PreviousSolutionFunction::PreviousSolutionFunction(SolutionPtr soln, VarPtr var, bool multiplyFluxesByCellParity) : Function(var->rank()) {
_soln = soln;
_solnExpression = 1.0 * var;
_overrideMeshCheck = false;
if ((var->varType() == FLUX) && multiplyFluxesByCellParity) {
FunctionPtr parity = Teuchos::rcp( new SideParityFunction );
_solnExpression = parity * var;
}
}
PreviousSolutionFunction<Scalar>::PreviousSolutionFunction(TSolutionPtr<Scalar> soln, VarPtr var, bool multiplyFluxesByCellParity) : TFunction<Scalar>(var->rank())
{
_soln = soln;
_solnExpression = 1.0 * var;
_overrideMeshCheck = false;
if ((var->varType() == FLUX) && multiplyFluxesByCellParity)
{
TFunctionPtr<double> parity = TFunction<double>::sideParity();
_solnExpression = parity * var;
}
}
virtual void localStiffnessMatrixAndRHS(FieldContainer<double> &localStiffness, FieldContainer<double> &rhsVector,
IPPtr ip, BasisCachePtr ipBasisCache,
RHSPtr rhs, BasisCachePtr basisCache) {
double testMatrixAssemblyTime = 0, testMatrixInversionTime = 0, localStiffnessDeterminationFromTestsTime = 0;
#ifdef HAVE_MPI
Epetra_MpiComm Comm(MPI_COMM_WORLD);
//cout << "rank: " << rank << " of " << numProcs << endl;
#else
Epetra_SerialComm Comm;
#endif
Epetra_Time timer(Comm);
// localStiffness should have dim. (numCells, numTrialFields, numTrialFields)
MeshPtr mesh = basisCache->mesh();
if (mesh.get() == NULL) {
cout << "localStiffnessMatrix requires BasisCache to have mesh set.\n";
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "localStiffnessMatrix requires BasisCache to have mesh set.");
}
const vector<GlobalIndexType>* cellIDs = &basisCache->cellIDs();
int numCells = cellIDs->size();
if (numCells != localStiffness.dimension(0)) {
cout << "localStiffnessMatrix requires basisCache->cellIDs() to have the same # of cells as the first dimension of localStiffness\n";
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "localStiffnessMatrix requires basisCache->cellIDs() to have the same # of cells as the first dimension of localStiffness");
}
ElementTypePtr elemType = mesh->getElementType((*cellIDs)[0]); // we assume all cells provided are of the same type
DofOrderingPtr trialOrder = elemType->trialOrderPtr;
DofOrderingPtr fieldOrder = mesh->getDofOrderingFactory().getFieldOrdering(trialOrder);
DofOrderingPtr traceOrder = mesh->getDofOrderingFactory().getTraceOrdering(trialOrder);
map<int, int> stiffnessIndexForTraceIndex;
map<int, int> stiffnessIndexForFieldIndex;
set<int> varIDs = trialOrder->getVarIDs();
for (set<int>::iterator varIt = varIDs.begin(); varIt != varIDs.end(); varIt++) {
int varID = *varIt;
const vector<int>* sidesForVar = &trialOrder->getSidesForVarID(varID);
bool isTrace = (sidesForVar->size() > 1);
for (vector<int>::const_iterator sideIt = sidesForVar->begin(); sideIt != sidesForVar->end(); sideIt++) {
int sideOrdinal = *sideIt;
vector<int> dofIndices = trialOrder->getDofIndices(varID,sideOrdinal);
if (isTrace) {
vector<int> traceDofIndices = traceOrder->getDofIndices(varID,sideOrdinal);
for (int i=0; i<traceDofIndices.size(); i++) {
stiffnessIndexForTraceIndex[traceDofIndices[i]] = dofIndices[i];
}
} else {
vector<int> fieldDofIndices = fieldOrder->getDofIndices(varID);
for (int i=0; i<fieldDofIndices.size(); i++) {
stiffnessIndexForFieldIndex[fieldDofIndices[i]] = dofIndices[i];
}
}
}
}
int numTrialDofs = trialOrder->totalDofs();
if ((numTrialDofs != localStiffness.dimension(1)) || (numTrialDofs != localStiffness.dimension(2))) {
cout << "localStiffness should have dimensions (C,numTrialFields,numTrialFields).\n";
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "localStiffness should have dimensions (C,numTrialFields,numTrialFields).");
}
map<int,int> traceTestMap, fieldTestMap;
int numEquations = _virtualTerms.getFieldTestVars().size();
for (int eqn=0; eqn<numEquations; eqn++) {
VarPtr testVar = _virtualTerms.getFieldTestVars()[eqn];
VarPtr traceVar = _virtualTerms.getAssociatedTrace(testVar);
VarPtr fieldVar = _virtualTerms.getAssociatedField(testVar);
traceTestMap[traceVar->ID()] = testVar->ID();
fieldTestMap[fieldVar->ID()] = testVar->ID();
}
int maxDegreeField = fieldOrder->maxBasisDegree();
int testDegreeInterior = maxDegreeField + _virtualTerms.getTestEnrichment();
int testDegreeTrace = testDegreeInterior + 2;
cout << "ERROR in Virtual: getRelabeledDofOrdering() is commented out in DofOrderingFactory. Need to rewrite for the new caching scheme.\n";
DofOrderingPtr testOrderInterior; // = mesh->getDofOrderingFactory().getRelabeledDofOrdering(fieldOrder, fieldTestMap);
testOrderInterior = mesh->getDofOrderingFactory().setBasisDegree(testOrderInterior, testDegreeInterior, false);
DofOrderingPtr testOrderTrace = mesh->getDofOrderingFactory().setBasisDegree(testOrderInterior, testDegreeTrace, true); // this has a bunch of extra dofs (interior guys)
map<int, int> remappedTraceIndices; // go from the index that includes the interior dofs to one that doesn't
set<int> testIDs = testOrderTrace->getVarIDs();
int testTraceIndex = 0;
for (set<int>::iterator testIDIt = testIDs.begin(); testIDIt != testIDs.end(); testIDIt++) {
int testID = *testIDIt;
BasisPtr basis = testOrderTrace->getBasis(testID);
vector<int> interiorDofs = basis->dofOrdinalsForInterior();
for (int basisOrdinal=0; basisOrdinal<basis->getCardinality(); basisOrdinal++) {
if (std::find(interiorDofs.begin(),interiorDofs.end(),basisOrdinal) == interiorDofs.end()) {
int dofIndex = testOrderTrace->getDofIndex(testID, basisOrdinal);
remappedTraceIndices[dofIndex] = testTraceIndex;
testTraceIndex++;
}
}
}
// DofOrderingPtr testOrderTrace = mesh->getDofOrderingFactory().getRelabeledDofOrdering(traceOrder, traceTestMap);
// testOrderTrace = mesh->getDofOrderingFactory().setBasisDegree(testOrderTrace, testDegreeTrace);
int numTestInteriorDofs = testOrderInterior->totalDofs();
int numTestTraceDofsIncludingInterior = testOrderTrace->totalDofs();
int numTestTraceDofs = testTraceIndex;
int numTestDofs = numTestTraceDofs + numTestInteriorDofs;
timer.ResetStartTime();
bool printTimings = true;
if (printTimings) {
cout << "numCells: " << numCells << endl;
cout << "numTestDofs: " << numTestDofs << endl;
}
FieldContainer<double> rhsVectorTest(numCells,testOrderInterior->totalDofs()); // rhsVector is zero for the "trace" test dofs
{
// project the load f onto the space of interior test dofs.
LinearTermPtr f = rhs->linearTerm();
set<int> testIDs = f->varIDs();
for (int eqn=0; eqn<numEquations; eqn++) {
VarPtr v = _virtualTerms.getFieldTestVars()[eqn];
if (testIDs.find(v->ID()) != testIDs.end()) {
BasisPtr testInteriorBasis = testOrderInterior->getBasis(v->ID());
FieldContainer<double> fValues(numCells,testInteriorBasis->getCardinality());
// DofOrderingPtr oneVarOrderingTest = Teuchos::rcp(new DofOrdering(testInteriorBasis->domainTopology()));
DofOrderingPtr oneVarOrderingTest = Teuchos::rcp(new DofOrdering);
oneVarOrderingTest->addEntry(v->ID(), testInteriorBasis, testInteriorBasis->rangeRank());
LinearTermPtr f_v = Teuchos::rcp( new LinearTerm );
typedef pair< FunctionPtr, VarPtr > LinearSummand;
vector<LinearSummand> summands = f->summands();
for (int i=0; i<summands.size(); i++) {
FunctionPtr f = summands[i].first;
if (v->ID() == summands[i].second->ID()) {
f_v->addTerm(f * v);
f_v->integrate(fValues, oneVarOrderingTest, basisCache);
}
}
LinearTermPtr v_lt = 1.0 * v;
FieldContainer<double> l2(numCells,testInteriorBasis->getCardinality(),testInteriorBasis->getCardinality());
v_lt->integrate(l2,oneVarOrderingTest,v_lt,oneVarOrderingTest,basisCache,basisCache->isSideCache());
Teuchos::Array<int> testTestDim(2), testOneDim(2);
testTestDim[0] = testInteriorBasis->getCardinality();
testTestDim[1] = testInteriorBasis->getCardinality();
testOneDim[0] = testInteriorBasis->getCardinality();
testOneDim[1] = 1;
FieldContainer<double> projection(testOneDim);
for (int cellOrdinal=0; cellOrdinal<numCells; cellOrdinal++) {
FieldContainer<double> l2cell(testTestDim,&l2(cellOrdinal,0,0));
FieldContainer<double> f_cell(testOneDim,&fValues(cellOrdinal,0));
SerialDenseWrapper::solveSystemUsingQR(projection, l2cell, f_cell);
// rows in projection correspond to Ae_i, columns to the e_j. I.e. projection coefficients for e_i are found in the ith row
for (int basisOrdinal_j=0; basisOrdinal_j<projection.dimension(0); basisOrdinal_j++) {
int testIndex = testOrderInterior->getDofIndex(v->ID(), basisOrdinal_j);
rhsVectorTest(cellOrdinal,testIndex) = projection(basisOrdinal_j,0);
}
}
}
}
}
// project strong operator applied to field terms, and use this to populate the top left portion of stiffness matrix:
{
FieldContainer<double> trialFieldTestInterior(numCells, fieldOrder->totalDofs(), testOrderInterior->totalDofs());
for (int eqn=0; eqn<numEquations; eqn++) {
LinearTermPtr Au = _virtualTerms.getFieldOperators()[eqn];
VarPtr v = _virtualTerms.getFieldTestVars()[eqn];
set<int> fieldIDs = Au->varIDs();
for (set<int>::iterator fieldIt = fieldIDs.begin(); fieldIt != fieldIDs.end(); fieldIt++) {
int fieldID = *fieldIt;
// int testID = fieldTestMap[fieldID];
//
// LinearTermPtr testInteriorVar = 1.0 * this->varFactory().test(testID);
BasisPtr vBasis = testOrderInterior->getBasis(v->ID());
BasisPtr fieldTrialBasis = fieldOrder->getBasis(fieldID);
// DofOrderingPtr oneVarOrderingTest = Teuchos::rcp(new DofOrdering(vBasis->domainTopology()));
DofOrderingPtr oneVarOrderingTest = Teuchos::rcp(new DofOrdering());
oneVarOrderingTest->addEntry(v->ID(), vBasis, vBasis->rangeRank());
FieldContainer<double> Au_values(numCells,vBasis->getCardinality(),fieldTrialBasis->getCardinality());
FieldContainer<double> l2(numCells,vBasis->getCardinality(),vBasis->getCardinality());
DofOrderingPtr oneVarOrderingTrial = Teuchos::rcp(new DofOrdering());
// DofOrderingPtr oneVarOrderingTrial = Teuchos::rcp(new DofOrdering(fieldTrialBasis->domainTopology()));
oneVarOrderingTrial->addEntry(fieldID, fieldTrialBasis, fieldTrialBasis->rangeRank());
LinearTermPtr Au_restricted_to_field = Teuchos::rcp( new LinearTerm );
typedef pair< FunctionPtr, VarPtr > LinearSummand;
vector<LinearSummand> summands = Au->summands();
for (int i=0; i<summands.size(); i++) {
FunctionPtr f = summands[i].first;
VarPtr v = summands[i].second;
if (v->ID() == fieldID) {
Au_restricted_to_field->addTerm(f * v);
}
}
LinearTermPtr v_lt = 1.0 * v;
Au_restricted_to_field->integrate(Au_values,oneVarOrderingTrial,v_lt,oneVarOrderingTest,basisCache,basisCache->isSideCache());
v_lt->integrate(l2,oneVarOrderingTest,v_lt,oneVarOrderingTest,basisCache,basisCache->isSideCache());
double maxValue = 0;
for (int i=0; i<l2.size(); i++) {
maxValue = max(abs(l2[i]),maxValue);
}
cout << "maxValue in l2 is " << maxValue << endl;
Teuchos::Array<int> testTestDim(2), trialTestDim(2);
testTestDim[0] = vBasis->getCardinality();
testTestDim[1] = vBasis->getCardinality();
trialTestDim[0] = vBasis->getCardinality();
trialTestDim[1] = fieldTrialBasis->getCardinality();
FieldContainer<double> projection(trialTestDim);
for (int cellOrdinal=0; cellOrdinal<numCells; cellOrdinal++) {
FieldContainer<double> l2cell(testTestDim,&l2(cellOrdinal,0,0));
FieldContainer<double> AuCell(trialTestDim,&Au_values(cellOrdinal,0,0));
// TODO: confirm that I'm doing the right projection here. I could be missing a key point, but it seems to me that we must
// project onto an *orthonormal* basis here, to achieve the required identity structure of the (field,field) part of the
// Gram matrix. OTOH, it looks to me like the computation here achieves exactly that, even though I didn't initially
// have that in mind...
// SerialDenseWrapper::solveSystemUsingQR(projection, l2cell, AuCell);
SerialDenseWrapper::solveSystemMultipleRHS(projection, l2cell, AuCell);
// rows in projection correspond to Ae_i, columns to the e_j. I.e. projection coefficients for e_i are found in the ith row
for (int basisOrdinal_i=0; basisOrdinal_i<projection.dimension(0); basisOrdinal_i++) {
int testIndex = testOrderInterior->getDofIndex(v->ID(), basisOrdinal_i);
for (int basisOrdinal_j=0; basisOrdinal_j<projection.dimension(1); basisOrdinal_j++) {
int trialIndex = fieldOrder->getDofIndex(fieldID, basisOrdinal_j); // in the *trial* space
trialFieldTestInterior(cellOrdinal,trialIndex,testIndex) = projection(basisOrdinal_i,basisOrdinal_j);
}
}
}
}
}
Teuchos::Array<int> trialTestDim(2);
trialTestDim[0] = fieldOrder->totalDofs();
trialTestDim[1] = testOrderInterior->totalDofs();
for (int cellOrdinal=0; cellOrdinal<numCells; cellOrdinal++) {
FieldContainer<double> trialFieldTrialField(fieldOrder->totalDofs(), fieldOrder->totalDofs());
FieldContainer<double> trialTestCell(trialTestDim, &trialFieldTestInterior(cellOrdinal,0,0));
SerialDenseWrapper::multiply(trialFieldTrialField, trialTestCell, trialTestCell, 'N', 'T'); // transpose the second one
// now, accumulate into localStiffness
for (int i=0; i<trialFieldTrialField.dimension(0); i++) {
int stiff_i = stiffnessIndexForFieldIndex[i];
for (int j=0; j<trialFieldTrialField.dimension(1); j++) {
int stiff_j = stiffnessIndexForFieldIndex[j];
localStiffness(cellOrdinal,stiff_i,stiff_j) = trialFieldTrialField(i,j);
}
}
}
// multiply RHS integrated against the interior test space by the trialFieldTestInterior
for (int cellOrdinal=0; cellOrdinal<numCells; cellOrdinal++) {
Teuchos::Array<int> trialTestDim(2), oneTestDim(2);
trialTestDim[0] = fieldOrder->totalDofs();
trialTestDim[1] = testOrderInterior->totalDofs();
oneTestDim[0] = 1;
oneTestDim[1] = testOrderInterior->totalDofs();
FieldContainer<double> trialTestCell(trialTestDim, &trialFieldTestInterior(cellOrdinal,0,0));
FieldContainer<double> rhsTestCell(oneTestDim, &rhsVectorTest(cellOrdinal,0));
FieldContainer<double> rhsTrialCell(1, fieldOrder->totalDofs());
SerialDenseWrapper::multiply(rhsTrialCell, rhsTestCell, trialTestCell, 'N', 'T');
for (int fieldIndex=0; fieldIndex<fieldOrder->totalDofs(); fieldIndex++) {
int stiffIndex = stiffnessIndexForFieldIndex[fieldIndex];
rhsVector(cellOrdinal,stiffIndex) = rhsTrialCell(0, fieldIndex);
}
}
}
FieldContainer<double> ipMatrixTraceIncludingInterior(numCells,numTestTraceDofsIncludingInterior,numTestTraceDofsIncludingInterior);
int numTestTerms = _virtualTerms.getTestNormOperators().size();
for (int i=0; i<numTestTerms; i++) {
LinearTermPtr testTerm = _virtualTerms.getTestNormOperators()[i];
LinearTermPtr boundaryTerm = _virtualTerms.getTestNormBoundaryOperators()[i];
testTerm->integrate(ipMatrixTraceIncludingInterior,testOrderTrace,boundaryTerm,testOrderTrace,ipBasisCache,ipBasisCache->isSideCache());
}
FieldContainer<double> ipMatrixTrace(numCells,numTestTraceDofs,numTestTraceDofs);
for (int cellOrdinal=0; cellOrdinal<numCells; cellOrdinal++) {
for (int i_dofIndex=0; i_dofIndex<numTestTraceDofsIncludingInterior; i_dofIndex++) {
if (remappedTraceIndices.find(i_dofIndex) == remappedTraceIndices.end()) {
continue;
}
int i_remapped = remappedTraceIndices[i_dofIndex];
for (int j_dofIndex=0; j_dofIndex<numTestTraceDofsIncludingInterior; j_dofIndex++) {
if (remappedTraceIndices.find(j_dofIndex) == remappedTraceIndices.end()) {
continue;
}
int j_remapped = remappedTraceIndices[j_dofIndex];
ipMatrixTrace(cellOrdinal,i_remapped,j_remapped) = ipMatrixTraceIncludingInterior(cellOrdinal,i_dofIndex,j_dofIndex);
}
}
}
testMatrixAssemblyTime += timer.ElapsedTime();
// cout << "ipMatrix:\n" << ipMatrix;
timer.ResetStartTime();
cout << "NOTE: we do not yet enforce continuity on the trace test space.\n"; // I *think* this is fine, but I'm not dead certain -- we do of course in the end enforce continuity in GDAMinimumRule
// now, determine the trace part of the bilinear form matrix
FieldContainer<double> bfMatrixTraceTraceIncludingTestInterior(numCells,testOrderTrace->totalDofs(),traceOrder->totalDofs());
FieldContainer<double> bfMatrixFieldTraceIncludingTestInterior(numCells,testOrderTrace->totalDofs(),fieldOrder->totalDofs());
for (int eqn=0; eqn<numEquations; eqn++) {
VarPtr traceVar = _virtualTerms.getTraceVars()[eqn];
LinearTermPtr termTraced = traceVar->termTraced();
LinearTermPtr strongOperator = _virtualTerms.getFieldOperators()[eqn];
VarPtr testVar = _virtualTerms.getFieldTestVars()[eqn];
// want to determine \hat{C}(\hat{e}_i, \phi_j) for \phi_j with support on the boundary
// the \phi_j's with support on the boundary are the ones associated with the trace
LinearTermPtr trialTerm = 1.0 * traceVar;
LinearTermPtr testTerm;
if (traceVar->varType() == TRACE) {
testTerm = Function::normal() * testVar;
} else {
testTerm = 1.0 * testVar;
}
// trialTerm->integrate(bfMatrixTrace,traceOrder,testTerm,testOrderTrace,basisCache,basisCache->isSideCache());
trialTerm->integrate(bfMatrixTraceTraceIncludingTestInterior,traceOrder,testTerm,testOrderTrace,basisCache,basisCache->isSideCache());
termTraced->integrate(bfMatrixFieldTraceIncludingTestInterior,fieldOrder,-testTerm,testOrderTrace,basisCache,basisCache->isSideCache());
}
FieldContainer<double> bfMatrixFieldTrace(numCells,numTestTraceDofs,bfMatrixFieldTraceIncludingTestInterior.dimension(2));
FieldContainer<double> bfMatrixTraceTrace(numCells,numTestTraceDofs,bfMatrixTraceTraceIncludingTestInterior.dimension(2));
for (int cellOrdinal=0; cellOrdinal<numCells; cellOrdinal++) {
for (int i_dofIndex=0; i_dofIndex<numTestTraceDofsIncludingInterior; i_dofIndex++) {
if (remappedTraceIndices.find(i_dofIndex) == remappedTraceIndices.end()) {
continue;
}
int i_remapped = remappedTraceIndices[i_dofIndex];
for (int j_dofIndex=0; j_dofIndex<bfMatrixFieldTrace.dimension(2); j_dofIndex++) {
bfMatrixFieldTrace(cellOrdinal,i_remapped,j_dofIndex) = bfMatrixFieldTraceIncludingTestInterior(cellOrdinal,i_dofIndex,j_dofIndex);
}
for (int j_dofIndex=0; j_dofIndex<bfMatrixTraceTrace.dimension(2); j_dofIndex++) {
bfMatrixTraceTrace(cellOrdinal,i_remapped,j_dofIndex) = bfMatrixTraceTraceIncludingTestInterior(cellOrdinal,i_dofIndex,j_dofIndex);
}
}
}
Teuchos::Array<int> ipMatrixDim(2), bfMatrixTraceTraceDim(2), bfMatrixFieldTraceDim(2);
Teuchos::Array<int> traceTraceStiffDim(2), fieldTraceStiffDim(2), fieldFieldStiffDim(2);
ipMatrixDim[0] = ipMatrixTrace.dimension(1);
ipMatrixDim[1] = ipMatrixTrace.dimension(2);
bfMatrixTraceTraceDim[0] = bfMatrixTraceTrace.dimension(1);
bfMatrixTraceTraceDim[1] = bfMatrixTraceTrace.dimension(2);
bfMatrixFieldTraceDim[0] = bfMatrixFieldTrace.dimension(1);
bfMatrixFieldTraceDim[1] = bfMatrixFieldTrace.dimension(2);
traceTraceStiffDim[0] = traceOrder->totalDofs();
traceTraceStiffDim[1] = traceTraceStiffDim[0];
fieldTraceStiffDim[0] = fieldOrder->totalDofs();
fieldTraceStiffDim[1] = traceOrder->totalDofs(); // rectangular
fieldFieldStiffDim[0] = fieldOrder->totalDofs();
fieldFieldStiffDim[1] = fieldOrder->totalDofs();
FieldContainer<double> traceTraceStiffCell(traceTraceStiffDim);
FieldContainer<double> fieldTraceStiffCell(fieldTraceStiffDim);
FieldContainer<double> fieldFieldStiffCell(fieldFieldStiffDim);
for (int cellOrdinal=0; cellOrdinal<numCells; cellOrdinal++) {
FieldContainer<double> ipMatrixCell(ipMatrixDim,&ipMatrixTrace(cellOrdinal,0,0));
FieldContainer<double> optTestCoeffsTraceTrace(numTestTraceDofs,traceOrder->totalDofs());
FieldContainer<double> bfMatrixTraceTraceCell(bfMatrixTraceTraceDim,&bfMatrixTraceTrace(cellOrdinal,0,0));
int result = SerialDenseWrapper::solveSystemUsingQR(optTestCoeffsTraceTrace, ipMatrixCell, bfMatrixTraceTraceCell);
SerialDenseWrapper::multiply(traceTraceStiffCell, bfMatrixTraceTraceCell, optTestCoeffsTraceTrace, 'T', 'N');
// copy into the appropriate spot in localStiffness:
for (int i=0; i<traceTraceStiffDim[0]; i++) {
int i_stiff = stiffnessIndexForTraceIndex[i];
for (int j=0; j<traceTraceStiffDim[1]; j++) {
int j_stiff = stiffnessIndexForTraceIndex[j];
localStiffness(cellOrdinal,i_stiff,j_stiff) = traceTraceStiffCell(i,j);
}
}
// because of the way the matrix blocks line up, we actually don't have to do a second inversion of ipMatrixCell for this part
FieldContainer<double> bfMatrixFieldTraceCell(bfMatrixFieldTraceDim,&bfMatrixFieldTrace(cellOrdinal,0,0));
SerialDenseWrapper::multiply(fieldTraceStiffCell, bfMatrixFieldTraceCell, optTestCoeffsTraceTrace, 'T', 'N');
// copy into the appropriate spots in localStiffness (taking advantage of symmetry):
for (int i=0; i<fieldTraceStiffDim[0]; i++) {
int i_stiff = stiffnessIndexForFieldIndex[i];
for (int j=0; j<fieldTraceStiffDim[1]; j++) {
int j_stiff = stiffnessIndexForTraceIndex[j];
localStiffness(cellOrdinal,i_stiff,j_stiff) = fieldTraceStiffCell(i,j);
localStiffness(cellOrdinal,j_stiff,i_stiff) = fieldTraceStiffCell(i,j);
}
}
// because of the way the matrix blocks line up, we do have some trace contributions in the (field, field) portion of the matrix
// these get added to the field contributions (hence the +=)
FieldContainer<double> optTestCoeffsFieldTrace(numTestTraceDofs,fieldOrder->totalDofs());
result = SerialDenseWrapper::solveSystemUsingQR(optTestCoeffsFieldTrace, ipMatrixCell, bfMatrixFieldTraceCell);
SerialDenseWrapper::multiply(fieldFieldStiffCell, bfMatrixFieldTraceCell, optTestCoeffsFieldTrace, 'T', 'N');
for (int i=0; i<fieldFieldStiffDim[0]; i++) {
int i_stiff = stiffnessIndexForFieldIndex[i];
for (int j=0; j<fieldFieldStiffDim[1]; j++) {
int j_stiff = stiffnessIndexForFieldIndex[j];
localStiffness(cellOrdinal,i_stiff,j_stiff) += fieldFieldStiffCell(i,j);
}
}
}
testMatrixInversionTime += timer.ElapsedTime();
// cout << "optTestCoeffs:\n" << optTestCoeffs;
if (printTimings) {
cout << "testMatrixAssemblyTime: " << testMatrixAssemblyTime << " seconds.\n";
cout << "testMatrixInversionTime: " << testMatrixInversionTime << " seconds.\n";
cout << "localStiffnessDeterminationFromTestsTime: " << localStiffnessDeterminationFromTestsTime << " seconds.\n";
}
}