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;
}
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_HEX_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_HEX_I1_FEM<double, FieldContainer<double> > hexBasis;
int errorFlag = 0;
// Initialize throw counter for exception testing
int nException = 0;
int throwCounter = 0;
// Define array containing the 8 vertices of the reference HEX, its center and 6 face centers
FieldContainer<double> hexNodes(15, 3);
hexNodes(0,0) = -1.0; hexNodes(0,1) = -1.0; hexNodes(0,2) = -1.0;
hexNodes(1,0) = 1.0; hexNodes(1,1) = -1.0; hexNodes(1,2) = -1.0;
hexNodes(2,0) = 1.0; hexNodes(2,1) = 1.0; hexNodes(2,2) = -1.0;
hexNodes(3,0) = -1.0; hexNodes(3,1) = 1.0; hexNodes(3,2) = -1.0;
hexNodes(4,0) = -1.0; hexNodes(4,1) = -1.0; hexNodes(4,2) = 1.0;
hexNodes(5,0) = 1.0; hexNodes(5,1) = -1.0; hexNodes(5,2) = 1.0;
hexNodes(6,0) = 1.0; hexNodes(6,1) = 1.0; hexNodes(6,2) = 1.0;
hexNodes(7,0) = -1.0; hexNodes(7,1) = 1.0; hexNodes(7,2) = 1.0;
hexNodes(8,0) = 0.0; hexNodes(8,1) = 0.0; hexNodes(8,2) = 0.0;
hexNodes(9,0) = 1.0; hexNodes(9,1) = 0.0; hexNodes(9,2) = 0.0;
hexNodes(10,0)= -1.0; hexNodes(10,1)= 0.0; hexNodes(10,2)= 0.0;
hexNodes(11,0)= 0.0; hexNodes(11,1)= 1.0; hexNodes(11,2)= 0.0;
hexNodes(12,0)= 0.0; hexNodes(12,1)= -1.0; hexNodes(12,2)= 0.0;
hexNodes(13,0)= 0.0; hexNodes(13,1)= 0.0; hexNodes(13,2)= 1.0;
hexNodes(14,0)= 0.0; hexNodes(14,1)= 0.0; hexNodes(14,2)= -1.0;
// Generic array for the output values; needs to be properly resized depending on the operator type
FieldContainer<double> vals;
try{
// 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(hexBasis.getCardinality(), hexNodes.dimension(0), 3 );
INTREPID_TEST_COMMAND( hexBasis.getValues(vals, hexNodes, OPERATOR_GRAD), throwCounter, nException );
// exception #2: CURL cannot be applied to HDIV functions
INTREPID_TEST_COMMAND( hexBasis.getValues(vals, hexNodes, 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( hexBasis.getDofOrdinal(3,0,0), throwCounter, nException );
// exception #4
INTREPID_TEST_COMMAND( hexBasis.getDofOrdinal(1,1,1), throwCounter, nException );
// exception #5
INTREPID_TEST_COMMAND( hexBasis.getDofOrdinal(0,4,1), throwCounter, nException );
// exception #6
INTREPID_TEST_COMMAND( hexBasis.getDofTag(12), throwCounter, nException );
// exception #7
INTREPID_TEST_COMMAND( hexBasis.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( hexBasis.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, 2);
INTREPID_TEST_COMMAND( hexBasis.getValues(vals, badPoints2, OPERATOR_VALUE), throwCounter, nException );
// exception #10 output values must be of rank-3 for OPERATOR_VALUE
FieldContainer<double> badVals1(4, 3);
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals1, hexNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #11 output values must be of rank-2 for OPERATOR_DIV
FieldContainer<double> badVals2(4, 3, 3);
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals2, hexNodes, OPERATOR_DIV), throwCounter, nException );
// exception #12 incorrect 0th dimension of output array (must equal number of basis functions)
FieldContainer<double> badVals3(hexBasis.getCardinality() + 1, hexNodes.dimension(0), 3);
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals3, hexNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #13 incorrect 0th dimension of output array (must equal number of basis functions)
FieldContainer<double> badVals4(hexBasis.getCardinality() + 1, hexNodes.dimension(0));
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals4, hexNodes, OPERATOR_DIV), throwCounter, nException );
// exception #14 incorrect 1st dimension of output array (must equal number of points)
FieldContainer<double> badVals5(hexBasis.getCardinality(), hexNodes.dimension(0) + 1, 3);
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals5, hexNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #15 incorrect 1st dimension of output array (must equal number of points)
FieldContainer<double> badVals6(hexBasis.getCardinality(), hexNodes.dimension(0) + 1);
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals6, hexNodes, OPERATOR_DIV), throwCounter, nException );
// exception #16: incorrect 2nd dimension of output array (must equal the space dimension)
FieldContainer<double> badVals7(hexBasis.getCardinality(), hexNodes.dimension(0), 4);
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals7, hexNodes, 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 = hexBasis.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 = hexBasis.getDofOrdinal(allTags[i][0], allTags[i][1], allTags[i][2]);
std::vector<int> myTag = hexBasis.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 < hexBasis.getCardinality(); bfOrd++) {
std::vector<int> myTag = hexBasis.getDofTag(bfOrd);
int myBfOrd = hexBasis.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[] = {
// bottom 4 vertices
0.,-0.25,0., 0.,0.,0., 0.,0.,0., -0.25,0.,0., 0.,0.,-0.25, 0.,0.,0.,
0.,-0.25,0., 0.25,0.,0., 0.,0.,0., 0.,0.,0., 0.,0.,-0.25, 0.,0.,0.,
0.,0.,0., 0.25,0.,0., 0.,0.25,0., 0.,0.,0., 0.,0.,-0.25, 0.,0.,0.,
0.,0.,0., 0.,0.,0., 0.,0.25,0., -0.25,0.,0., 0.,0.,-0.25, 0.,0.,0.,
// top 4 vertices
0.,-0.25,0., 0.,0.,0., 0.,0.,0., -0.25,0.,0., 0.,0.,0., 0.,0.,0.25,
0.,-0.25,0., 0.25,0.,0., 0.,0.,0., 0.,0.,0., 0.,0.,0., 0.,0.,0.25,
0.,0.,0., 0.25,0.,0., 0.,0.25,0., 0.,0.,0., 0.,0.,0., 0.,0.,0.25,
0.,0.,0., 0.,0.,0., 0.,0.25,0., -0.25,0.,0., 0.,0.,0., 0.,0.,0.25,
// center {0, 0, 0}
0.,-0.125,0., 0.125,0.,0., 0.,0.125,0., -0.125,0.,0., 0.,0.,-0.125, 0.,0.,0.125,
// faces { 1, 0, 0} and {-1, 0, 0}
0.,-0.125,0., 0.25,0.,0., 0.,0.125,0., 0.,0.,0., 0.,0.,-0.125, 0.,0.,0.125,
0.,-0.125,0., 0.,0.,0., 0.,0.125,0., -0.25,0.,0., 0.,0.,-0.125, 0.,0.,0.125,
// faces { 0, 1, 0} and { 0,-1, 0}
0.,0.,0., 0.125,0.,0., 0.,0.25,0., -0.125,0.,0., 0.,0.,-0.125, 0.,0.,0.125,
0.,-0.25,0., 0.125,0.,0., 0.,0.,0., -0.125,0.,0., 0.,0.,-0.125, 0.,0.,0.125,
// faces {0, 0, 1} and {0, 0, -1}
0.,-0.125,0., 0.125,0.,0., 0.,0.125,0., -0.125,0.,0., 0.,0.,0., 0.,0.,0.25,
0.,-0.125,0., 0.125,0.,0., 0.,0.125,0., -0.125,0.,0., 0.,0.,-0.25, 0.,0.,0.
};
// DIV: each row gives the 6 correct values of the divergence of the 6 basis functions: (P,F) layout
double basisDivs[] = {
// bottom 4 vertices
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
// top 4 vertices
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
// center {0, 0, 0}
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
// faces { 1, 0, 0} and {-1, 0, 0}
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
// faces { 0, 1, 0} and { 0,-1, 0}
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
// faces {0, 0, 1} and {0, 0, -1}
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
};
try{
// Dimensions for the output arrays:
int numPoints = hexNodes.dimension(0);
int numFields = hexBasis.getCardinality();
int spaceDim = hexBasis.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);
hexBasis.getValues(vals, hexNodes, 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);
hexBasis.getValues(vals, hexNodes, 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;
}
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 (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]). |\n" \
<< "| |\n" \
<< "| Intrepid's website: http://trilinos.sandia.gov/packages/intrepid |\n" \
<< "| Trilinos website: http://trilinos.sandia.gov |\n" \
<< "| |\n" \
<< "===============================================================================\n";
int errorFlag = 0;
typedef FunctionSpaceTools fst;
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 1: correctness of math operations |\n"\
<< "===============================================================================\n";
outStream->precision(20);
try {
shards::CellTopology cellType = shards::getCellTopologyData< shards::Hexahedron<> >(); // cell type: hex
/* Related to cubature. */
DefaultCubatureFactory<double> cubFactory; // create cubature factory
int cubDegree = 20; // cubature degree
Teuchos::RCP<Cubature<double> > myCub = cubFactory.create(cellType, cubDegree); // create default cubature
int spaceDim = myCub->getDimension(); // get spatial dimension
int numCubPoints = myCub->getNumPoints(); // get number of cubature points
/* Related to basis. */
Basis_HDIV_HEX_I1_FEM<double, FieldContainer<double> > hexBasis; // create H-div basis on a hex
int numFields = hexBasis.getCardinality(); // get basis cardinality
/* Cell geometries and orientations. */
int numCells = 4;
int numNodes = 8;
int numCellData = numCells*numNodes*spaceDim;
int numSignData = numCells*numFields;
double 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
};
short 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. */
FieldContainer<double> cub_points(numCubPoints, spaceDim);
FieldContainer<double> cub_weights(numCubPoints);
FieldContainer<double> cell_nodes(numCells, numNodes, spaceDim);
FieldContainer<short> field_signs(numCells, numFields);
FieldContainer<double> jacobian(numCells, numCubPoints, spaceDim, spaceDim);
//FieldContainer<double> jacobian_inv(numCells, numCubPoints, spaceDim, spaceDim);
FieldContainer<double> jacobian_det(numCells, numCubPoints);
FieldContainer<double> weighted_measure(numCells, numCubPoints);
FieldContainer<double> div_of_basis_at_cub_points(numFields, numCubPoints);
FieldContainer<double> transformed_div_of_basis_at_cub_points(numCells, numFields, numCubPoints);
FieldContainer<double> weighted_transformed_div_of_basis_at_cub_points(numCells, numFields, numCubPoints);
FieldContainer<double> stiffness_matrices(numCells, numFields, numFields);
FieldContainer<double> value_of_basis_at_cub_points(numFields, numCubPoints, spaceDim);
FieldContainer<double> transformed_value_of_basis_at_cub_points(numCells, numFields, numCubPoints, spaceDim);
FieldContainer<double> weighted_transformed_value_of_basis_at_cub_points(numCells, numFields, numCubPoints, spaceDim);
FieldContainer<double> 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(hexnodes, numCellData);
// set basis function signs, for each cell
field_signs.setValues(facesigns, numSignData);
// 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 divergences of basis functions at (reference) cubature points
hexBasis.getValues(div_of_basis_at_cub_points, cub_points, OPERATOR_DIV);
// transform divergences of basis functions
fst::HDIVtransformDIV<double>(transformed_div_of_basis_at_cub_points,
jacobian_det,
div_of_basis_at_cub_points);
// multiply with weighted measure
fst::multiplyMeasure<double>(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<double>(transformed_div_of_basis_at_cub_points, field_signs);
fst::applyFieldSigns<double>(weighted_transformed_div_of_basis_at_cub_points, field_signs);
// compute stiffness matrices
fst::integrate<double>(stiffness_matrices,
transformed_div_of_basis_at_cub_points,
weighted_transformed_div_of_basis_at_cub_points,
COMP_CPP);
// Computing mass matrices:
// tabulate values of basis functions at (reference) cubature points
hexBasis.getValues(value_of_basis_at_cub_points, cub_points, OPERATOR_VALUE);
// transform values of basis functions
fst::HDIVtransformVALUE<double>(transformed_value_of_basis_at_cub_points,
jacobian,
jacobian_det,
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);
// apply field signs
fst::applyLeftFieldSigns<double>(mass_matrices, field_signs);
fst::applyRightFieldSigns<double>(mass_matrices, field_signs);
/******************* STOP COMPUTATION ***********************/
/******************* START COMPARISON ***********************/
string basedir = "./testdata";
for (int cell_id = 0; cell_id < numCells-1; cell_id++) {
stringstream namestream;
string filename;
namestream << basedir << "/mass_HDIV_HEX_I1_FEM" << "_" << "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, iprint) > 0)
errorFlag++;
massfile.close();
}
else {
errorFlag = -1;
std::cout << "End Result: TEST FAILED\n";
return errorFlag;
}
namestream.clear();
namestream << basedir << "/stiff_HDIV_HEX_I1_FEM" << "_" << "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, iprint) > 0)
errorFlag++;
stifffile.close();
}
else {
errorFlag = -1;
std::cout << "End Result: TEST FAILED\n";
return errorFlag;
}
}
for (int cell_id = 3; cell_id < numCells; cell_id++) {
stringstream namestream;
string filename;
namestream << basedir << "/mass_fp_HDIV_HEX_I1_FEM" << "_" << "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-4, iprint, INTREPID2_UTILS_SCALAR) > 0)
errorFlag++;
massfile.close();
}
else {
errorFlag = -1;
std::cout << "End Result: TEST FAILED\n";
return errorFlag;
}
namestream.clear();
namestream << basedir << "/stiff_fp_HDIV_HEX_I1_FEM" << "_" << "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-4, iprint, INTREPID2_UTILS_SCALAR) > 0)
errorFlag++;
stifffile.close();
}
else {
errorFlag = -1;
std::cout << "End Result: TEST FAILED\n";
return errorFlag;
}
}
/******************* STOP COMPARISON ***********************/
*outStream << "\n";
}// try Basis_HDIV_HEX_I1
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);
Kokkos::finalize();
return errorFlag;
}
int main(int argc, char *argv[]) {
//Check number of arguments
if (argc < 13) {
std::cout <<"\n>>> ERROR: Invalid number of arguments.\n\n";
std::cout <<"Usage:\n\n";
std::cout <<" ./Intrepid_example_Drivers_Example_02.exe NX NY NZ randomMesh mu1 mu2 mu1LX mu1RX mu1LY mu1RY mu1LZ mu1RZ verbose\n\n";
std::cout <<" where \n";
std::cout <<" int NX - num intervals in x direction (assumed box domain, -1,1) \n";
std::cout <<" int NY - num intervals in y direction (assumed box domain, -1,1) \n";
std::cout <<" int NZ - num intervals in z direction (assumed box domain, -1,1) \n";
std::cout <<" int randomMesh - 1 if mesh randomizer is to be used 0 if not \n";
std::cout <<" double mu1 - material property value for region 1 \n";
std::cout <<" double mu2 - material property value for region 2 \n";
std::cout <<" double mu1LX - left X boundary for region 1 \n";
std::cout <<" double mu1RX - right X boundary for region 1 \n";
std::cout <<" double mu1LY - left Y boundary for region 1 \n";
std::cout <<" double mu1RY - right Y boundary for region 1 \n";
std::cout <<" double mu1LZ - bottom Z boundary for region 1 \n";
std::cout <<" double mu1RZ - top Z boundary for region 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 > 12)
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 Mass and Stiffness Matrices and Right-Hand Side Vector |\n"
<< "| for Div-Curl System on Hexahedral Mesh with Div-Conforming Elements |\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 **************************************
/* In the implementation for discontinuous material properties only the boundaries for
region 1, associated with mu1, are input. The remainder of the grid is assumed to use mu2.
Note that the material properties are assigned using the undeformed grid. */
int NX = atoi(argv[1]); // num intervals in x direction (assumed box domain, -1,1)
int NY = atoi(argv[2]); // num intervals in y direction (assumed box domain, -1,1)
int NZ = atoi(argv[3]); // num intervals in z direction (assumed box domain, -1,1)
int randomMesh = atoi(argv[4]); // 1 if mesh randomizer is to be used 0 if not
double mu1 = atof(argv[5]); // material property value for region 1
double mu2 = atof(argv[6]); // material property value for region 2
double mu1LeftX = atof(argv[7]); // left X boundary for region 1
double mu1RightX = atof(argv[8]); // right X boundary for region 1
double mu1LeftY = atof(argv[9]); // left Y boundary for region 1
double mu1RightY = atof(argv[10]); // right Y boundary for region 1
double mu1LeftZ = atof(argv[11]); // left Z boundary for region 1
double mu1RightZ = atof(argv[12]); // right Z boundary for region 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 numEdgesPerElem = hex_8.getEdgeCount();
int numFacesPerElem = hex_8.getSideCount();
int numNodesPerEdge = 2;
int numNodesPerFace = 4;
int numEdgesPerFace = 4;
int spaceDim = hex_8.getDimension();
// Build reference element edge to node map
FieldContainer<int> refEdgeToNode(numEdgesPerElem,numNodesPerEdge);
for (int i=0; i<numEdgesPerElem; i++){
refEdgeToNode(i,0)=hex_8.getNodeMap(1, i, 0);
refEdgeToNode(i,1)=hex_8.getNodeMap(1, i, 1);
}
// Build reference element face to node map
FieldContainer<int> refFaceToNode(numFacesPerElem,numNodesPerFace);
for (int i=0; i<numFacesPerElem; i++){
refFaceToNode(i,0)=hex_8.getNodeMap(2, i, 0);
refFaceToNode(i,1)=hex_8.getNodeMap(2, i, 1);
refFaceToNode(i,2)=hex_8.getNodeMap(2, i, 2);
refFaceToNode(i,3)=hex_8.getNodeMap(2, i, 3);
}
// *********************************** 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);
int numEdges = (NX)*(NY + 1)*(NZ + 1) + (NX + 1)*(NY)*(NZ + 1) + (NX + 1)*(NY + 1)*(NZ);
int numFaces = (NX)*(NY)*(NZ + 1) + (NX)*(NY + 1)*(NZ) + (NX + 1)*(NY)*(NZ);
*outStream << " Number of Elements: " << numElems << " \n";
*outStream << " Number of Nodes: " << numNodes << " \n";
*outStream << " Number of Edges: " << numEdges << " \n";
*outStream << " Number of Faces: " << numFaces << " \n\n";
// Cube
double leftX = -1.0, rightX = 1.0;
double leftY = -1.0, rightY = 1.0;
double leftZ = -1.0, 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;
}
inode++;
}
}
}
// 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++;
}
}
}
// Get edge connectivity
FieldContainer<int> edgeToNode(numEdges, numNodesPerEdge);
FieldContainer<int> elemToEdge(numElems, numEdgesPerElem);
int iedge = 0;
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++) {
if (i < NX){
edgeToNode(iedge,0) = inode;
edgeToNode(iedge,1) = inode + 1;
if (j < NY && k < NZ){
ielem=i+j*NX+k*NX*NY;
elemToEdge(ielem,0) = iedge;
if (j > 0)
elemToEdge(ielem-NX,2) = iedge;
if (k > 0)
elemToEdge(ielem-NX*NY,4) = iedge;
if (j > 0 && k > 0)
elemToEdge(ielem-NX*NY-NX,6) = iedge;
}
else if (j == NY && k == NZ){
ielem=i+(NY-1)*NX+(NZ-1)*NX*NY;
elemToEdge(ielem,6) = iedge;
}
else if (k == NZ && j < NY){
ielem=i+j*NX+(NZ-1)*NX*NY;
elemToEdge(ielem,4) = iedge;
if (j > 0)
elemToEdge(ielem-NX,6) = iedge;
}
else if (k < NZ && j == NY){
ielem=i+(NY-1)*NX+k*NX*NY;
elemToEdge(ielem,2) = iedge;
if (k > 0)
elemToEdge(ielem-NX*NY,6) = iedge;
}
iedge++;
}
if (j < NY){
edgeToNode(iedge,0) = inode;
edgeToNode(iedge,1) = inode + NX+1;
if (i < NX && k < NZ){
ielem=i+j*NX+k*NX*NY;
elemToEdge(ielem,3) = iedge;
if (i > 0)
elemToEdge(ielem-1,1) = iedge;
if (k > 0)
elemToEdge(ielem-NX*NY,7) = iedge;
if (i > 0 && k > 0)
elemToEdge(ielem-NX*NY-1,5) = iedge;
}
else if (i == NX && k == NZ){
ielem=NX-1+j*NX+(NZ-1)*NX*NY;
elemToEdge(ielem,5) = iedge;
}
else if (k == NZ && i < NX){
ielem=i+j*NX+(NZ-1)*NX*NY;
elemToEdge(ielem,7) = iedge;
if (i > 0)
elemToEdge(ielem-1,5) = iedge;
}
else if (k < NZ && i == NX){
ielem=NX-1+j*NX+k*NX*NY;
elemToEdge(ielem,1) = iedge;
if (k > 0)
elemToEdge(ielem-NX*NY,5) = iedge;
}
iedge++;
}
if (k < NZ){
edgeToNode(iedge,0) = inode;
edgeToNode(iedge,1) = inode + (NX+1)*(NY+1);
if (i < NX && j < NY){
ielem=i+j*NX+k*NX*NY;
elemToEdge(ielem,8) = iedge;
if (i > 0)
elemToEdge(ielem-1,9) = iedge;
if (j > 0)
elemToEdge(ielem-NX,11) = iedge;
if (i > 0 && j > 0)
elemToEdge(ielem-NX-1,10) = iedge;
}
else if (i == NX && j == NY){
ielem=NX-1+(NY-1)*NX+k*NX*NY;
elemToEdge(ielem,10) = iedge;
}
else if (j == NY && i < NX){
ielem=i+(NY-1)*NX+k*NX*NY;
elemToEdge(ielem,11) = iedge;
if (i > 0)
elemToEdge(ielem-1,10) = iedge;
}
else if (j < NY && i == NX){
ielem=NX-1+j*NX+k*NX*NY;
elemToEdge(ielem,9) = iedge;
if (j > 0)
elemToEdge(ielem-NX,10) = iedge;
}
iedge++;
}
inode++;
}
}
}
// Find boundary edges
FieldContainer<int> edgeOnBoundary(numEdges);
for (int i=0; i<numEdges; i++){
if (nodeOnBoundary(edgeToNode(i,0)) && nodeOnBoundary(edgeToNode(i,1))){
edgeOnBoundary(i)=1;
}
}
// Get face connectivity
FieldContainer<int> faceToNode(numFaces, numNodesPerFace);
FieldContainer<int> elemToFace(numElems, numFacesPerElem);
FieldContainer<int> faceToEdge(numFaces, numEdgesPerFace);
int iface = 0;
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++) {
if (i < NX && k < NZ) {
faceToNode(iface,0)=inode;
faceToNode(iface,1)=inode + 1;
faceToNode(iface,2)=inode + (NX+1)*(NY+1)+1;
faceToNode(iface,3)=inode + (NX+1)*(NY+1);
if (j < NY) {
ielem=i+j*NX+k*NX*NY;
faceToEdge(iface,0)=elemToEdge(ielem,0);
faceToEdge(iface,1)=elemToEdge(ielem,9);
faceToEdge(iface,2)=elemToEdge(ielem,4);
faceToEdge(iface,3)=elemToEdge(ielem,8);
elemToFace(ielem,0)=iface;
if (j > 0) {
elemToFace(ielem-NX,2)=iface;
}
}
else if (j == NY) {
ielem=i+(NY-1)*NX+k*NX*NY;
faceToEdge(iface,0)=elemToEdge(ielem,2);
faceToEdge(iface,1)=elemToEdge(ielem,10);
faceToEdge(iface,2)=elemToEdge(ielem,6);
faceToEdge(iface,3)=elemToEdge(ielem,11);
elemToFace(ielem,2)=iface;
}
iface++;
}
if (j < NY && k < NZ) {
faceToNode(iface,0)=inode;
faceToNode(iface,1)=inode + NX+1;
faceToNode(iface,2)=inode + (NX+1)*(NY+1) + NX+1;
faceToNode(iface,3)=inode + (NX+1)*(NY+1);
if (i < NX) {
ielem=i+j*NX+k*NX*NY;
faceToEdge(iface,0)=elemToEdge(ielem,3);
faceToEdge(iface,1)=elemToEdge(ielem,11);
faceToEdge(iface,2)=elemToEdge(ielem,7);
faceToEdge(iface,3)=elemToEdge(ielem,8);
elemToFace(ielem,3)=iface;
if (i > 0) {
elemToFace(ielem-1,1)=iface;
}
}
else if (i == NX) {
ielem=NX-1+j*NX+k*NX*NY;
faceToEdge(iface,0)=elemToEdge(ielem,1);
faceToEdge(iface,1)=elemToEdge(ielem,10);
faceToEdge(iface,2)=elemToEdge(ielem,5);
faceToEdge(iface,3)=elemToEdge(ielem,9);
elemToFace(ielem,1)=iface;
}
iface++;
}
if (i < NX && j < NY) {
faceToNode(iface,0)=inode;
faceToNode(iface,1)=inode + 1;
faceToNode(iface,2)=inode + NX+2;
faceToNode(iface,3)=inode + NX+1;
if (k < NZ) {
ielem=i+j*NX+k*NX*NY;
faceToEdge(iface,0)=elemToEdge(ielem,0);
faceToEdge(iface,1)=elemToEdge(ielem,1);
faceToEdge(iface,2)=elemToEdge(ielem,2);
faceToEdge(iface,3)=elemToEdge(ielem,3);
elemToFace(ielem,4)=iface;
if (k > 0) {
elemToFace(ielem-NX*NY,5)=iface;
}
}
else if (k == NZ) {
ielem=i+j*NX+(NZ-1)*NX*NY;
faceToEdge(iface,0)=elemToEdge(ielem,4);
faceToEdge(iface,1)=elemToEdge(ielem,5);
faceToEdge(iface,2)=elemToEdge(ielem,6);
faceToEdge(iface,3)=elemToEdge(ielem,7);
elemToFace(ielem,5)=iface;
}
iface++;
}
inode++;
}
}
}
// Find boundary faces
FieldContainer<int> faceOnBoundary(numFaces);
for (int i=0; i<numFaces; i++){
if (nodeOnBoundary(faceToNode(i,0)) && nodeOnBoundary(faceToNode(i,1))
&& nodeOnBoundary(faceToNode(i,2)) && nodeOnBoundary(faceToNode(i,3))){
faceOnBoundary(i)=1;
}
}
#define DUMP_DATA
#ifdef DUMP_DATA
// Output connectivity
ofstream fe2nout("elem2node.dat");
ofstream fe2fout("elem2face.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";
for (int n=0; n<numFacesPerElem; n++) {
fe2fout << elemToFace(ielem,n) << " ";
}
fe2fout << "\n";
}
}
}
fe2nout.close();
fe2fout.close();
#endif
#ifdef DUMP_DATA_EXTRA
ofstream ff2nout("face2node.dat");
ofstream ff2eout("face2edge.dat");
for (int i=0; i<numFaces; i++) {
for (int j=0; j<numNodesPerFace; j++) {
ff2nout << faceToNode(i,j) << " ";
}
for (int k=0; k<numEdgesPerFace; k++) {
ff2eout << faceToEdge(i,k) << " ";
}
ff2nout << "\n";
ff2eout << "\n";
}
ff2nout.close();
ff2eout.close();
ofstream fBnodeout("nodeOnBndy.dat");
ofstream fBfaceout("faceOnBndy.dat");
for (int i=0; i<numNodes; i++) {
fBnodeout << nodeOnBoundary(i) <<"\n";
}
for (int i=0; i<numFaces; i++) {
fBfaceout << faceOnBoundary(i) <<"\n";
}
fBnodeout.close();
fBfaceout.close();
#endif
// Set material properties using undeformed grid assuming each element has only one value of mu
FieldContainer<double> muVal(numElems);
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;
double midElemX = nodeCoord(elemToNode(ielem,0),0) + hx/2.0;
double midElemY = nodeCoord(elemToNode(ielem,0),1) + hy/2.0;
double midElemZ = nodeCoord(elemToNode(ielem,0),2) + hz/2.0;
if ( (midElemX > mu1LeftX) && (midElemY > mu1LeftY) && (midElemZ > mu1LeftZ) &&
(midElemX <= mu1RightX) && (midElemY <= mu1RightY) && (midElemZ <= mu1RightZ) ){
muVal(ielem) = mu1;
}
else {
muVal(ielem) = mu2;
}
}
}
}
// Perturb mesh coordinates (only interior nodes)
if (randomMesh){
for (int k=1; k<NZ; k++) {
for (int j=1; j<NY; j++) {
for (int i=1; i<NX; i++) {
int inode = i + j * (NX + 1) + k * (NX + 1) * (NY + 1);
// random numbers between -1.0 and 1.0
double rx = 2.0 * (double)rand()/RAND_MAX - 1.0;
double ry = 2.0 * (double)rand()/RAND_MAX - 1.0;
double rz = 2.0 * (double)rand()/RAND_MAX - 1.0;
// limit variation to 1/4 edge length
nodeCoord(inode,0) = nodeCoord(inode,0) + 0.125 * hx * rx;
nodeCoord(inode,1) = nodeCoord(inode,1) + 0.125 * hy * ry;
nodeCoord(inode,2) = nodeCoord(inode,2) + 0.125 * hz * rz;
}
}
}
}
#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
// **************************** INCIDENCE MATRIX **************************************
// Edge to face incidence matrix
*outStream << "Building incidence matrix ... \n\n";
Epetra_SerialComm Comm;
Epetra_Map globalMapD(numFaces, 0, Comm);
Epetra_Map globalMapC(numEdges, 0, Comm);
Epetra_FECrsMatrix DCurl(Copy, globalMapD, globalMapC, 2);
double vals[4];
vals[0]=1.0; vals[1]=1.0; vals[2]=-1.0; vals[3]=-1.0;
for (int j=0; j<numFaces; j++){
int rowNum = j;
int colNum[4];
colNum[0] = faceToEdge(j,0);
colNum[1] = faceToEdge(j,1);
colNum[2] = faceToEdge(j,2);
colNum[3] = faceToEdge(j,3);
DCurl.InsertGlobalValues(1, &rowNum, 4, colNum, vals);
}
// ************************************ CUBATURE **************************************
// Get numerical integration points and weights
*outStream << "Getting cubature ... \n\n";
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);
// Get numerical integration points and weights for hexahedron face
// (needed for rhs boundary term)
// Define topology of the face parametrization domain as [-1,1]x[-1,1]
CellTopology paramQuadFace(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
// Define cubature
DefaultCubatureFactory<double> cubFactoryFace;
Teuchos::RCP<Cubature<double> > hexFaceCubature = cubFactoryFace.create(paramQuadFace, 3);
int cubFaceDim = hexFaceCubature -> getDimension();
int numFacePoints = hexFaceCubature -> getNumPoints();
// Define storage for cubature points and weights on [-1,1]x[-1,1]
FieldContainer<double> paramGaussWeights(numFacePoints);
FieldContainer<double> paramGaussPoints(numFacePoints,cubFaceDim);
// Define storage for cubature points on workset faces
hexFaceCubature -> getCubature(paramGaussPoints, paramGaussWeights);
// ************************************** BASIS ***************************************
// Define basis
*outStream << "Getting basis ... \n\n";
Basis_HCURL_HEX_I1_FEM<double, FieldContainer<double> > hexHCurlBasis;
Basis_HDIV_HEX_I1_FEM<double, FieldContainer<double> > hexHDivBasis;
int numFieldsC = hexHCurlBasis.getCardinality();
int numFieldsD = hexHDivBasis.getCardinality();
// Evaluate basis at cubature points
FieldContainer<double> hexCVals(numFieldsC, numCubPoints, spaceDim);
FieldContainer<double> hexDVals(numFieldsD, numCubPoints, spaceDim);
FieldContainer<double> hexDivs(numFieldsD, numCubPoints);
FieldContainer<double> worksetDVals(numFieldsD, numFacePoints, spaceDim);
hexHCurlBasis.getValues(hexCVals, cubPoints, OPERATOR_VALUE);
hexHDivBasis.getValues(hexDVals, cubPoints, OPERATOR_VALUE);
hexHDivBasis.getValues(hexDivs, cubPoints, OPERATOR_DIV);
// ******** LOOP OVER ELEMENTS TO CREATE LOCAL MASS and STIFFNESS MATRICES *************
*outStream << "Building mass and stiffness matrices ... \n\n";
// Settings and data structures for mass and stiffness matrices
typedef CellTools<double> CellTools;
typedef FunctionSpaceTools fst;
int numCells = 1;
// Containers for nodes, edge and face signs
FieldContainer<double> hexNodes(numCells, numNodesPerElem, spaceDim);
FieldContainer<double> hexEdgeSigns(numCells, numFieldsC);
FieldContainer<double> hexFaceSigns(numCells, numFieldsD);
// 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 HCURL mass matrix
FieldContainer<double> massMatrixC(numCells, numFieldsC, numFieldsC);
FieldContainer<double> weightedMeasure(numCells, numCubPoints);
FieldContainer<double> weightedMeasureMuInv(numCells, numCubPoints);
FieldContainer<double> hexCValsTransformed(numCells, numFieldsC, numCubPoints, spaceDim);
FieldContainer<double> hexCValsTransformedWeighted(numCells, numFieldsC, numCubPoints, spaceDim);
// Containers for element HDIV mass matrix
FieldContainer<double> massMatrixD(numCells, numFieldsD, numFieldsD);
FieldContainer<double> weightedMeasureMu(numCells, numCubPoints);
FieldContainer<double> hexDValsTransformed(numCells, numFieldsD, numCubPoints, spaceDim);
FieldContainer<double> hexDValsTransformedWeighted(numCells, numFieldsD, numCubPoints, spaceDim);
// Containers for element HDIV stiffness matrix
FieldContainer<double> stiffMatrixD(numCells, numFieldsD, numFieldsD);
FieldContainer<double> hexDivsTransformed(numCells, numFieldsD, numCubPoints);
FieldContainer<double> hexDivsTransformedWeighted(numCells, numFieldsD, numCubPoints);
// Containers for right hand side vectors
FieldContainer<double> rhsDatag(numCells, numCubPoints, cubDim);
FieldContainer<double> rhsDatah(numCells, numCubPoints);
FieldContainer<double> gD(numCells, numFieldsD);
FieldContainer<double> hD(numCells, numFieldsD);
FieldContainer<double> gDBoundary(numCells, numFieldsD);
FieldContainer<double> refGaussPoints(numFacePoints,spaceDim);
FieldContainer<double> worksetGaussPoints(numCells,numFacePoints,spaceDim);
FieldContainer<double> worksetJacobians(numCells, numFacePoints, spaceDim, spaceDim);
FieldContainer<double> worksetJacobDet(numCells, numFacePoints);
FieldContainer<double> worksetFaceN(numCells, numFacePoints, spaceDim);
FieldContainer<double> worksetVFieldVals(numCells, numFacePoints, spaceDim);
FieldContainer<double> worksetDValsTransformed(numCells, numFieldsD, numFacePoints, spaceDim);
FieldContainer<double> curluFace(numCells, numFacePoints, spaceDim);
FieldContainer<double> worksetDataCrossField(numCells, numFieldsD, numFacePoints, spaceDim);
// Container for cubature points in physical space
FieldContainer<double> physCubPoints(numCells,numCubPoints, cubDim);
// Global arrays in Epetra format
Epetra_FECrsMatrix MassC(Copy, globalMapC, numFieldsC);
Epetra_FECrsMatrix MassD(Copy, globalMapD, numFieldsD);
Epetra_FECrsMatrix StiffD(Copy, globalMapD, numFieldsD);
Epetra_FEVector rhsD(globalMapD);
#ifdef DUMP_DATA
ofstream fSignsout("faceSigns.dat");
#endif
// *** 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);
}
// Face signs
for (int j=0; j<numFacesPerElem; j++) {
hexFaceSigns(0,j) = -1.0;
for (int i=0; i<numNodesPerFace; i++) {
int indf=i+1;
if (indf > numNodesPerFace) indf=0;
if (elemToNode(k,refFaceToNode(j,0))==faceToNode(elemToFace(k,j),i) &&
elemToNode(k,refFaceToNode(j,1))==faceToNode(elemToFace(k,j),indf))
hexFaceSigns(0,j) = 1.0;
}
#ifdef DUMP_DATA
fSignsout << hexFaceSigns(0,j) << " ";
#endif
}
#ifdef DUMP_DATA
fSignsout << "\n";
#endif
// Edge signs
for (int j=0; j<numEdgesPerElem; j++) {
if (elemToNode(k,refEdgeToNode(j,0))==edgeToNode(elemToEdge(k,j),0) &&
elemToNode(k,refEdgeToNode(j,1))==edgeToNode(elemToEdge(k,j),1))
hexEdgeSigns(0,j) = 1.0;
else
hexEdgeSigns(0,j) = -1.0;
}
// 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 HCurl mass matrices *******************************
// transform to physical coordinates
fst::HCURLtransformVALUE<double>(hexCValsTransformed, hexJacobInv,
hexCVals);
// compute weighted measure
fst::computeCellMeasure<double>(weightedMeasure, hexJacobDet, cubWeights);
// multiply by weighted measure
fst::multiplyMeasure<double>(hexCValsTransformedWeighted,
weightedMeasure, hexCValsTransformed);
// integrate to compute element mass matrix
fst::integrate<double>(massMatrixC,
hexCValsTransformed, hexCValsTransformedWeighted,
COMP_CPP);
// apply edge signs
fst::applyLeftFieldSigns<double>(massMatrixC, hexEdgeSigns);
fst::applyRightFieldSigns<double>(massMatrixC, hexEdgeSigns);
// assemble into global matrix
for (int row = 0; row < numFieldsC; row++){
for (int col = 0; col < numFieldsC; col++){
int rowIndex = elemToEdge(k,row);
int colIndex = elemToEdge(k,col);
double val = massMatrixC(0,row,col);
MassC.InsertGlobalValues(1, &rowIndex, 1, &colIndex, &val);
}
}
// ************************** Compute element HDiv mass matrices *******************************
// transform to physical coordinates
fst::HDIVtransformVALUE<double>(hexDValsTransformed, hexJacobian, hexJacobDet,
hexDVals);
// multiply by weighted measure
fst::multiplyMeasure<double>(hexDValsTransformedWeighted,
weightedMeasure, hexDValsTransformed);
// integrate to compute element mass matrix
fst::integrate<double>(massMatrixD,
hexDValsTransformed, hexDValsTransformedWeighted,
COMP_CPP);
// apply face signs
fst::applyLeftFieldSigns<double>(massMatrixD, hexFaceSigns);
fst::applyRightFieldSigns<double>(massMatrixD, hexFaceSigns);
// assemble into global matrix
for (int row = 0; row < numFieldsD; row++){
for (int col = 0; col < numFieldsD; col++){
int rowIndex = elemToFace(k,row);
int colIndex = elemToFace(k,col);
double val = massMatrixD(0,row,col);
MassD.InsertGlobalValues(1, &rowIndex, 1, &colIndex, &val);
}
}
// ************************ Compute element HDiv stiffness matrices *****************************
// transform to physical coordinates
fst::HDIVtransformDIV<double>(hexDivsTransformed, hexJacobDet,
hexDivs);
// multiply by weighted measure
fst::multiplyMeasure<double>(hexDivsTransformedWeighted,
weightedMeasure, hexDivsTransformed);
// integrate to compute element stiffness matrix
fst::integrate<double>(stiffMatrixD,
hexDivsTransformed, hexDivsTransformedWeighted,
COMP_CPP);
// apply face signs
fst::applyLeftFieldSigns<double>(stiffMatrixD, hexFaceSigns);
fst::applyRightFieldSigns<double>(stiffMatrixD, hexFaceSigns);
// assemble into global matrix
for (int row = 0; row < numFieldsD; row++){
for (int col = 0; col < numFieldsD; col++){
int rowIndex = elemToFace(k,row);
int colIndex = elemToFace(k,col);
double val = stiffMatrixD(0,row,col);
StiffD.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 functions 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);
double du1, du2, du3;
evalCurlCurlu(du1, du2, du3, x, y, z);
rhsDatag(0,nPt,0) = du1;
rhsDatag(0,nPt,1) = du2;
rhsDatag(0,nPt,2) = du3;
rhsDatah(0,nPt) = evalDivu(x, y, z);
}
// integrate (curl g, w) term
fst::integrate<double>(gD, rhsDatag, hexDValsTransformedWeighted,
COMP_CPP);
// integrate (h,div w) term
fst::integrate<double>(hD, rhsDatah, hexDivsTransformedWeighted,
COMP_CPP);
// apply signs
fst::applyFieldSigns<double>(gD, hexFaceSigns);
fst::applyFieldSigns<double>(hD, hexFaceSigns);
// calculate boundary term, (g x w, n)_{\Gamma}
for (int i = 0; i < numFacesPerElem; i++){
if (faceOnBoundary(elemToFace(k,i))){
// map Gauss points on quad to reference face: paramGaussPoints -> refGaussPoints
CellTools::mapToReferenceSubcell(refGaussPoints,
paramGaussPoints,
2, i, hex_8);
// get basis values at points on reference cell
hexHDivBasis.getValues(worksetDVals, refGaussPoints, OPERATOR_VALUE);
// compute Jacobians at Gauss pts. on reference face for all parent cells
CellTools::setJacobian(worksetJacobians, refGaussPoints,
hexNodes, hex_8);
CellTools::setJacobianDet(worksetJacobDet, worksetJacobians);
// transform to physical coordinates
fst::HDIVtransformVALUE<double>(worksetDValsTransformed, worksetJacobians,
worksetJacobDet, worksetDVals);
// map Gauss points on quad from ref. face to face workset: refGaussPoints -> worksetGaussPoints
CellTools::mapToPhysicalFrame(worksetGaussPoints,
refGaussPoints,
hexNodes, hex_8);
// compute face normals
CellTools::getPhysicalFaceNormals(worksetFaceN,
worksetJacobians,
i, hex_8);
// evaluate curl u at face points
for(int nPt = 0; nPt < numFacePoints; nPt++){
double x = worksetGaussPoints(0, nPt, 0);
double y = worksetGaussPoints(0, nPt, 1);
double z = worksetGaussPoints(0, nPt, 2);
evalCurlu(curluFace(0,nPt,0), curluFace(0,nPt,1), curluFace(0,nPt,2), x, y, z);
}
// compute the cross product of curluFace with basis and multiply by weights
for (int nF = 0; nF < numFieldsD; nF++){
for(int nPt = 0; nPt < numFacePoints; nPt++){
worksetDataCrossField(0,nF,nPt,0) = (curluFace(0,nPt,1)*worksetDValsTransformed(0,nF,nPt,2)
- curluFace(0,nPt,2)*worksetDValsTransformed(0,nF,nPt,1))
* paramGaussWeights(nPt);
worksetDataCrossField(0,nF,nPt,1) = (curluFace(0,nPt,2)*worksetDValsTransformed(0,nF,nPt,0)
- curluFace(0,nPt,0)*worksetDValsTransformed(0,nF,nPt,2))
* paramGaussWeights(nPt);
worksetDataCrossField(0,nF,nPt,2) = (curluFace(0,nPt,0)*worksetDValsTransformed(0,nF,nPt,1)
- curluFace(0,nPt,1)*worksetDValsTransformed(0,nF,nPt,0))
*paramGaussWeights(nPt);
} //nPt
} //nF
// Integrate
fst::integrate<double>(gDBoundary, worksetFaceN, worksetDataCrossField,
COMP_CPP);
// apply signs
fst::applyFieldSigns<double>(gDBoundary, hexFaceSigns);
// add into gD term
for (int nF = 0; nF < numFieldsD; nF++){
gD(0,nF) = gD(0,nF) - gDBoundary(0,nF);
}
} // if faceOnBoundary
} // numFaces
// assemble into global vector
for (int row = 0; row < numFieldsD; row++){
int rowIndex = elemToFace(k,row);
double val = hD(0,row)+gD(0,row);
rhsD.SumIntoGlobalValues(1, &rowIndex, &val);
}
} // *** end element loop ***
// Assemble over multiple processors, if necessary
DCurl.GlobalAssemble(); DCurl.FillComplete(MassC.RowMap(),MassD.RowMap());
MassC.GlobalAssemble(); MassC.FillComplete();
MassD.GlobalAssemble(); MassD.FillComplete();
StiffD.GlobalAssemble(); StiffD.FillComplete();
rhsD.GlobalAssemble();
#ifdef DUMP_DATA
fSignsout.close();
#endif
// Build the inverse diagonal for MassC
Epetra_CrsMatrix MassCinv(Copy,MassC.RowMap(),MassC.RowMap(),1);
Epetra_Vector DiagC(MassC.RowMap());
DiagC.PutScalar(1.0);
MassC.Multiply(false,DiagC,DiagC);
for(int i=0; i<DiagC.MyLength(); i++) {
DiagC[i]=1.0/DiagC[i];
}
for(int i=0; i<DiagC.MyLength(); i++) {
int CID=MassC.GCID(i);
MassCinv.InsertGlobalValues(MassC.GRID(i),1,&(DiagC[i]),&CID);
}
MassCinv.FillComplete();
// Set value to zero on diagonal that cooresponds to boundary edge
for(int i=0;i<numEdges;i++) {
if (edgeOnBoundary(i)){
double val=0.0;
MassCinv.ReplaceGlobalValues(i,1,&val,&i);
}
}
int numEntries;
double *values;
int *cols;
// Adjust matrices and rhs due to boundary conditions
for (int row = 0; row<numFaces; row++){
MassD.ExtractMyRowView(row,numEntries,values,cols);
for (int i=0; i<numEntries; i++){
if (faceOnBoundary(cols[i])) {
values[i]=0;
}
}
StiffD.ExtractMyRowView(row,numEntries,values,cols);
for (int i=0; i<numEntries; i++){
if (faceOnBoundary(cols[i])) {
values[i]=0;
}
}
}
for (int row = 0; row<numFaces; row++){
if (faceOnBoundary(row)) {
int rowindex = row;
StiffD.ExtractMyRowView(row,numEntries,values,cols);
for (int i=0; i<numEntries; i++){
values[i]=0;
}
MassD.ExtractMyRowView(row,numEntries,values,cols);
for (int i=0; i<numEntries; i++){
values[i]=0;
}
rhsD[0][row]=0;
double val = 1.0;
StiffD.ReplaceGlobalValues(1, &rowindex, 1, &rowindex, &val);
}
}
#ifdef DUMP_DATA
// Dump matrices to disk
EpetraExt::RowMatrixToMatlabFile("mag_m1inv_matrix.dat",MassCinv);
EpetraExt::RowMatrixToMatlabFile("mag_m2_matrix.dat",MassD);
EpetraExt::RowMatrixToMatlabFile("mag_k2_matrix.dat",StiffD);
EpetraExt::RowMatrixToMatlabFile("mag_t1_matrix.dat",DCurl);
EpetraExt::MultiVectorToMatrixMarketFile("mag_rhs2_vector.dat",rhsD,0,0,false);
#endif
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return 0;
}