPACED );
// Get a lattice
const int np_lattice = PointTools::getLatticeSize( myBasis.getBaseCellTopology() , deg , 0 );
FieldContainer<double> lattice( np_lattice , 2 );
FieldContainer<double> myBasisDivs( myBasis.getCardinality() , np_lattice );
PointTools::getLattice<double,FieldContainer<double> >( lattice ,
myBasis.getBaseCellTopology() ,
deg ,
0 ,
POINTTYPE_EQUISPACED );
myBasis.getValues( myBasisDivs , lattice , OPERATOR_DIV );
const double fiat_divs[] = {
7.000000000000000e+00,
2.500000000000000e+00,
-2.000000000000000e+00,
2.500000000000000e+00,
-2.000000000000000e+00,
-2.000000000000000e+00,
-2.000000000000000e+00,
2.500000000000000e+00,
7.000000000000000e+00,
-2.000000000000000e+00,
2.500000000000000e+00,
-2.000000000000000e+00,
-2.000000000000000e+00,
2.500000000000000e+00,
7.000000000000000e+00,
-2.000000000000000e+00,
2.500000000000000e+00,
-2.000000000000000e+00,
-2.000000000000000e+00,
-2.000000000000000e+00,
-2.000000000000000e+00,
2.500000000000000e+00,
2.500000000000000e+00,
7.000000000000000e+00,
-2.000000000000000e+00,
-2.000000000000000e+00,
-2.000000000000000e+00,
2.500000000000000e+00,
2.500000000000000e+00,
7.000000000000000e+00,
7.000000000000000e+00,
2.500000000000000e+00,
-2.000000000000000e+00,
2.500000000000000e+00,
-2.000000000000000e+00,
-2.000000000000000e+00,
9.000000000000000e+00,
0.000000000000000e+00,
-9.000000000000000e+00,
4.500000000000000e+00,
-4.500000000000000e+00,
0.000000000000000e+00,
9.000000000000000e+00,
4.500000000000000e+00,
0.000000000000000e+00,
0.000000000000000e+00,
-4.500000000000000e+00,
-9.000000000000000e+00
};
int cur=0;
for (int i=0;i<myBasisDivs.dimension(0);i++) {
for (int j=0;j<myBasisDivs.dimension(1);j++) {
if (std::abs( myBasisDivs(i,j) - fiat_divs[cur] ) > INTREPID_TOL ) {
errorFlag++;
*outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
// Output the multi-index of the value where the error is:
*outStream << " At multi-index { ";
*outStream << i << " " << j;
*outStream << "} computed value: " << myBasisDivs(i,j)
<< " but correct value: " << fiat_divs[cur] << "\n";
*outStream << "Difference: " << std::abs( myBasisDivs(i,j) - fiat_divs[cur] ) << "\n";
}
cur++;
}
}
}
catch (std::exception err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
}
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
Kokkos::initialize();
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (CubatureDirect,CubatureTensor,DefaultCubatureFactory) |\n" \
<< "| |\n" \
<< "| 1) Computing integrals of monomials on reference cells in 3D |\n" \
<< "| - using Level 2 BLAS - |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]) or |\n" \
<< "| Denis Ridzal ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n"\
<< "| TEST 1: integrals of monomials in 3D (Level 2 BLAS version) |\n"\
<< "===============================================================================\n";
// internal variables:
int errorFlag = 0;
int polyCt = 0;
int offset = 0;
Teuchos::Array< Teuchos::Array<double> > testInt;
Teuchos::Array< Teuchos::Array<double> > analyticInt;
Teuchos::Array<double> tmparray(1);
double reltol = 1.0e+04 * INTREPID_TOL;
int maxDeg[4];
int maxOffset[4];
int numPoly[4];
int numAnalytic[4];
// max polynomial degree tested, per cell type:
maxDeg[0] = INTREPID2_CUBATURE_TET_DEFAULT_MAX;
maxDeg[1] = 20; // can be as large as INTREPID2_CUBATURE_LINE_GAUSS_MAX, but runtime is excessive
maxDeg[2] = std::min(INTREPID2_CUBATURE_LINE_GAUSS_MAX, INTREPID2_CUBATURE_TRI_DEFAULT_MAX);
maxDeg[3] = std::min(INTREPID2_CUBATURE_LINE_GAUSS_MAX, INTREPID2_CUBATURE_LINE_GAUSSJACOBI20_MAX);
// max polynomial degree recorded in analytic comparison files, per cell type:
maxOffset[0] = INTREPID2_CUBATURE_TET_DEFAULT_MAX;
maxOffset[1] = INTREPID2_CUBATURE_LINE_GAUSS_MAX;
maxOffset[2] = std::min(INTREPID2_CUBATURE_LINE_GAUSS_MAX, INTREPID2_CUBATURE_TRI_DEFAULT_MAX);
maxOffset[3] = std::min(INTREPID2_CUBATURE_LINE_GAUSS_MAX, INTREPID2_CUBATURE_LINE_GAUSSJACOBI20_MAX);
for (int i=0; i<4; i++) {
numPoly[i] = (maxDeg[i]+1)*(maxDeg[i]+2)*(maxDeg[i]+3)/6;
}
for (int i=0; i<4; i++) {
numAnalytic[i] = (maxOffset[i]+1)*(maxOffset[i]+2)*(maxOffset[i]+3)/6;
}
// get names of files with analytic values
std::string basedir = "./data";
std::stringstream namestream[4];
std::string filename[4];
namestream[0] << basedir << "/TET_integrals" << ".dat";
namestream[0] >> filename[0];
namestream[1] << basedir << "/HEX_integrals" << ".dat";
namestream[1] >> filename[1];
namestream[2] << basedir << "/TRIPRISM_integrals" << ".dat";
namestream[2] >> filename[2];
namestream[3] << basedir << "/PYR_integrals" << ".dat";
namestream[3] >> filename[3];
// reference cells tested
shards::CellTopology cellType[] = {shards::getCellTopologyData< shards::Tetrahedron<> >(),
shards::getCellTopologyData< shards::Hexahedron<> >(),
shards::getCellTopologyData< shards::Wedge<> >(),
shards::getCellTopologyData< shards::Pyramid<> >() };
// format of data files with analytic values
TypeOfExactData dataFormat[] = {INTREPID2_UTILS_SCALAR, INTREPID_UTILS_FRACTION, INTREPID_UTILS_FRACTION, INTREPID_UTILS_FRACTION};
// compute and compare integrals
try {
for (int cellCt=0; cellCt < 4; cellCt++) {
testInt.assign(numPoly[cellCt], tmparray);
analyticInt.assign(numAnalytic[cellCt], tmparray);
*outStream << "\nIntegrals of monomials on a reference " << cellType[cellCt].getBaseCellTopologyData()->name << ":\n";
std::ifstream filecompare(&filename[cellCt][0]);
// compute integrals
for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) {
int numMonomials = (cubDeg+1)*(cubDeg+2)*(cubDeg+3)/6;
testInt[cubDeg].resize(numMonomials);
computeIntegral(testInt[cubDeg], cellType[cellCt], cubDeg);
}
// get analytic values
if (filecompare.is_open()) {
getAnalytic(analyticInt, filecompare, dataFormat[cellCt]);
// close file
filecompare.close();
}
// perform comparison
for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) {
polyCt = 0;
offset = 0;
int oldErrorFlag = errorFlag;
for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
for (int zDeg=0; zDeg <= cubDeg-xDeg-yDeg; zDeg++) {
double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) );
double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]);
if (absdiff > abstol) {
*outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
<< "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg
<< " * z^" << std::setw(2) << zDeg << ":" << " "
<< std::scientific << std::setprecision(16)
<< testInt[cubDeg][polyCt] << " " << analyticInt[polyCt+offset][0] << " "
<< std::setprecision(4) << absdiff << " " << "<?" << " " << abstol << "\n";
errorFlag++;
*outStream << std::right << std::setw(118) << "^^^^---FAILURE!\n";
}
polyCt++;
}
offset = offset + maxOffset[cellCt] - cubDeg;
}
offset = offset + (maxOffset[cellCt] - cubDeg)*(maxOffset[cellCt] - cubDeg + 1)/2;
}
*outStream << "Cubature order " << std::setw(2) << std::left << cubDeg;
if (errorFlag == oldErrorFlag)
*outStream << " passed.\n";
else
*outStream << " failed.\n";
}
*outStream << "\n";
} // end for cellCt
}
catch (std::logic_error err) {
*outStream << err.what() << "\n";
errorFlag = -1;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return errorFlag;
}
int main(int argc, char *argv[]) {
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
Kokkos::initialize();
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 0)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Unit Test (Basis_HGRAD_HEX_In_FEM) |\n" \
<< "| |\n" \
<< "| 1) Patch test involving H(div) matrices |\n" \
<< "| for the Dirichlet problem on a hexahedron |\n" \
<< "| Omega with boundary Gamma. |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Robert Kirby ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n" \
<< "| TEST 1: Patch test |\n" \
<< "===============================================================================\n";
int errorFlag = 0;
outStream -> precision(16);
try {
DefaultCubatureFactory<double> cubFactory; // create cubature factory
shards::CellTopology cell(shards::getCellTopologyData< shards::Hexahedron<> >()); // create parent cell topology
shards::CellTopology side(shards::getCellTopologyData< shards::Quadrilateral<> >()); // create relevant subcell (side) topology
shards::CellTopology line(shards::getCellTopologyData< shards::Line<> >() ); // for getting points to construct the basis
int cellDim = cell.getDimension();
int sideDim = side.getDimension();
int min_order = 0;
int max_order = 3;
int numIntervals = 2;
int numInterpPoints = (numIntervals + 1)*(numIntervals + 1)*(numIntervals+1);
FieldContainer<double> interp_points_ref(numInterpPoints, cellDim);
int counter = 0;
for (int k=0;k<numIntervals;k++) {
for (int j=0; j<=numIntervals; j++) {
for (int i=0; i<=numIntervals; i++) {
interp_points_ref(counter,0) = i*(1.0/numIntervals);
interp_points_ref(counter,1) = j*(1.0/numIntervals);
interp_points_ref(counter,2) = k*(1.0/numIntervals);
counter++;
}
}
}
for (int basis_order=min_order;basis_order<=max_order;basis_order++) {
// create bases
// get the points for the vector basis
Teuchos::RCP<Basis<double,FieldContainer<double> > > vectorBasis =
Teuchos::rcp(new Basis_HDIV_HEX_In_FEM<double,FieldContainer<double> >(basis_order+1,POINTTYPE_SPECTRAL) );
Teuchos::RCP<Basis<double,FieldContainer<double> > > scalarBasis =
Teuchos::rcp(new Basis_HGRAD_HEX_Cn_FEM<double,FieldContainer<double> >(basis_order,POINTTYPE_SPECTRAL) );
int numVectorFields = vectorBasis->getCardinality();
int numScalarFields = scalarBasis->getCardinality();
int numTotalFields = numVectorFields + numScalarFields;
// create cubatures
Teuchos::RCP<Cubature<double> > cellCub = cubFactory.create(cell, 2*(basis_order+1));
Teuchos::RCP<Cubature<double> > sideCub = cubFactory.create(side, 2*(basis_order+1));
int numCubPointsCell = cellCub->getNumPoints();
int numCubPointsSide = sideCub->getNumPoints();
// hold cubature information
FieldContainer<double> cub_points_cell(numCubPointsCell, cellDim);
FieldContainer<double> cub_weights_cell(numCubPointsCell);
FieldContainer<double> cub_points_side( numCubPointsSide, sideDim );
FieldContainer<double> cub_weights_side( numCubPointsSide );
FieldContainer<double> cub_points_side_refcell( numCubPointsSide , cellDim );
// hold basis function information on refcell
FieldContainer<double> value_of_v_basis_at_cub_points_cell(numVectorFields, numCubPointsCell, cellDim );
FieldContainer<double> w_value_of_v_basis_at_cub_points_cell(1, numVectorFields, numCubPointsCell, cellDim);
FieldContainer<double> div_of_v_basis_at_cub_points_cell( numVectorFields, numCubPointsCell );
FieldContainer<double> w_div_of_v_basis_at_cub_points_cell( 1, numVectorFields , numCubPointsCell );
FieldContainer<double> value_of_s_basis_at_cub_points_cell(numScalarFields,numCubPointsCell);
FieldContainer<double> w_value_of_s_basis_at_cub_points_cell(1,numScalarFields,numCubPointsCell);
// containers for side integration:
// I just need the normal component of the vector basis
// and the exact solution at the cub points
FieldContainer<double> value_of_v_basis_at_cub_points_side(numVectorFields,numCubPointsSide,cellDim);
FieldContainer<double> n_of_v_basis_at_cub_points_side(numVectorFields,numCubPointsSide);
FieldContainer<double> w_n_of_v_basis_at_cub_points_side(1,numVectorFields,numCubPointsSide);
FieldContainer<double> diri_data_at_cub_points_side(1,numCubPointsSide);
FieldContainer<double> side_normal(cellDim);
// holds rhs data
FieldContainer<double> rhs_at_cub_points_cell(1,numCubPointsCell);
// FEM matrices and vectors
FieldContainer<double> fe_matrix_M(1,numVectorFields,numVectorFields);
FieldContainer<double> fe_matrix_B(1,numVectorFields,numScalarFields);
FieldContainer<double> fe_matrix(1,numTotalFields,numTotalFields);
FieldContainer<double> rhs_vector_vec(1,numVectorFields);
FieldContainer<double> rhs_vector_scal(1,numScalarFields);
FieldContainer<double> rhs_and_soln_vec(1,numTotalFields);
FieldContainer<int> ipiv(numTotalFields);
FieldContainer<double> value_of_s_basis_at_interp_points( numScalarFields , numInterpPoints);
FieldContainer<double> interpolant( 1 , numInterpPoints );
// set test tolerance
double zero = (basis_order+1)*(basis_order+1)*1000.0*INTREPID_TOL;
// build matrices outside the loop, and then just do the rhs
// for each iteration
cellCub->getCubature(cub_points_cell, cub_weights_cell);
sideCub->getCubature(cub_points_side, cub_weights_side);
// need the vector basis & its divergences
vectorBasis->getValues(value_of_v_basis_at_cub_points_cell,
cub_points_cell,
OPERATOR_VALUE);
vectorBasis->getValues(div_of_v_basis_at_cub_points_cell,
cub_points_cell,
OPERATOR_DIV);
// need the scalar basis as well
scalarBasis->getValues(value_of_s_basis_at_cub_points_cell,
cub_points_cell,
OPERATOR_VALUE);
// construct mass matrix
cub_weights_cell.resize(1,numCubPointsCell);
FunctionSpaceTools::multiplyMeasure<double>(w_value_of_v_basis_at_cub_points_cell ,
cub_weights_cell ,
value_of_v_basis_at_cub_points_cell );
cub_weights_cell.resize(numCubPointsCell);
value_of_v_basis_at_cub_points_cell.resize( 1 , numVectorFields , numCubPointsCell , cellDim );
FunctionSpaceTools::integrate<double>(fe_matrix_M,
w_value_of_v_basis_at_cub_points_cell ,
value_of_v_basis_at_cub_points_cell ,
COMP_BLAS );
value_of_v_basis_at_cub_points_cell.resize( numVectorFields , numCubPointsCell , cellDim );
// div matrix
cub_weights_cell.resize(1,numCubPointsCell);
FunctionSpaceTools::multiplyMeasure<double>(w_div_of_v_basis_at_cub_points_cell,
cub_weights_cell,
div_of_v_basis_at_cub_points_cell);
cub_weights_cell.resize(numCubPointsCell);
value_of_s_basis_at_cub_points_cell.resize(1,numScalarFields,numCubPointsCell);
FunctionSpaceTools::integrate<double>(fe_matrix_B,
w_div_of_v_basis_at_cub_points_cell ,
value_of_s_basis_at_cub_points_cell ,
COMP_BLAS );
value_of_s_basis_at_cub_points_cell.resize(numScalarFields,numCubPointsCell);
for (int x_order=0;x_order<=basis_order;x_order++) {
for (int y_order=0;y_order<=basis_order;y_order++) {
for (int z_order=0;z_order<=basis_order;z_order++) {
// reset global matrix since I destroyed it in LU factorization.
fe_matrix.initialize();
// insert mass matrix into global matrix
for (int i=0;i<numVectorFields;i++) {
for (int j=0;j<numVectorFields;j++) {
fe_matrix(0,i,j) = fe_matrix_M(0,i,j);
}
}
// insert div matrix into global matrix
for (int i=0;i<numVectorFields;i++) {
for (int j=0;j<numScalarFields;j++) {
fe_matrix(0,i,numVectorFields+j)=-fe_matrix_B(0,i,j);
fe_matrix(0,j+numVectorFields,i)=fe_matrix_B(0,i,j);
}
}
// clear old vector data
rhs_vector_vec.initialize();
rhs_vector_scal.initialize();
rhs_and_soln_vec.initialize();
// now get rhs vector
// rhs_vector_scal is just (rhs,w) for w in the scalar basis
// I already have the scalar basis tabulated.
cub_points_cell.resize(1,numCubPointsCell,cellDim);
rhsFunc(rhs_at_cub_points_cell,
cub_points_cell,
x_order,
y_order,
z_order);
cub_points_cell.resize(numCubPointsCell,cellDim);
cub_weights_cell.resize(1,numCubPointsCell);
FunctionSpaceTools::multiplyMeasure<double>(w_value_of_s_basis_at_cub_points_cell,
cub_weights_cell,
value_of_s_basis_at_cub_points_cell);
cub_weights_cell.resize(numCubPointsCell);
FunctionSpaceTools::integrate<double>(rhs_vector_scal,
rhs_at_cub_points_cell,
w_value_of_s_basis_at_cub_points_cell,
COMP_BLAS);
for (int i=0;i<numScalarFields;i++) {
rhs_and_soln_vec(0,numVectorFields+i) = rhs_vector_scal(0,i);
}
// now get <u,v.n> on boundary
for (unsigned side_cur=0;side_cur<6;side_cur++) {
// map side cubature to current side
CellTools<double>::mapToReferenceSubcell( cub_points_side_refcell ,
cub_points_side ,
sideDim ,
(int)side_cur ,
cell );
// Evaluate dirichlet data
cub_points_side_refcell.resize(1,numCubPointsSide,cellDim);
u_exact(diri_data_at_cub_points_side,
cub_points_side_refcell,x_order,y_order,z_order);
cub_points_side_refcell.resize(numCubPointsSide,cellDim);
// get normal direction, this has the edge weight factored into it already
CellTools<double>::getReferenceSideNormal(side_normal ,
(int)side_cur,cell );
// v.n at cub points on side
vectorBasis->getValues(value_of_v_basis_at_cub_points_side ,
cub_points_side_refcell ,
OPERATOR_VALUE );
for (int i=0;i<numVectorFields;i++) {
for (int j=0;j<numCubPointsSide;j++) {
n_of_v_basis_at_cub_points_side(i,j) = 0.0;
for (int k=0;k<cellDim;k++) {
n_of_v_basis_at_cub_points_side(i,j) += side_normal(k) *
value_of_v_basis_at_cub_points_side(i,j,k);
}
}
}
cub_weights_side.resize(1,numCubPointsSide);
FunctionSpaceTools::multiplyMeasure<double>(w_n_of_v_basis_at_cub_points_side,
cub_weights_side,
n_of_v_basis_at_cub_points_side);
cub_weights_side.resize(numCubPointsSide);
FunctionSpaceTools::integrate<double>(rhs_vector_vec,
diri_data_at_cub_points_side,
w_n_of_v_basis_at_cub_points_side,
COMP_BLAS,
false);
for (int i=0;i<numVectorFields;i++) {
rhs_and_soln_vec(0,i) -= rhs_vector_vec(0,i);
}
}
// solve linear system
int info = 0;
Teuchos::LAPACK<int, double> solver;
solver.GESV(numTotalFields, 1, &fe_matrix(0,0,0), numTotalFields, &ipiv(0), &rhs_and_soln_vec(0,0),
numTotalFields, &info);
// compute interpolant; the scalar entries are last
scalarBasis->getValues(value_of_s_basis_at_interp_points,
interp_points_ref,
OPERATOR_VALUE);
for (int pt=0;pt<numInterpPoints;pt++) {
interpolant(0,pt)=0.0;
for (int i=0;i<numScalarFields;i++) {
interpolant(0,pt) += rhs_and_soln_vec(0,numVectorFields+i)
* value_of_s_basis_at_interp_points(i,pt);
}
}
interp_points_ref.resize(1,numInterpPoints,cellDim);
// get exact solution for comparison
FieldContainer<double> exact_solution(1,numInterpPoints);
u_exact( exact_solution , interp_points_ref , x_order, y_order, z_order);
interp_points_ref.resize(numInterpPoints,cellDim);
RealSpaceTools<double>::add(interpolant,exact_solution);
double nrm= RealSpaceTools<double>::vectorNorm(&interpolant(0,0),interpolant.dimension(1), NORM_TWO);
*outStream << "\nNorm-2 error between scalar components of exact solution of order ("
<< x_order << ", " << y_order << ", " << z_order
<< ") and finite element interpolant of order " << basis_order << ": "
<< nrm << "\n";
if (nrm > zero) {
*outStream << "\n\nPatch test failed for solution polynomial order ("
<< x_order << ", " << y_order << ", " << z_order << ") and basis order (scalar, vector) ("
<< basis_order << ", " << basis_order+1 << ")\n\n";
errorFlag++;
}
}
}
}
}
}
catch (std::logic_error err) {
*outStream << err.what() << "\n\n";
errorFlag = -1000;
};
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return errorFlag;
}
int Integration_Test10(const bool verbose) {
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (verbose)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
typedef typename
Kokkos::Impl::is_space<DeviceSpaceType>::host_mirror_space::execution_space HostSpaceType ;
*outStream << "DeviceSpace:: "; DeviceSpaceType::print_configuration(*outStream, false);
*outStream << "HostSpace:: "; HostSpaceType::print_configuration(*outStream, false);
*outStream
<< "===============================================================================\n"
<< "| |\n"
<< "| Unit Test (CubaturePolylib) |\n"
<< "| |\n"
<< "| 1) Computing integrals of monomials on reference cells in 1D |\n"
<< "| |\n"
<< "| Questions? Contact Pavel Bochev ([email protected]) or |\n"
<< "| Denis Ridzal ([email protected]) or |\n"
<< "| Kyungjoo Kim ([email protected]). |\n"
<< "| |\n"
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n"
<< "| Trilinos website: http://trilinos.sandia.gov |\n"
<< "| |\n"
<< "===============================================================================\n"
<< "| TEST 1: integrals of monomials in 1D |\n"
<< "===============================================================================\n";
typedef Kokkos::DynRankView<ValueType,DeviceSpaceType> DynRankView;
#define ConstructWithLabel(obj, ...) obj(#obj, __VA_ARGS__)
typedef ValueType pointValueType;
typedef ValueType weightValueType;
typedef CubaturePolylib<DeviceSpaceType,pointValueType,weightValueType> CubatureLineType;
const auto tol = 10.0 * tolerence();
int errorFlag = 0;
// open file with analytic values
std::string basedir = "../data";
std::stringstream namestream;
std::string filename;
namestream << basedir << "/EDGE_integrals" << ".dat";
namestream >> filename;
*outStream << "filename = " << filename << std::endl;
std::ifstream filecompare(filename);
*outStream << "\n-> Integrals of monomials on a reference line (edge):\n";
// compute and compare integrals
try {
const auto maxDeg = Parameters::MaxCubatureDegreeEdge;
const auto polySize = maxDeg + 1;
// test inegral values
DynRankView ConstructWithLabel(testInt, maxDeg+1, polySize);
// analytic integral values
DynRankView ConstructWithLabel(analyticInt, maxDeg+1, polySize);
// get analytic values
if (filecompare.is_open()) {
getAnalytic(analyticInt, filecompare);
filecompare.close();
} else {
INTREPID2_TEST_FOR_EXCEPTION( true, std::runtime_error,
">>> ERROR (Integration::Test02): Cannot open analytic solution file" );
}
// storage for cubatrue points and weights
DynRankView ConstructWithLabel(cubPoints,
Parameters::MaxIntegrationPoints,
Parameters::MaxDimension);
DynRankView ConstructWithLabel(cubWeights,
Parameters::MaxIntegrationPoints);
// compute integrals
EPolyType polyType[4] = { POLYTYPE_GAUSS,
POLYTYPE_GAUSS_RADAU_LEFT,
POLYTYPE_GAUSS_RADAU_RIGHT,
POLYTYPE_GAUSS_LOBATTO };
for (size_type pid=0;pid<4;++pid) {
const auto ptype = polyType[pid];
*outStream << "\n -> Testing poly type " << EPolyTypeToString(ptype) << "\n";
for (size_type cubDeg=0;cubDeg<=maxDeg;++cubDeg) {
CubatureLineType lineCub(cubDeg, ptype);
for (auto polyDeg=0;polyDeg<=cubDeg;++polyDeg)
testInt(cubDeg, polyDeg) = computeIntegralOfMonomial<ValueType>(lineCub,
cubPoints,
cubWeights,
polyDeg);
}
// perform comparison
for (size_type cubDeg=0;cubDeg<=maxDeg;++cubDeg) {
for (auto polyDeg=0;polyDeg<=cubDeg;++polyDeg) {
const auto abstol = ( analyticInt(polyDeg,0) == 0 ? tol : std::fabs(tol*analyticInt(polyDeg,0)) );
const auto absdiff = std::fabs(analyticInt(polyDeg,0) - testInt(cubDeg,polyDeg));
*outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
<< "x^" << std::setw(2) << std::left << polyDeg << ":" << " "
<< std::scientific << std::setprecision(16) << testInt(cubDeg,polyDeg) << " " << analyticInt(polyDeg,0) << " "
<< std::setprecision(4) << absdiff << " " << "<?" << " " << abstol << "\n";
if (absdiff > abstol) {
errorFlag++;
*outStream << std::right << std::setw(104) << "^^^^---FAILURE!\n";
}
}
*outStream << "\n";
}
}
} catch (std::logic_error err) {
*outStream << err.what() << "\n";
errorFlag = -1;
}
if (errorFlag != 0)
std::cout << "End Result: TEST FAILED\n";
else
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return errorFlag;
}
int main(int argc, char *argv[]) {
Kokkos::initialize();
//Check number of arguments
if (argc < 4) {
std::cout <<"\n>>> ERROR: Invalid number of arguments.\n\n";
std::cout <<"Usage:\n\n";
std::cout <<" ./Intrepid_example_Drivers_Example_06.exe deg NX NY verbose\n\n";
std::cout <<" where \n";
std::cout <<" int deg - polynomial degree to be used (assumed > 1) \n";
std::cout <<" int NX - num intervals in x direction (assumed box domain, 0,1) \n";
std::cout <<" int NY - num intervals in y direction (assumed box domain, 0,1) \n";
std::cout <<" verbose (optional) - any character, indicates verbose output \n\n";
exit(1);
}
// This little trick lets us print to std::cout only if
// a (dummy) command-line argument is provided.
int iprint = argc - 1;
Teuchos::RCP<std::ostream> outStream;
Teuchos::oblackholestream bhs; // outputs nothing
if (iprint > 2)
outStream = Teuchos::rcp(&std::cout, false);
else
outStream = Teuchos::rcp(&bhs, false);
// Save the format state of the original std::cout.
Teuchos::oblackholestream oldFormatState;
oldFormatState.copyfmt(std::cout);
*outStream \
<< "===============================================================================\n" \
<< "| |\n" \
<< "| Example: Apply Stiffness Matrix for |\n" \
<< "| Poisson Equation on Quadrilateral Mesh |\n" \
<< "| |\n" \
<< "| Questions? Contact Pavel Bochev ([email protected]), |\n" \
<< "| Denis Ridzal ([email protected]), |\n" \
<< "| Kara Peterson ([email protected]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n";
// ************************************ GET INPUTS **************************************
int deg = atoi(argv[1]); // polynomial degree to use
int NX = atoi(argv[2]); // num intervals in x direction (assumed box domain, 0,1)
int NY = atoi(argv[3]); // num intervals in y direction (assumed box domain, 0,1)
// *********************************** CELL TOPOLOGY **********************************
// Get cell topology for base hexahedron
typedef shards::CellTopology CellTopology;
CellTopology quad_4(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
// Get dimensions
int numNodesPerElem = quad_4.getNodeCount();
int spaceDim = quad_4.getDimension();
// *********************************** GENERATE MESH ************************************
*outStream << "Generating mesh ... \n\n";
*outStream << " NX" << " NY\n";
*outStream << std::setw(5) << NX <<
std::setw(5) << NY << "\n\n";
// Print mesh information
int numElems = NX*NY;
int numNodes = (NX+1)*(NY+1);
*outStream << " Number of Elements: " << numElems << " \n";
*outStream << " Number of Nodes: " << numNodes << " \n\n";
// Square
double leftX = 0.0, rightX = 1.0;
double leftY = 0.0, rightY = 1.0;
// Mesh spacing
double hx = (rightX-leftX)/((double)NX);
double hy = (rightY-leftY)/((double)NY);
// Get nodal coordinates
FieldContainer<double> nodeCoord(numNodes, spaceDim);
FieldContainer<int> nodeOnBoundary(numNodes);
int inode = 0;
for (int j=0; j<NY+1; j++) {
for (int i=0; i<NX+1; i++) {
nodeCoord(inode,0) = leftX + (double)i*hx;
nodeCoord(inode,1) = leftY + (double)j*hy;
if (j==0 || i==0 || j==NY || i==NX){
nodeOnBoundary(inode)=1;
}
else {
nodeOnBoundary(inode)=0;
}
inode++;
}
}
#define DUMP_DATA
#ifdef DUMP_DATA
// Print nodal coords
ofstream fcoordout("coords.dat");
for (int i=0; i<numNodes; i++) {
fcoordout << nodeCoord(i,0) <<" ";
fcoordout << nodeCoord(i,1) <<"\n";
}
fcoordout.close();
#endif
// Element to Node map
// We'll keep it around, but this is only the DOFMap if you are in the lowest order case.
FieldContainer<int> elemToNode(numElems, numNodesPerElem);
int ielem = 0;
for (int j=0; j<NY; j++) {
for (int i=0; i<NX; i++) {
elemToNode(ielem,0) = (NX + 1)*j + i;
elemToNode(ielem,1) = (NX + 1)*j + i + 1;
elemToNode(ielem,2) = (NX + 1)*(j + 1) + i + 1;
elemToNode(ielem,3) = (NX + 1)*(j + 1) + i;
ielem++;
}
}
#ifdef DUMP_DATA
// Output connectivity
ofstream fe2nout("elem2node.dat");
for (int j=0; j<NY; j++) {
for (int i=0; i<NX; i++) {
int ielem = i + j * NX;
for (int m=0; m<numNodesPerElem; m++){
fe2nout << elemToNode(ielem,m) <<" ";
}
fe2nout <<"\n";
}
}
fe2nout.close();
#endif
// ************************************ CUBATURE **************************************
*outStream << "Getting cubature ... \n\n";
// Get numerical integration points and weights
DefaultCubatureFactory<double> cubFactory;
int cubDegree = 2*deg;
Teuchos::RCP<Cubature<double> > quadCub = cubFactory.create(quad_4, cubDegree);
int cubDim = quadCub->getDimension();
int numCubPoints = quadCub->getNumPoints();
FieldContainer<double> cubPoints(numCubPoints, cubDim);
FieldContainer<double> cubWeights(numCubPoints);
quadCub->getCubature(cubPoints, cubWeights);
// ************************************** BASIS ***************************************
*outStream << "Getting basis ... \n\n";
// Define basis
Basis_HGRAD_QUAD_Cn_FEM<double, FieldContainer<double> > quadHGradBasis(deg,POINTTYPE_SPECTRAL);
int numFieldsG = quadHGradBasis.getCardinality();
FieldContainer<double> quadGVals(numFieldsG, numCubPoints);
FieldContainer<double> quadGrads(numFieldsG, numCubPoints, spaceDim);
// Evaluate basis values and gradients at cubature points
quadHGradBasis.getValues(quadGVals, cubPoints, OPERATOR_VALUE);
quadHGradBasis.getValues(quadGrads, cubPoints, OPERATOR_GRAD);
// create the local-global mapping for higher order elements
FieldContainer<int> ltgMapping(numElems,numFieldsG);
const int numDOF = (NX*deg+1)*(NY*deg+1);
ielem=0;
for (int j=0;j<NY;j++) {
for (int i=0;i<NX;i++) {
const int start = deg * j * ( NX * deg + 1 ) + i * deg;
// loop over local dof on this cell
int local_dof_cur=0;
for (int vertical=0;vertical<=deg;vertical++) {
for (int horizontal=0;horizontal<=deg;horizontal++) {
ltgMapping(ielem,local_dof_cur) = start + vertical*(NX*deg+1)+horizontal;
local_dof_cur++;
}
}
ielem++;
}
}
#ifdef DUMP_DATA
// Output ltg mapping
// ofstream ltgout("ltg.dat");
// for (int j=0; j<NY; j++) {
// for (int i=0; i<NX; i++) {
// int ielem = i + j * NX;
// for (int m=0; m<numFieldsG; m++){
// ltgout << ltgMapping(ielem,m) <<" ";
// }
// ltgout <<"\n";
// }
// }
// ltgout.close();
#endif
// ******** CREATE A SINGLE STIFFNESS MATRIX, WHICH IS REPLICATED ON ALL ELEMENTS *********
*outStream << "Applying stiffness matrix and right hand side ... \n\n";
// Settings and data structures for mass and stiffness matrices
typedef CellTools<double> CellTools;
typedef FunctionSpaceTools fst;
int numCells = 1;
// Container for nodes
FieldContainer<double> refQuadNodes(numCells, numNodesPerElem, spaceDim);
// Containers for Jacobian
FieldContainer<double> refQuadJacobian(numCells, numCubPoints, spaceDim, spaceDim);
FieldContainer<double> refQuadJacobInv(numCells, numCubPoints, spaceDim, spaceDim);
FieldContainer<double> refQuadJacobDet(numCells, numCubPoints);
// Containers for element HGRAD stiffness matrix
FieldContainer<double> localStiffMatrix(numCells, numFieldsG, numFieldsG);
FieldContainer<double> weightedMeasure(numCells, numCubPoints);
FieldContainer<double> quadGradsTransformed(numCells, numFieldsG, numCubPoints, spaceDim);
FieldContainer<double> quadGradsTransformedWeighted(numCells, numFieldsG, numCubPoints, spaceDim);
// Containers for right hand side vectors
FieldContainer<double> rhsData(numCells, numCubPoints);
FieldContainer<double> localRHS(numCells, numFieldsG);
FieldContainer<double> quadGValsTransformed(numCells, numFieldsG, numCubPoints);
FieldContainer<double> quadGValsTransformedWeighted(numCells, numFieldsG, numCubPoints);
// Container for cubature points in physical space
FieldContainer<double> physCubPoints(numCells, numCubPoints, cubDim);
// Global arrays in Epetra format
Epetra_SerialComm Comm;
Epetra_Map globalMapG(numDOF, 0, Comm);
Epetra_FEVector u(globalMapG);
Epetra_FEVector Ku(globalMapG);
u.Random();
std::cout << "About to start ref element matrix\n";
// ************************** Compute element HGrad stiffness matrices *******************************
refQuadNodes(0,0,0) = 0.0;
refQuadNodes(0,0,1) = 0.0;
refQuadNodes(0,1,0) = hx;
refQuadNodes(0,1,1) = 0.0;
refQuadNodes(0,2,0) = hx;
refQuadNodes(0,2,1) = hy;
refQuadNodes(0,3,0) = 0.0;
refQuadNodes(0,3,1) = hy;
// Compute cell Jacobians, their inverses and their determinants
CellTools::setJacobian(refQuadJacobian, cubPoints, refQuadNodes, quad_4);
CellTools::setJacobianInv(refQuadJacobInv, refQuadJacobian );
CellTools::setJacobianDet(refQuadJacobDet, refQuadJacobian );
// transform from [-1,1]^2 to [0,hx]x[0,hy]
fst::HGRADtransformGRAD<double>(quadGradsTransformed, refQuadJacobInv, quadGrads);
// compute weighted measure
fst::computeCellMeasure<double>(weightedMeasure, refQuadJacobDet, cubWeights);
// multiply values with weighted measure
fst::multiplyMeasure<double>(quadGradsTransformedWeighted,
weightedMeasure, quadGradsTransformed);
// integrate to compute element stiffness matrix
fst::integrate<double>(localStiffMatrix,
quadGradsTransformed, quadGradsTransformedWeighted, COMP_BLAS);
std::cout << "Finished with reference element matrix\n";
// now we will scatter global degrees of freedom, apply the local stiffness matrix
// with BLAS, and then gather the results
FieldContainer<double> uScattered(numElems,numFieldsG);
FieldContainer<double> KuScattered(numElems,numFieldsG);
// to extract info from u
u.GlobalAssemble();
Epetra_Time multTimer(Comm);
Ku.PutScalar(0.0);
Ku.GlobalAssemble();
double *uVals = u[0];
double *KuVals = Ku[0];
Teuchos::BLAS<int,double> blas;
Epetra_Time scatterTime(Comm);
std::cout << "Scattering\n";
// Scatter
for (int k=0; k<numElems; k++)
{
for (int i=0;i<numFieldsG;i++)
{
uScattered(k,i) = uVals[ltgMapping(k,i)];
}
}
const double scatTime = scatterTime.ElapsedTime();
std::cout << "Scattered in time " << scatTime << "\n";
Epetra_Time blasTimer(Comm);
blas.GEMM(Teuchos::NO_TRANS , Teuchos::NO_TRANS ,
numFieldsG , numElems, numFieldsG ,
1.0 ,
&localStiffMatrix(0,0,0) ,
numFieldsG ,
&uScattered(0,0) ,
numFieldsG ,
0.0 ,
&KuScattered(0,0) ,
numFieldsG );
const double blasTime = blasTimer.ElapsedTime();
std::cout << "Element matrices applied in " << blasTime << "\n";
Epetra_Time gatherTimer(Comm);
// Gather
for (int k=0;k<numElems;k++)
{
for (int i=0;i<numFieldsG;i++)
{
KuVals[ltgMapping(k,i)] += KuScattered(k,i);
}
}
const double gatherTime = gatherTimer.ElapsedTime();
std::cout << "Gathered in " << gatherTime << "\n";
const double applyTime = gatherTime + blasTime + scatTime;
std::cout << "Time to do matrix-free product: " << applyTime << std::endl;
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return 0;
}