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;
}
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_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_HEX_C1_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: CURL cannot be applied to scalar functions in 3D
// resize vals to rank-3 container with dimensions (num. basis functions, num. points, arbitrary)
vals.resize(hexBasis.getCardinality(), hexNodes.dimension(0), 4 );
INTREPID_TEST_COMMAND( hexBasis.getValues(vals, hexNodes, OPERATOR_CURL), throwCounter, nException );
// exception #2: DIV cannot be applied to scalar functions in 3D
// resize vals to rank-2 container with dimensions (num. basis functions, num. points)
vals.resize(hexBasis.getCardinality(), hexNodes.dimension(0) );
INTREPID_TEST_COMMAND( hexBasis.getValues(vals, hexNodes, 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( 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(8), throwCounter, nException );
// exception #7
INTREPID_TEST_COMMAND( hexBasis.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( 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-2 for OPERATOR_VALUE
FieldContainer<double> badVals1(4, 3, 1);
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals1, hexNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #11 output values must be of rank-3 for OPERATOR_GRAD
FieldContainer<double> badVals2(4, 3);
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals2, hexNodes, OPERATOR_GRAD), throwCounter, nException );
// exception #12 output values must be of rank-3 for OPERATOR_D1
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals2, hexNodes, OPERATOR_D1), throwCounter, nException );
// exception #13 output values must be of rank-3 for OPERATOR_D2
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals2, hexNodes, OPERATOR_D2), throwCounter, nException );
// exception #14 incorrect 0th dimension of output array (must equal number of basis functions)
FieldContainer<double> badVals3(hexBasis.getCardinality() + 1, hexNodes.dimension(0));
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals3, hexNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #15 incorrect 1st dimension of output array (must equal number of points)
FieldContainer<double> badVals4(hexBasis.getCardinality(), hexNodes.dimension(0) + 1);
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals4, hexNodes, OPERATOR_VALUE), throwCounter, nException );
// exception #16: incorrect 2nd dimension of output array (must equal the space dimension)
FieldContainer<double> badVals5(hexBasis.getCardinality(), hexNodes.dimension(0), 4);
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals5, hexNodes, OPERATOR_GRAD), throwCounter, nException );
// exception #17: incorrect 2nd dimension of output array (must equal D2 cardinality in 3D)
FieldContainer<double> badVals6(hexBasis.getCardinality(), hexNodes.dimension(0), 40);
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals6, hexNodes, OPERATOR_D2), throwCounter, nException );
// exception #18: incorrect 2nd dimension of output array (must equal D3 cardinality in 3D)
FieldContainer<double> badVals7(hexBasis.getCardinality(), hexNodes.dimension(0), 50);
INTREPID_TEST_COMMAND( hexBasis.getValues(badVals7, hexNodes, 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
// Note Teuchos throw number will not pick up exceptions 3-7 and therefore will not match.
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 gives the 8 correct basis set values at an evaluation point
double basisValues[] = {
// bottom 4 vertices
1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0,
// top 4 vertices
0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0,
// center {0, 0, 0}
0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125,
// faces { 1, 0, 0} and {-1, 0, 0}
0.0, 0.25, 0.25, 0.0, 0.0, 0.25, 0.25, 0.0,
0.25, 0.0, 0.0, 0.25, 0.25, 0.0, 0.0, 0.25,
// faces { 0, 1, 0} and { 0,-1, 0}
0.0, 0.0, 0.25, 0.25, 0.0, 0.0, 0.25, 0.25,
0.25, 0.25, 0.0, 0.0, 0.25, 0.25, 0.0, 0.0,
// faces {0, 0, 1} and {0, 0, -1}
0.0, 0.0, 0.0, 0.0, 0.25, 0.25, 0.25, 0.25,
0.25, 0.25, 0.25, 0.25, 0.0, 0.0, 0.0, 0.0,
};
// GRAD and D1: each row gives the 3x8 correct values of the gradients of the 8 basis functions
double basisGrads[] = {
// points 0-3
-0.5,-0.5,-0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-0.5, 0.0, 0.0, 0.5,-0.5,-0.5, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0,-0.5, 0.0, 0.5, 0.5,-0.5, -0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0,
0.0,-0.5, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, -0.5, 0.5,-0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5,
// points 4-7
0.0, 0.0,-0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.5,-0.5, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0,-0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.5, 0.0, 0.0, 0.5,-0.5, 0.5, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,-0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,-0.5, 0.0, 0.5, 0.5, 0.5, -0.5, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,-0.5, 0.0,-0.5, 0.0, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, -0.5, 0.5, 0.5,
// point 8
-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,
// point 9
-0.125, 0.0, 0.0, 0.125,-0.25, -0.25, 0.125, 0.25, -0.25, -0.125, 0.0, 0.0, \
-0.125, 0.0, 0.0, 0.125,-0.25, 0.25, 0.125, 0.25, 0.25, -0.125, 0.0, 0.0,
// point 10
-0.125,-0.25, -0.25, 0.125, 0.0, 0.0, 0.125, 0.0, 0.0, -0.125, 0.25, -0.25,\
-0.125,-0.25, 0.25, 0.125, 0.0, 0.0, 0.125, 0.0, 0.0, -0.125, 0.25, 0.25,
// point 11
0.0, -0.125, 0.0, 0.0, -0.125, 0.0, 0.25, 0.125,-0.25, -0.25, 0.125,-0.25,\
0.0, -0.125, 0.0, 0.0, -0.125, 0.0, 0.25, 0.125, 0.25, -0.25, 0.125, 0.25,
// point 12
-0.25, -0.125,-0.25, 0.25, -0.125,-0.25, 0.0, 0.125, 0.0, 0.0, 0.125, 0.0, \
-0.25, -0.125, 0.25, 0.25, -0.125, 0.25, 0.0, 0.125, 0.0, 0.0, 0.125, 0.0,
// point 13
0.0, 0.0, -0.125, 0.0, 0.0, -0.125, 0.0, 0.0, -0.125, 0.0, 0.0, -0.125, \
-0.25, -0.25, 0.125, 0.25, -0.25, 0.125, 0.25, 0.25, 0.125, -0.25, 0.25, 0.125,
// point 14
-0.25, -0.25, -0.125, 0.25, -0.25, -0.125, 0.25, 0.25, -0.125, -0.25, 0.25, -0.125, \
0.0, 0.0, 0.125, 0.0, 0.0, 0.125, 0.0, 0.0, 0.125, 0.0, 0.0, 0.125
};
//D2: flat array with the values of D2 applied to basis functions. Multi-index is (P,F,K)
double basisD2[] = {
// point 0
0, 0.25, 0.25, 0, 0.25, 0, 0, -0.25, -0.25, 0, 0., 0, 0, 0.25, 0., 0, \
0., 0, 0, -0.25, 0., 0, -0.25, 0, 0, 0., -0.25, 0, -0.25, 0, 0, 0., \
0.25, 0, 0., 0, 0, 0., 0., 0, 0., 0, 0, 0., 0., 0, 0.25, 0., \
// point 1
0, 0.25, 0.25, 0, 0., 0, 0, -0.25, -0.25, 0, 0.25, 0, 0, 0.25, 0., 0, \
-0.25, 0, 0, -0.25, 0., 0, 0., 0, 0, 0., -0.25, 0, 0., 0, 0, 0., \
0.25, 0, -0.25, 0, 0, 0., 0., 0, 0.25, 0, 0, 0., 0., 0, 0., 0., \
// Point 2
0, 0.25, 0., 0, 0., 0, 0, -0.25, 0., 0, 0.25, 0, 0, 0.25, -0.25, 0, \
-0.25, 0, 0, -0.25, 0.25, 0, 0., 0, 0, 0., 0., 0, 0., 0, 0, 0., 0., \
0, -0.25, 0, 0, 0., 0.25, 0, 0.25, 0, 0, 0., -0.25, 0, 0., 0., \
// Point 3
0, 0.25, 0., 0, 0.25, 0, 0, -0.25, 0., 0, 0., 0, 0, 0.25, -0.25, 0, \
0., 0, 0, -0.25, 0.25, 0, -0.25, 0, 0, 0., 0., 0, -0.25, 0, 0, 0., \
0., 0, 0., 0, 0, 0., 0.25, 0, 0., 0, 0, 0., -0.25, 0, 0.25, 0.,\
// Point 4
0, 0., 0.25, 0, 0.25, 0, 0, 0., -0.25, 0, 0., 0, 0, 0., 0., 0, 0., 0, \
0, 0., 0., 0, -0.25, 0, 0, 0.25, -0.25, 0, -0.25, 0, 0, -0.25, 0.25, \
0, 0., 0, 0, 0.25, 0., 0, 0., 0, 0, -0.25, 0., 0, 0.25, 0., \
// Point 5
0, 0., 0.25, 0, 0., 0, 0, 0., -0.25, 0, 0.25, 0, 0, 0., 0., 0, -0.25, \
0, 0, 0., 0., 0, 0., 0, 0, 0.25, -0.25, 0, 0., 0, 0, -0.25, 0.25, 0, \
-0.25, 0, 0, 0.25, 0., 0, 0.25, 0, 0, -0.25, 0., 0, 0., 0., \
// Point 6
0, 0., 0., 0, 0., 0, 0, 0., 0., 0, 0.25, 0, 0, 0., -0.25, 0, -0.25, \
0, 0, 0., 0.25, 0, 0., 0, 0, 0.25, 0., 0, 0., 0, 0, -0.25, 0., 0, \
-0.25, 0, 0, 0.25, 0.25, 0, 0.25, 0, 0, -0.25, -0.25, 0, 0., 0., \
// Point 7
0, 0., 0., 0, 0.25, 0, 0, 0., 0., 0, 0., 0, 0, 0., -0.25, 0, 0., 0, \
0, 0., 0.25, 0, -0.25, 0, 0, 0.25, 0., 0, -0.25, 0, 0, -0.25, 0., 0, \
0., 0, 0, 0.25, 0.25, 0, 0., 0, 0, -0.25, -0.25, 0, 0.25, 0., \
// Point 8
0, 0.125, 0.125, 0, 0.125, 0, 0, -0.125, -0.125, 0, 0.125, 0, 0, \
0.125, -0.125, 0, -0.125, 0, 0, -0.125, 0.125, 0, -0.125, 0, 0, \
0.125, -0.125, 0, -0.125, 0, 0, -0.125, 0.125, 0, -0.125, 0, 0, \
0.125, 0.125, 0, 0.125, 0, 0, -0.125, -0.125, 0, 0.125, 0., \
// Point 9
0, 0.125, 0.125, 0, 0., 0, 0, -0.125, -0.125, 0, 0.25, 0, 0, 0.125, \
-0.125, 0, -0.25, 0, 0, -0.125, 0.125, 0, 0., 0, 0, 0.125, -0.125, 0, \
0., 0, 0, -0.125, 0.125, 0, -0.25, 0, 0, 0.125, 0.125, 0, 0.25, 0, 0, \
-0.125, -0.125, 0, 0., 0., \
// Point 10
0, 0.125, 0.125, 0, 0.25, 0, 0, -0.125, -0.125, 0, 0., 0, 0, 0.125, \
-0.125, 0, 0., 0, 0, -0.125, 0.125, 0, -0.25, 0, 0, 0.125, -0.125, 0, \
-0.25, 0, 0, -0.125, 0.125, 0, 0., 0, 0, 0.125, 0.125, 0, 0., 0, 0, \
-0.125, -0.125, 0, 0.25, 0., \
// Point 11
0, 0.125, 0., 0, 0.125, 0, 0, -0.125, 0., 0, 0.125, 0, 0, 0.125, \
-0.25, 0, -0.125, 0, 0, -0.125, 0.25, 0, -0.125, 0, 0, 0.125, 0., 0, \
-0.125, 0, 0, -0.125, 0., 0, -0.125, 0, 0, 0.125, 0.25, 0, 0.125, 0, \
0, -0.125, -0.25, 0, 0.125, 0., \
// Point 12
0, 0.125, 0.25, 0, 0.125, 0, 0, -0.125, -0.25, 0, 0.125, 0, 0, 0.125, \
0., 0, -0.125, 0, 0, -0.125, 0., 0, -0.125, 0, 0, 0.125, -0.25, 0, \
-0.125, 0, 0, -0.125, 0.25, 0, -0.125, 0, 0, 0.125, 0., 0, 0.125, 0, \
0, -0.125, 0., 0, 0.125, 0., \
// Point 13
0, 0., 0.125, 0, 0.125, 0, 0, 0., -0.125, 0, 0.125, 0, 0, 0., -0.125, \
0, -0.125, 0, 0, 0., 0.125, 0, -0.125, 0, 0, 0.25, -0.125, 0, -0.125, \
0, 0, -0.25, 0.125, 0, -0.125, 0, 0, 0.25, 0.125, 0, 0.125, 0, 0, \
-0.25, -0.125, 0, 0.125, 0., \
// Point 14
0, 0.25, 0.125, 0, 0.125, 0, 0, -0.25, -0.125, 0, 0.125, 0, 0, 0.25, \
-0.125, 0, -0.125, 0, 0, -0.25, 0.125, 0, -0.125, 0, 0, 0., -0.125, \
0, -0.125, 0, 0, 0., 0.125, 0, -0.125, 0, 0, 0., 0.125, 0, 0.125, 0, \
0, 0., -0.125, 0, 0.125, 0.
};
try {
// Dimensions for the output arrays:
int numFields = hexBasis.getCardinality();
int numPoints = hexNodes.dimension(0);
int spaceDim = hexBasis.getBaseCellTopology().getDimension();
int D2Cardin = Intrepid2::getDkCardinality(OPERATOR_D2, spaceDim);
// 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);
hexBasis.getValues(vals, hexNodes, 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);
hexBasis.getValues(vals, hexNodes, 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)
hexBasis.getValues(vals, hexNodes, 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 D2 of basis function
vals.resize(numFields, numPoints, D2Cardin);
hexBasis.getValues(vals, hexNodes, OPERATOR_D2);
for (int i = 0; i < numFields; i++) {
for (int j = 0; j < numPoints; j++) {
for (int k = 0; k < D2Cardin; k++) {
int l = k + i * D2Cardin + j * D2Cardin * numFields;
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);
hexBasis.getValues(vals, hexNodes, 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;
};
*outStream \
<< "\n"
<< "===============================================================================\n"\
<< "| TEST 4: correctness of DoF locations |\n"\
<< "===============================================================================\n";
try {
Teuchos::RCP<Basis<double, FieldContainer<double> > > basis =
Teuchos::rcp(new Basis_HGRAD_HEX_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_INTREPID2_DEBUG
cvals.resize(1,2,3);
INTREPID_TEST_COMMAND( coord_iface->getDofCoords(cvals), throwCounter, nException );
cvals.resize(3,2);
INTREPID_TEST_COMMAND( coord_iface->getDofCoords(cvals), throwCounter, nException );
cvals.resize(8,2);
INTREPID_TEST_COMMAND( coord_iface->getDofCoords(cvals), throwCounter, nException );
#endif
cvals.resize(8,3);
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, %6.4e) is %6.4e but should be %6.4e!\n", i, cvals(i,0), cvals(i,1), cvals(i,2), 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, %6.4e) is %6.4e but should be %6.4e!\n", i, cvals(i,0), cvals(i,1), cvals(i,2), 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);
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_01.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 Curl-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);
}
// *********************************** 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 fe2eout("elem2edge.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 l=0; l<numEdgesPerElem; l++) {
fe2eout << elemToEdge(ielem,l) << " ";
}
fe2eout << "\n";
}
}
}
fe2nout.close();
fe2eout.close();
#endif
#ifdef DUMP_DATA_EXTRA
ofstream fed2nout("edge2node.dat");
for (int i=0; i<numEdges; i++) {
fed2nout << edgeToNode(i,0) <<" ";
fed2nout << edgeToNode(i,1) <<"\n";
}
fed2nout.close();
ofstream fBnodeout("nodeOnBndy.dat");
ofstream fBedgeout("edgeOnBndy.dat");
for (int i=0; i<numNodes; i++) {
fBnodeout << nodeOnBoundary(i) <<"\n";
}
for (int i=0; i<numEdges; i++) {
fBedgeout << edgeOnBoundary(i) <<"\n";
}
fBnodeout.close();
fBedgeout.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 **************************************
// Node to edge incidence matrix
*outStream << "Building incidence matrix ... \n\n";
Epetra_SerialComm Comm;
Epetra_Map globalMapC(numEdges, 0, Comm);
Epetra_Map globalMapG(numNodes, 0, Comm);
Epetra_FECrsMatrix DGrad(Copy, globalMapC, globalMapG, 2);
double vals[2];
vals[0]=-1.0; vals[1]=1.0;
for (int j=0; j<numEdges; j++){
int rowNum = j;
int colNum[2];
colNum[0] = edgeToNode(j,0);
colNum[1] = edgeToNode(j,1);
DGrad.InsertGlobalValues(1, &rowNum, 2, colNum, vals);
}
// ************************************ CUBATURE **************************************
// Get numerical integration points and weights for element
*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_HGRAD_HEX_C1_FEM<double, FieldContainer<double> > hexHGradBasis;
int numFieldsC = hexHCurlBasis.getCardinality();
int numFieldsG = hexHGradBasis.getCardinality();
// Evaluate basis at cubature points
FieldContainer<double> hexGVals(numFieldsG, numCubPoints);
FieldContainer<double> hexCVals(numFieldsC, numCubPoints, spaceDim);
FieldContainer<double> hexCurls(numFieldsC, numCubPoints, spaceDim);
FieldContainer<double> worksetCVals(numFieldsC, numFacePoints, spaceDim);
hexHCurlBasis.getValues(hexCVals, cubPoints, OPERATOR_VALUE);
hexHCurlBasis.getValues(hexCurls, cubPoints, OPERATOR_CURL);
hexHGradBasis.getValues(hexGVals, cubPoints, OPERATOR_VALUE);
// ******** 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;
//typedef ArrayTools art;
int numCells = 1;
// Containers for nodes and edge signs
FieldContainer<double> hexNodes(numCells, numNodesPerElem, spaceDim);
FieldContainer<double> hexEdgeSigns(numCells, numFieldsC);
// 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 mass matrix
FieldContainer<double> massMatrixG(numCells, numFieldsG, numFieldsG);
FieldContainer<double> weightedMeasure(numCells, numCubPoints);
FieldContainer<double> weightedMeasureMuInv(numCells, numCubPoints);
FieldContainer<double> hexGValsTransformed(numCells, numFieldsG, numCubPoints);
FieldContainer<double> hexGValsTransformedWeighted(numCells, numFieldsG, numCubPoints);
// Containers for element HCURL mass matrix
FieldContainer<double> massMatrixC(numCells, numFieldsC, numFieldsC);
FieldContainer<double> hexCValsTransformed(numCells, numFieldsC, numCubPoints, spaceDim);
FieldContainer<double> hexCValsTransformedWeighted(numCells, numFieldsC, numCubPoints, spaceDim);
// Containers for element HCURL stiffness matrix
FieldContainer<double> stiffMatrixC(numCells, numFieldsC, numFieldsC);
FieldContainer<double> weightedMeasureMu(numCells, numCubPoints);
FieldContainer<double> hexCurlsTransformed(numCells, numFieldsC, numCubPoints, spaceDim);
FieldContainer<double> hexCurlsTransformedWeighted(numCells, numFieldsC, numCubPoints, spaceDim);
// Containers for right hand side vectors
FieldContainer<double> rhsDatag(numCells, numCubPoints, cubDim);
FieldContainer<double> rhsDatah(numCells, numCubPoints, cubDim);
FieldContainer<double> gC(numCells, numFieldsC);
FieldContainer<double> hC(numCells, numFieldsC);
FieldContainer<double> hCBoundary(numCells, numFieldsC);
FieldContainer<double> refGaussPoints(numFacePoints,spaceDim);
FieldContainer<double> worksetGaussPoints(numCells,numFacePoints,spaceDim);
FieldContainer<double> worksetJacobians(numCells, numFacePoints, spaceDim, spaceDim);
FieldContainer<double> worksetJacobInv(numCells, numFacePoints, spaceDim, spaceDim);
FieldContainer<double> worksetFaceN(numCells, numFacePoints, spaceDim);
FieldContainer<double> worksetFaceNweighted(numCells, numFacePoints, spaceDim);
FieldContainer<double> worksetVFieldVals(numCells, numFacePoints, spaceDim);
FieldContainer<double> worksetCValsTransformed(numCells, numFieldsC, numFacePoints, spaceDim);
FieldContainer<double> divuFace(numCells, numFacePoints);
FieldContainer<double> worksetFieldDotNormal(numCells, numFieldsC, numFacePoints);
// Container for cubature points in physical space
FieldContainer<double> physCubPoints(numCells,numCubPoints, cubDim);
// Global arrays in Epetra format
Epetra_FECrsMatrix MassG(Copy, globalMapG, numFieldsG);
Epetra_FECrsMatrix MassC(Copy, globalMapC, numFieldsC);
Epetra_FECrsMatrix StiffC(Copy, globalMapC, numFieldsC);
Epetra_FEVector rhsC(globalMapC);
#ifdef DUMP_DATA
ofstream fSignsout("edgeSigns.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);
}
// 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;
#ifdef DUMP_DATA
fSignsout << hexEdgeSigns(0,j) << " ";
#endif
}
#ifdef DUMP_DATA
fSignsout << "\n";
#endif
// 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 mass matrices *******************************
// transform to physical coordinates
fst::HGRADtransformVALUE<double>(hexGValsTransformed, hexGVals);
// compute weighted measure
fst::computeCellMeasure<double>(weightedMeasure, hexJacobDet, cubWeights);
// combine mu value with weighted measure
for (int nC = 0; nC < numCells; nC++){
for (int nPt = 0; nPt < numCubPoints; nPt++){
weightedMeasureMuInv(nC,nPt) = weightedMeasure(nC,nPt) / muVal(k);
}
}
// multiply values with weighted measure
fst::multiplyMeasure<double>(hexGValsTransformedWeighted,
weightedMeasureMuInv, hexGValsTransformed);
// integrate to compute element mass matrix
fst::integrate<double>(massMatrixG,
hexGValsTransformed, hexGValsTransformedWeighted, COMP_CPP);
// assemble into global matrix
// int err = 0;
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 = massMatrixG(0,row,col);
MassG.InsertGlobalValues(1, &rowIndex, 1, &colIndex, &val);
}
}
// ************************** Compute element HCurl mass matrices *******************************
// transform to physical coordinates
fst::HCURLtransformVALUE<double>(hexCValsTransformed, hexJacobInv,
hexCVals);
// 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
//err = 0;
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 HCurl stiffness matrices *****************************
// transform to physical coordinates
fst::HCURLtransformCURL<double>(hexCurlsTransformed, hexJacobian, hexJacobDet,
hexCurls);
// combine mu value with weighted measure
for (int nC = 0; nC < numCells; nC++){
for (int nPt = 0; nPt < numCubPoints; nPt++){
weightedMeasureMu(nC,nPt) = weightedMeasure(nC,nPt) / muVal(k);
}
}
// multiply by weighted measure
fst::multiplyMeasure<double>(hexCurlsTransformedWeighted,
weightedMeasureMu, hexCurlsTransformed);
// integrate to compute element stiffness matrix
fst::integrate<double>(stiffMatrixC,
hexCurlsTransformed, hexCurlsTransformedWeighted,
COMP_CPP);
// apply edge signs
fst::applyLeftFieldSigns<double>(stiffMatrixC, hexEdgeSigns);
fst::applyRightFieldSigns<double>(stiffMatrixC, hexEdgeSigns);
// assemble into global matrix
//err = 0;
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 = stiffMatrixC(0,row,col);
StiffC.InsertGlobalValues(1, &rowIndex, 1, &colIndex, &val);
}
}
// ******************************* Build right hand side ************************************
// transform integration points to physical points
FieldContainer<double> physCubPoints(numCells,numCubPoints, cubDim);
CellTools::mapToPhysicalFrame(physCubPoints, cubPoints, hexNodes, hex_8);
// evaluate right hand side functions at physical points
FieldContainer<double> rhsDatag(numCells, numCubPoints, cubDim);
FieldContainer<double> rhsDatah(numCells, numCubPoints, cubDim);
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;
evalCurlu(du1, du2, du3, x, y, z);
rhsDatag(0,nPt,0) = du1;
rhsDatag(0,nPt,1) = du2;
rhsDatag(0,nPt,2) = du3;
evalGradDivu(du1, du2, du3, x, y, z);
rhsDatah(0,nPt,0) = du1;
rhsDatah(0,nPt,1) = du2;
rhsDatah(0,nPt,2) = du3;
}
// integrate (g,curl w) term
fst::integrate<double>(gC, rhsDatag, hexCurlsTransformedWeighted,
COMP_CPP);
// integrate -(grad h, w)
fst::integrate<double>(hC, rhsDatah, hexCValsTransformedWeighted,
COMP_CPP);
// apply signs
fst::applyFieldSigns<double>(gC, hexEdgeSigns);
fst::applyFieldSigns<double>(hC, hexEdgeSigns);
// calculate boundary term, (h*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
hexHCurlBasis.getValues(worksetCVals, refGaussPoints, OPERATOR_VALUE);
// Compute Jacobians at Gauss pts. on reference face for all parent cells
CellTools::setJacobian(worksetJacobians,
refGaussPoints,
hexNodes, hex_8);
CellTools::setJacobianInv(worksetJacobInv, worksetJacobians );
// transform to physical coordinates
fst::HCURLtransformVALUE<double>(worksetCValsTransformed, worksetJacobInv,
worksetCVals);
// 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);
// multiply with weights
for(int nPt = 0; nPt < numFacePoints; nPt++){
for (int dim = 0; dim < spaceDim; dim++){
worksetFaceNweighted(0,nPt,dim) = worksetFaceN(0,nPt,dim) * paramGaussWeights(nPt);
} //dim
} //nPt
fst::dotMultiplyDataField<double>(worksetFieldDotNormal, worksetFaceNweighted,
worksetCValsTransformed);
// Evaluate div 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);
divuFace(0,nPt)=evalDivu(x, y, z);
}
// Integrate
fst::integrate<double>(hCBoundary, divuFace, worksetFieldDotNormal,
COMP_CPP);
// apply signs
fst::applyFieldSigns<double>(hCBoundary, hexEdgeSigns);
// add into hC term
for (int nF = 0; nF < numFieldsC; nF++){
hC(0,nF) = hC(0,nF) - hCBoundary(0,nF);
}
} // if faceOnBoundary
} // numFaces
// assemble into global vector
for (int row = 0; row < numFieldsC; row++){
int rowIndex = elemToEdge(k,row);
double val = gC(0,row)-hC(0,row);
rhsC.SumIntoGlobalValues(1, &rowIndex, &val);
}
} // *** end element loop ***
#ifdef DUMP_DATA
fSignsout.close();
#endif
// Assemble over multiple processors, if necessary
MassG.GlobalAssemble(); MassG.FillComplete();
MassC.GlobalAssemble(); MassC.FillComplete();
StiffC.GlobalAssemble(); StiffC.FillComplete();
rhsC.GlobalAssemble();
DGrad.GlobalAssemble(); DGrad.FillComplete(MassG.RowMap(),MassC.RowMap());
// Build the inverse diagonal for MassG
Epetra_CrsMatrix MassGinv(Copy,MassG.RowMap(),MassG.RowMap(),1);
Epetra_Vector DiagG(MassG.RowMap());
DiagG.PutScalar(1.0);
MassG.Multiply(false,DiagG,DiagG);
for(int i=0; i<DiagG.MyLength(); i++) {
DiagG[i]=1.0/DiagG[i];
}
for(int i=0; i<DiagG.MyLength(); i++) {
int CID=MassG.GCID(i);
MassGinv.InsertGlobalValues(MassG.GRID(i),1,&(DiagG[i]),&CID);
}
MassGinv.FillComplete();
// Set value to zero on diagonal that cooresponds to boundary node
for(int i=0;i<numNodes;i++) {
if (nodeOnBoundary(i)){
double val=0.0;
MassGinv.ReplaceGlobalValues(i,1,&val,&i);
}
}
int numEntries;
double *values;
int *cols;
// Adjust matrices and rhs due to boundary conditions
for (int row = 0; row<numEdges; row++){
MassC.ExtractMyRowView(row,numEntries,values,cols);
for (int i=0; i<numEntries; i++){
if (edgeOnBoundary(cols[i])) {
values[i]=0;
}
}
StiffC.ExtractMyRowView(row,numEntries,values,cols);
for (int i=0; i<numEntries; i++){
if (edgeOnBoundary(cols[i])) {
values[i]=0;
}
}
}
for (int row = 0; row<numEdges; row++){
if (edgeOnBoundary(row)) {
int rowindex = row;
StiffC.ExtractMyRowView(row,numEntries,values,cols);
for (int i=0; i<numEntries; i++){
values[i]=0;
}
MassC.ExtractMyRowView(row,numEntries,values,cols);
for (int i=0; i<numEntries; i++){
values[i]=0;
}
rhsC[0][row]=0;
double val = 1.0;
StiffC.ReplaceGlobalValues(1, &rowindex, 1, &rowindex, &val);
}
}
#ifdef DUMP_DATA
// Dump matrices to disk
EpetraExt::RowMatrixToMatlabFile("mag_m0inv_matrix.dat",MassGinv);
EpetraExt::RowMatrixToMatlabFile("mag_m1_matrix.dat",MassC);
EpetraExt::RowMatrixToMatlabFile("mag_k1_matrix.dat",StiffC);
EpetraExt::RowMatrixToMatlabFile("mag_t0_matrix.dat",DGrad);
EpetraExt::MultiVectorToMatrixMarketFile("mag_rhs1_vector.dat",rhsC,0,0,false);
fSignsout.close();
#endif
std::cout << "End Result: TEST PASSED\n";
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
return 0;
}
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_03NL.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 PDE Jacobian for a Nonlinear Reaction-Diffusion |\n" \
<< "| 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++;
}
}
}
#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);
// ******** FEM ASSEMBLY *************
*outStream << "Building PDE Jacobian ... \n\n";
// Settings and data structures for mass and stiffness matrices
typedef CellTools<double> CellTools;
typedef FunctionSpaceTools fst;
int numCells = BATCH_SIZE;
int numBatches = numElems/numCells;
// 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 HGRAD bases
FieldContainer<double> localPDEjacobian(numCells, numFieldsG, numFieldsG);
FieldContainer<double> weightedMeasure(numCells, numCubPoints);
FieldContainer<double> hexGValsTransformed(numCells, numFieldsG, numCubPoints);
FieldContainer<double> hexGValsTransformedWeighted(numCells, numFieldsG, numCubPoints);
FieldContainer<double> hexGradsTransformed(numCells, numFieldsG, numCubPoints, spaceDim);
FieldContainer<double> hexGradsTransformedWeighted(numCells, numFieldsG, numCubPoints, spaceDim);
// Global arrays in Epetra format
Epetra_SerialComm Comm;
Epetra_Map globalMapG(numNodes, 0, Comm);
Epetra_FECrsMatrix StiffMatrix(Copy, globalMapG, 64);
// Additional arrays used in analytic assembly
FieldContainer<double> u_coeffs(numCells, numFieldsG);
FieldContainer<double> u_FE_val(numCells, numCubPoints);
FieldContainer<double> df_of_u(numCells, numCubPoints);
FieldContainer<double> df_of_u_times_basis(numCells, numFieldsG, numCubPoints);
// Additional arrays used in AD-based assembly.
FieldContainer<FadType> u_coeffsAD(numCells, numFieldsG);
FieldContainer<FadType> u_FE_gradAD(numCells, numCubPoints, spaceDim);
FieldContainer<FadType> u_FE_valAD(numCells, numCubPoints);
FieldContainer<FadType> f_of_u_AD(numCells, numCubPoints);
FieldContainer<FadType> cellResidualAD(numCells, numFieldsG);
for (int c=0; c<numCells; c++) {
for(int f=0; f<numFieldsG; f++) {
u_coeffsAD(c,f) = FadType(numFieldsG, f, 1.3);
}
}
Teuchos::Time timer_jac_analytic("Time to compute element PDE Jacobians analytically: ");
Teuchos::Time timer_jac_fad ("Time to compute element PDE Jacobians using AD: ");
Teuchos::Time timer_jac_insert ("Time for global insert, w/o graph: ");
Teuchos::Time timer_jac_insert_g("Time for global insert, w/ graph: ");
Teuchos::Time timer_jac_ga ("Time for GlobalAssemble, w/o graph: ");
Teuchos::Time timer_jac_ga_g ("Time for GlobalAssemble, w/ graph: ");
Teuchos::Time timer_jac_fc ("Time for FillComplete, w/o graph: ");
Teuchos::Time timer_jac_fc_g ("Time for FillComplete, w/ graph: ");
// *** Analytic element loop ***
for (int bi=0; bi<numBatches; bi++) {
// Physical cell coordinates
for (int ci=0; ci<numCells; ci++) {
int k = bi*numCells+ci;
for (int i=0; i<numNodesPerElem; i++) {
hexNodes(ci,i,0) = nodeCoord(elemToNode(k,i),0);
hexNodes(ci,i,1) = nodeCoord(elemToNode(k,i),1);
hexNodes(ci,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 WITHOUT AD *******************
// 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);
// u_coeffs equals the value of u_coeffsAD
for(int i=0; i<numFieldsG; i++){
u_coeffs(0,i) = u_coeffsAD(0,i).val();
}
timer_jac_analytic.start(); // START TIMER
// integrate to account for linear stiffness term
fst::integrate<double>(localPDEjacobian, hexGradsTransformed, hexGradsTransformedWeighted, INTREPID_INTEGRATE_COMP_ENGINE);
// represent value of the current state (iterate) as a linear combination of the basis functions
u_FE_val.initialize();
fst::evaluate<double>(u_FE_val, u_coeffs, hexGValsTransformed);
// evaluate derivative of the nonlinear term and multiply by basis function
dfunc_u(df_of_u, u_FE_val);
fst::scalarMultiplyDataField<double>(df_of_u_times_basis, df_of_u, hexGValsTransformed);
// integrate to account for nonlinear reaction term
fst::integrate<double>(localPDEjacobian, df_of_u_times_basis, hexGValsTransformedWeighted, INTREPID_INTEGRATE_COMP_ENGINE, true);
timer_jac_analytic.stop(); // STOP TIMER
// assemble into global matrix
for (int ci=0; ci<numCells; ci++) {
int k = bi*numCells+ci;
std::vector<int> rowIndex(numFieldsG);
std::vector<int> colIndex(numFieldsG);
for (int row = 0; row < numFieldsG; row++){
rowIndex[row] = elemToNode(k,row);
}
for (int col = 0; col < numFieldsG; col++){
colIndex[col] = elemToNode(k,col);
}
// We can insert an entire matrix at a time, but we opt for rows only.
//timer_jac_insert.start();
//StiffMatrix.InsertGlobalValues(numFieldsG, &rowIndex[0], numFieldsG, &colIndex[0], &localPDEjacobian(ci,0,0));
//timer_jac_insert.stop();
for (int row = 0; row < numFieldsG; row++){
timer_jac_insert.start();
StiffMatrix.InsertGlobalValues(1, &rowIndex[row], numFieldsG, &colIndex[0], &localPDEjacobian(ci,row,0));
timer_jac_insert.stop();
}
}
} // *** end analytic element loop ***
// Assemble global objects
timer_jac_ga.start(); StiffMatrix.GlobalAssemble(); timer_jac_ga.stop();
timer_jac_fc.start(); StiffMatrix.FillComplete(); timer_jac_fc.stop();
// *** AD element loop ***
Epetra_CrsGraph mgraph = StiffMatrix.Graph();
Epetra_FECrsMatrix StiffMatrixViaAD(Copy, mgraph);
for (int bi=0; bi<numBatches; bi++) {
// ******************** COMPUTE ELEMENT HGrad STIFFNESS MATRICES AND RIGHT-HAND SIDE WITH AD ********************
// Physical cell coordinates
for (int ci=0; ci<numCells; ci++) {
int k = bi*numCells+ci;
for (int i=0; i<numNodesPerElem; i++) {
hexNodes(ci,i,0) = nodeCoord(elemToNode(k,i),0);
hexNodes(ci,i,1) = nodeCoord(elemToNode(k,i),1);
hexNodes(ci,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 );
// 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);
// transform basis values to physical coordinates
fst::HGRADtransformVALUE<double>(hexGValsTransformed, hexGVals);
// multiply values with weighted measure
fst::multiplyMeasure<double>(hexGValsTransformedWeighted,
weightedMeasure, hexGValsTransformed);
timer_jac_fad.start(); // START TIMER
// represent gradient of the current state (iterate) as a linear combination of the gradients of basis functions
// use AD arrays !
u_FE_gradAD.initialize();
fst::evaluate<FadType>(u_FE_gradAD, u_coeffsAD, hexGradsTransformed);
// represent value of the current state (iterate) as a linear combination of the basis functions
// use AD arrays !
u_FE_valAD.initialize();
fst::evaluate<FadType>(u_FE_valAD, u_coeffsAD, hexGValsTransformed);
// compute nonlinear term
func_u(f_of_u_AD, u_FE_valAD);
// integrate to compute element residual
fst::integrate<FadType>(cellResidualAD, u_FE_gradAD, hexGradsTransformedWeighted, INTREPID_INTEGRATE_COMP_ENGINE);
fst::integrate<FadType>(cellResidualAD, f_of_u_AD, hexGValsTransformedWeighted, INTREPID_INTEGRATE_COMP_ENGINE, true);
timer_jac_fad.stop(); // STOP TIMER
// assemble into global matrix
for (int ci=0; ci<numCells; ci++) {
int k = bi*numCells+ci;
std::vector<int> rowIndex(numFieldsG);
std::vector<int> colIndex(numFieldsG);
for (int row = 0; row < numFieldsG; row++){
rowIndex[row] = elemToNode(k,row);
}
for (int col = 0; col < numFieldsG; col++){
colIndex[col] = elemToNode(k,col);
}
for (int row = 0; row < numFieldsG; row++){
timer_jac_insert_g.start();
StiffMatrixViaAD.SumIntoGlobalValues(1, &rowIndex[row], numFieldsG, &colIndex[0], cellResidualAD(ci,row).dx());
timer_jac_insert_g.stop();
}
}
} // *** end AD element loop ***
// Assemble global objects
timer_jac_ga_g.start(); StiffMatrixViaAD.GlobalAssemble(); timer_jac_ga_g.stop();
timer_jac_fc_g.start(); StiffMatrixViaAD.FillComplete(); timer_jac_fc_g.stop();
/****** Output *******/
#ifdef DUMP_DATA
// Dump matrices to disk
EpetraExt::RowMatrixToMatlabFile("stiff_matrix.dat",StiffMatrix);
EpetraExt::RowMatrixToMatlabFile("stiff_matrixAD.dat",StiffMatrixViaAD);
#endif
// take the infinity norm of the difference between StiffMatrix and StiffMatrixViaAD to see that
// the two matrices are the same
EpetraExt::MatrixMatrix::Add(StiffMatrix, false, 1.0, StiffMatrixViaAD, -1.0);
double normMat = StiffMatrixViaAD.NormInf();
*outStream << "Infinity norm of difference between stiffness matrices = " << normMat << "\n";
*outStream << "\n\nNumber of global nonzeros: " << StiffMatrix.NumGlobalNonzeros() << "\n\n";
*outStream << timer_jac_analytic.name() << " " << timer_jac_analytic.totalElapsedTime() << " sec\n";
*outStream << timer_jac_fad.name() << " " << timer_jac_fad.totalElapsedTime() << " sec\n\n";
*outStream << timer_jac_insert.name() << " " << timer_jac_insert.totalElapsedTime() << " sec\n";
*outStream << timer_jac_insert_g.name() << " " << timer_jac_insert_g.totalElapsedTime() << " sec\n\n";
*outStream << timer_jac_ga.name() << " " << timer_jac_ga.totalElapsedTime() << " sec\n";
*outStream << timer_jac_ga_g.name() << " " << timer_jac_ga_g.totalElapsedTime() << " sec\n\n";
*outStream << timer_jac_fc.name() << " " << timer_jac_fc.totalElapsedTime() << " sec\n";
*outStream << timer_jac_fc_g.name() << " " << timer_jac_fc_g.totalElapsedTime() << " sec\n\n";
if ((normMat < 1.0e4*INTREPID_TOL)) {
std::cout << "End Result: TEST PASSED\n";
}
else {
std::cout << "End Result: TEST FAILED\n";
}
// reset format state of std::cout
std::cout.copyfmt(oldFormatState);
Kokkos::finalize();
return 0;
}
