virtual void values(FieldContainer<double> &values, BasisCachePtr basisCache)
{
// not the most efficient implementation
_fxn->values(values,basisCache);
vector<GlobalIndexType> contextCellIDs = basisCache->cellIDs();
int cellIndex=0; // keep track of index into values
int entryCount = values.size();
int numCells = values.dimension(0);
int numEntriesPerCell = entryCount / numCells;
for (vector<GlobalIndexType>::iterator cellIt = contextCellIDs.begin(); cellIt != contextCellIDs.end(); cellIt++)
{
GlobalIndexType cellID = *cellIt;
if (_cellIDs.find(cellID) == _cellIDs.end())
{
// clear out the associated entries
for (int j=0; j<numEntriesPerCell; j++)
{
values[cellIndex*numEntriesPerCell + j] = 0;
}
}
cellIndex++;
}
}
bool checkLTSumConsistency(LinearTermPtr a, LinearTermPtr b, DofOrderingPtr dofOrdering, BasisCachePtr basisCache)
{
double tol = 1e-14;
int numCells = basisCache->cellIDs().size();
int numDofs = dofOrdering->totalDofs();
bool forceBoundaryTerm = false;
FieldContainer<double> aValues(numCells,numDofs), bValues(numCells,numDofs), sumValues(numCells,numDofs);
a->integrate(aValues,dofOrdering,basisCache,forceBoundaryTerm);
b->integrate(bValues,dofOrdering,basisCache,forceBoundaryTerm);
(a+b)->integrate(sumValues, dofOrdering, basisCache, forceBoundaryTerm);
int size = aValues.size();
for (int i=0; i<size; i++)
{
double expectedValue = aValues[i] + bValues[i];
double diff = abs( expectedValue - sumValues[i] );
if (diff > tol)
{
return false;
}
}
return true;
}
void values(FieldContainer<double> &values, BasisCachePtr sliceBasisCache) {
vector<GlobalIndexType> sliceCellIDs = sliceBasisCache->cellIDs();
Teuchos::Array<int> dim;
values.dimensions(dim);
dim[0] = 1; // one cell
Teuchos::Array<int> offset(dim.size());
for (int cellOrdinal = 0; cellOrdinal < sliceCellIDs.size(); cellOrdinal++) {
offset[0] = cellOrdinal;
int enumeration = values.getEnumeration(offset);
FieldContainer<double>valuesForCell(dim,&values[enumeration]);
GlobalIndexType sliceCellID = sliceCellIDs[cellOrdinal];
int numPoints = sliceBasisCache->getPhysicalCubaturePoints().dimension(1);
int spaceDim = sliceBasisCache->getPhysicalCubaturePoints().dimension(2);
FieldContainer<double> spaceTimePhysicalPoints(1,numPoints,spaceDim+1);
for (int ptOrdinal=0; ptOrdinal<numPoints; ptOrdinal++) {
for (int d=0; d<spaceDim; d++) {
spaceTimePhysicalPoints(0,ptOrdinal,d) = sliceBasisCache->getPhysicalCubaturePoints()(cellOrdinal,ptOrdinal,d);
}
spaceTimePhysicalPoints(0,ptOrdinal,spaceDim) = _t;
}
GlobalIndexType cellID = _cellIDMap[sliceCellID];
BasisCachePtr spaceTimeBasisCache = BasisCache::basisCacheForCell(_spaceTimeMesh, cellID);
FieldContainer<double> spaceTimeRefPoints(1,numPoints,spaceDim+1);
CamelliaCellTools::mapToReferenceFrame(spaceTimeRefPoints, spaceTimePhysicalPoints, _spaceTimeMesh, cellID);
spaceTimeRefPoints.resize(numPoints,spaceDim+1);
spaceTimeBasisCache->setRefCellPoints(spaceTimeRefPoints);
_spaceTimeFunction->values(valuesForCell, spaceTimeBasisCache);
}
}
void values(FieldContainer<double> &values, BasisCachePtr basisCache)
{
int numCells = values.dimension(0);
int numPoints = values.dimension(1);
MeshPtr mesh = basisCache->mesh();
vector<int> cellIDs = basisCache->cellIDs();
double tol=1e-14;
for (int cellIndex=0; cellIndex<numCells; cellIndex++)
{
double h = 1.0;
if (_spatialCoord==0)
{
h = mesh->getCellXSize(cellIDs[cellIndex]);
}
else if (_spatialCoord==1)
{
h = mesh->getCellYSize(cellIDs[cellIndex]);
}
for (int ptIndex=0; ptIndex<numPoints; ptIndex++)
{
values(cellIndex,ptIndex) = sqrt(h);
}
}
}
bool FunctionTests::testAdaptiveIntegrate()
{
bool success = true;
// we must create our own basisCache here because _basisCache
// has had its ref cell points set, which basically means it's
// opted out of having any help with integration.
BasisCachePtr basisCache = Teuchos::rcp( new BasisCache( _elemType, _spectralConfusionMesh ) );
vector<GlobalIndexType> cellIDs;
cellIDs.push_back(0);
basisCache->setPhysicalCellNodes( _spectralConfusionMesh->physicalCellNodesForCell(0), cellIDs, true );
double eps = .1; //
FunctionPtr boundaryLayerFunction = Teuchos::rcp( new BoundaryLayerFunction(eps) );
int numCells = basisCache->cellIDs().size();
FieldContainer<double> integrals(numCells);
double quadtol = 1e-2;
double computedIntegral = boundaryLayerFunction->integrate(_spectralConfusionMesh,quadtol);
double trueIntegral = (eps*(exp(1/eps) - exp(-1/eps)))*2.0;
double diff = trueIntegral-computedIntegral;
double relativeError = abs(diff)/abs(trueIntegral); // relative error
double tol = 1e-2;
if (relativeError > tol)
{
success = false;
cout << "failing testAdaptiveIntegrate() with computed integral " << computedIntegral << " and true integral " << trueIntegral << endl;
}
return success;
}
void values(FieldContainer<double> &values, BasisCachePtr basisCache){
vector<int> cellIDs = basisCache->cellIDs();
int numPoints = values.dimension(1);
for (int i = 0;i<cellIDs.size();i++){
double energyError = _energyErrorForCell[cellIDs[i]];
for (int j = 0;j<numPoints;j++){
values(i,j) = energyError;
}
}
}
void values(FieldContainer<double> &values, BasisCachePtr basisCache){
vector<int> cellIDs = basisCache->cellIDs();
int numPoints = values.dimension(1);
for (int i = 0;i<cellIDs.size();i++){
int partitionNumber = _mesh->partitionForCellID(cellIDs[i]);
for (int j = 0;j<numPoints;j++){
values(i,j) = partitionNumber;
}
}
}
void MeshTransformationFunction::values(FieldContainer<double> &values, BasisCachePtr basisCache)
{
CHECK_VALUES_RANK(values);
vector<GlobalIndexType> cellIDs = basisCache->cellIDs();
// identity map is the right thing most of the time
// we'll do something different only where necessary
int spaceDim = values.dimension(2);
TEUCHOS_TEST_FOR_EXCEPTION(basisCache->cellTopology()->getDimension() != spaceDim, std::invalid_argument, "cellTopology dimension does not match the shape of the values container");
if (_op == OP_VALUE)
{
values = basisCache->getPhysicalCubaturePoints(); // identity
}
else if (_op == OP_DX)
{
// identity map is 1 in all the x slots, 0 in all others
int mod_value = 0; // the x slots are the mod spaceDim = 0 slots;
for (int i=0; i<values.size(); i++)
{
values[i] = (i%spaceDim == mod_value) ? 1.0 : 0.0;
}
}
else if (_op == OP_DY)
{
// identity map is 1 in all the y slots, 0 in all others
int mod_value = 1; // the y slots are the mod spaceDim = 1 slots;
for (int i=0; i<values.size(); i++)
{
values[i] = (i%spaceDim == mod_value) ? 1.0 : 0.0;
}
}
else if (_op == OP_DZ)
{
// identity map is 1 in all the z slots, 0 in all others
int mod_value = 2; // the z slots are the mod spaceDim = 2 slots;
for (int i=0; i<values.size(); i++)
{
values[i] = (i%spaceDim == mod_value) ? 1.0 : 0.0;
}
}
// if (_op == OP_DX) {
// cout << "values before cellTransformation:\n" << values;
// }
for (int cellIndex=0; cellIndex < cellIDs.size(); cellIndex++)
{
GlobalIndexType cellID = cellIDs[cellIndex];
if (_cellTransforms.find(cellID) == _cellTransforms.end()) continue;
TFunctionPtr<double> cellTransformation = _cellTransforms[cellID];
((CellTransformationFunction*)cellTransformation.get())->setCellIndex(cellIndex);
cellTransformation->values(values, basisCache);
}
// if (_op == OP_DX) {
// cout << "values after cellTransformation:\n" << values;
// }
}
void MeshPolyOrderFunction::values(FieldContainer<double> &values, BasisCachePtr basisCache) {
vector<GlobalIndexType> cellIDs = basisCache->cellIDs();
IndexType cellIndex = 0;
int numPoints = values.dimension(1);
for (vector<GlobalIndexType>::iterator cellIDIt = cellIDs.begin(); cellIDIt != cellIDs.end(); cellIDIt++, cellIndex++) {
GlobalIndexType cellID = *cellIDIt;
int polyOrder = _mesh->cellPolyOrder(cellID); // H1 order
for (int ptIndex=0; ptIndex<numPoints; ptIndex++) {
values(cellIndex, ptIndex) = polyOrder-1;
}
}
}
// computes riesz representation over a single element - map is from int (testID) to FieldContainer of values (sized cellIndex, numPoints)
void RieszRep::computeRepresentationValues(FieldContainer<double> &values, int testID, IntrepidExtendedTypes::EOperatorExtended op, BasisCachePtr basisCache){
if (_repsNotComputed){
cout << "Computing riesz rep dofs" << endl;
computeRieszRep();
}
int spaceDim = _mesh->getTopology()->getSpaceDim();
int numCells = values.dimension(0);
int numPoints = values.dimension(1);
vector<GlobalIndexType> cellIDs = basisCache->cellIDs();
// all elems coming in should be of same type
ElementPtr elem = _mesh->getElement(cellIDs[0]);
ElementTypePtr elemTypePtr = elem->elementType();
DofOrderingPtr testOrderingPtr = elemTypePtr->testOrderPtr;
CellTopoPtrLegacy cellTopoPtr = elemTypePtr->cellTopoPtr;
int numTestDofsForVarID = testOrderingPtr->getBasisCardinality(testID, 0);
BasisPtr testBasis = testOrderingPtr->getBasis(testID);
bool testBasisIsVolumeBasis = (spaceDim == testBasis->domainTopology()->getDimension());
bool useCubPointsSideRefCell = testBasisIsVolumeBasis && basisCache->isSideCache();
Teuchos::RCP< const FieldContainer<double> > transformedBasisValues = basisCache->getTransformedValues(testBasis,op,useCubPointsSideRefCell);
int rank = values.rank() - 2; // if values are shaped as (C,P), scalar...
if (rank > 1) {
cout << "ranks greater than 1 not presently supported...\n";
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "ranks greater than 1 not presently supported...");
}
// Camellia::print("cellIDs",cellIDs);
values.initialize(0.0);
for (int cellIndex = 0;cellIndex<numCells;cellIndex++){
int cellID = cellIDs[cellIndex];
for (int j = 0;j<numTestDofsForVarID;j++) {
int dofIndex = testOrderingPtr->getDofIndex(testID, j);
for (int i = 0;i<numPoints;i++) {
if (rank==0) {
double basisValue = (*transformedBasisValues)(cellIndex,j,i);
values(cellIndex,i) += basisValue*_rieszRepDofsGlobal[cellID](dofIndex);
} else {
for (int d = 0; d<spaceDim; d++) {
double basisValue = (*transformedBasisValues)(cellIndex,j,i,d);
values(cellIndex,i,d) += basisValue*_rieszRepDofsGlobal[cellID](dofIndex);
}
}
}
}
}
// TestSuite::serializeOutput("rep values", values);
}
void values(FieldContainer<double> &values, BasisCachePtr basisCache) {
CHECK_VALUES_RANK(values);
FunctionPtr fsq = _f*_f;
int numCells = basisCache->cellIDs().size();
int numPoints = values.dimension(1);
FieldContainer<double> cellIntegs(numCells);
fsq->integrate(cellIntegs,basisCache);
for (int cellIndex=0; cellIndex<numCells; cellIndex++) {
for (int ptIndex=0; ptIndex<numPoints; ptIndex++) {
values(cellIndex,ptIndex) = cellIntegs(cellIndex);
}
}
}
void values(FieldContainer<double> &values, BasisCachePtr basisCache)
{
vector<GlobalIndexType> cellIDs = basisCache->cellIDs();
int numPoints = values.dimension(1);
FieldContainer<double> points = basisCache->getPhysicalCubaturePoints();
for (int i = 0; i<cellIDs.size(); i++)
{
for (int j = 0; j<numPoints; j++)
{
values(i,j) = cellIDs[i];
}
}
}
void SideParityFunction::values(Intrepid::FieldContainer<double> &values, BasisCachePtr sideBasisCache)
{
this->CHECK_VALUES_RANK(values);
int numCells = values.dimension(0);
int numPoints = values.dimension(1);
int sideIndex = sideBasisCache->getSideIndex();
if (sideIndex == -1)
{
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "non-sideBasisCache passed into SideParityFunction");
}
if (sideBasisCache->getCellSideParities().size() > 0)
{
// then we'll use this, and won't require that mesh and cellIDs are set
if (sideBasisCache->getCellSideParities().dimension(0) != numCells)
{
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "sideBasisCache->getCellSideParities() is non-empty, but the cell dimension doesn't match that of the values FieldContainer.");
}
for (int cellOrdinal=0; cellOrdinal<numCells; cellOrdinal++)
{
int parity = sideBasisCache->getCellSideParities()(cellOrdinal,sideIndex);
for (int ptOrdinal=0; ptOrdinal<numPoints; ptOrdinal++)
{
values(cellOrdinal,ptOrdinal) = parity;
}
}
}
else
{
vector<GlobalIndexType> cellIDs = sideBasisCache->cellIDs();
if (cellIDs.size() != numCells)
{
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "cellIDs.size() != numCells");
}
Teuchos::RCP<Mesh> mesh = sideBasisCache->mesh();
if (! mesh.get())
{
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "mesh unset in BasisCache.");
}
for (int cellIndex=0; cellIndex<numCells; cellIndex++)
{
int parity = mesh->cellSideParitiesForCell(cellIDs[cellIndex])(0,sideIndex);
for (int ptIndex=0; ptIndex<numPoints; ptIndex++)
{
values(cellIndex,ptIndex) = parity;
}
}
}
}
void values(FieldContainer<double> &values, BasisCachePtr basisCache){
MeshPtr mesh = basisCache->mesh();
vector<int> cellIDs = basisCache->cellIDs();
int numPoints = values.dimension(1);
for (int i = 0;i<cellIDs.size();i++){
double h = mesh->getCellXSize(cellIDs[i]); // default to x-direction
if (_xyDim == 1){
h = mesh->getCellYSize(cellIDs[i]);
}
double hPower = pow(h,_power);
for (int j = 0;j<numPoints;j++){
values(i,j) = hPower;
}
}
}
void values(FieldContainer<double> &values, BasisCachePtr basisCache)
{
double tol = 1e-11;
vector<GlobalIndexType> cellIDs = basisCache->cellIDs();
int numPoints = values.dimension(1);
FieldContainer<double> points = basisCache->getPhysicalCubaturePoints();
for (int i = 0; i<cellIDs.size(); i++)
{
for (int j = 0; j<numPoints; j++)
{
double x = points(i,j,0);
double y = points(i,j,1);
if (abs(x-.5)<tol)
{
values(i,j) = 1.0;
}
else
{
values(i,j) = 0.0;
}
}
}
}
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";
}
}
void PenaltyMethodFilter::filter(FieldContainer<double> &localStiffnessMatrix, FieldContainer<double> &localRHSVector,
BasisCachePtr basisCache, Teuchos::RCP<Mesh> mesh, Teuchos::RCP<BC> bc){
// assumption: filter gets elements of all the same type
TEUCHOS_TEST_FOR_EXCEPTION(basisCache->cellIDs().size()==0,std::invalid_argument,"no cell IDs given to filter");
ElementTypePtr elemTypePtr = mesh->getElement(basisCache->cellIDs()[0])->elementType();
int numCells = localStiffnessMatrix.dimension(0);
DofOrderingPtr trialOrderPtr = elemTypePtr->trialOrderPtr;
unsigned numSides = CamelliaCellTools::getSideCount( *elemTypePtr->cellTopoPtr );
// only allows for L2 inner products at the moment.
IntrepidExtendedTypes::EOperatorExtended trialOperator = IntrepidExtendedTypes::OP_VALUE;
// loop over sides first
for (unsigned int sideIndex = 0; sideIndex<numSides; sideIndex++){
// GET INTEGRATION INFO - get cubature points and side normals to send to Constraints (Cell,Point, spaceDim)
FieldContainer<double> sideCubPoints = basisCache->getPhysicalCubaturePointsForSide(sideIndex);
FieldContainer<double> sideNormals = basisCache->getSideUnitNormals(sideIndex);
int numPts = sideCubPoints.dimension(1);
// GET CONSTRAINT INFO
vector<map<int, FieldContainer<double> > > constrCoeffsVector;
vector<FieldContainer<double> > constraintValuesVector;
vector<FieldContainer<bool> > imposeHereVector;
_constraints->getConstraints(sideCubPoints,sideNormals,constrCoeffsVector,constraintValuesVector);
//loop thru constraints
int i = 0;
for (vector<map<int,FieldContainer<double> > >::iterator constrIt = constrCoeffsVector.begin();
constrIt !=constrCoeffsVector.end(); constrIt++) {
map<int,FieldContainer<double> > constrCoeffs = *constrIt;
FieldContainer<double> constrValues = constraintValuesVector[i];
i++;
double penaltyParameter = 1e7; // (single_precision)^(-1) - perhaps have this computed relative to terms in the matrix?
for (map<int,FieldContainer<double> >::iterator constrTestIDIt = constrCoeffs.begin();
constrTestIDIt !=constrCoeffs.end(); constrTestIDIt++) {
pair<int,FieldContainer<double> > constrTestPair = *constrTestIDIt;
int testTrialID = constrTestPair.first;
// get basis to integrate for testing fxns
BasisPtr testTrialBasis = trialOrderPtr->getBasis(testTrialID,sideIndex);
FieldContainer<double> testTrialValuesTransformedWeighted = *(basisCache->getTransformedWeightedValues(testTrialBasis,trialOperator,
sideIndex,false));
// make copies b/c we can't fudge with return values from basisCache (const) - dimensions (Cell,Field - basis ordinal, Point)
FieldContainer<double> testTrialValuesWeightedCopy = testTrialValuesTransformedWeighted;
int numDofs2 = trialOrderPtr->getBasisCardinality(testTrialID,sideIndex);
for (int cellIndex=0; cellIndex<numCells; cellIndex++){
for (int dofIndex=0; dofIndex<numDofs2; dofIndex++){
for (int ptIndex=0; ptIndex<numPts; ptIndex++){
testTrialValuesWeightedCopy(cellIndex, dofIndex, ptIndex) *= constrTestPair.second(cellIndex, ptIndex); // scale by constraint coeff
}
}
}
// loop thru pairs of trialIDs and constr coeffs
for (map<int,FieldContainer<double> >::iterator constrIDIt = constrCoeffs.begin();
constrIDIt !=constrCoeffs.end(); constrIDIt++) {
pair<int,FieldContainer<double> > constrPair = *constrIDIt;
int trialID = constrPair.first;
// get basis to integrate
BasisPtr trialBasis1 = trialOrderPtr->getBasis(trialID,sideIndex);
// for trial: the value lives on the side, so we don't use the volume coords either:
FieldContainer<double> trialValuesTransformed = *(basisCache->getTransformedValues(trialBasis1,trialOperator,sideIndex,false));
// make copies b/c we can't fudge with return values from basisCache (const) - dimensions (Cell,Field - basis ordinal, Point)
FieldContainer<double> trialValuesCopy = trialValuesTransformed;
// transform trial values
int numDofs1 = trialOrderPtr->getBasisCardinality(trialID,sideIndex);
for (int dofIndex=0; dofIndex<numDofs1; dofIndex++){
for (int cellIndex=0; cellIndex<numCells; cellIndex++){
for (int ptIndex=0; ptIndex<numPts; ptIndex++){
trialValuesCopy(cellIndex, dofIndex, ptIndex) *= constrPair.second(cellIndex, ptIndex); // scale by constraint coeff
}
}
}
/////////////////////////////////////////////////////////////////////////////////////
// integrate the transformed values, add them to the relevant trial/testTrialID dof combos
FieldContainer<double> unweightedPenaltyMatrix(numCells,numDofs1,numDofs2);
FunctionSpaceTools::integrate<double>(unweightedPenaltyMatrix,trialValuesCopy,testTrialValuesWeightedCopy,COMP_BLAS);
for (int cellIndex=0; cellIndex<numCells; cellIndex++){
for (int testDofIndex=0; testDofIndex<numDofs2; testDofIndex++){
int localTestDof = trialOrderPtr->getDofIndex(testTrialID, testDofIndex, sideIndex);
for (int trialDofIndex=0; trialDofIndex<numDofs1; trialDofIndex++){
int localTrialDof = trialOrderPtr->getDofIndex(trialID, trialDofIndex, sideIndex);
localStiffnessMatrix(cellIndex,localTrialDof,localTestDof)
+= penaltyParameter*unweightedPenaltyMatrix(cellIndex,trialDofIndex,testDofIndex);
}
}
}
}
/////////////////////////////////////////////////////////////////////////////////////
// set penalty load
FieldContainer<double> unweightedRHSVector(numCells,numDofs2);
FunctionSpaceTools::integrate<double>(unweightedRHSVector,constrValues,testTrialValuesWeightedCopy,COMP_BLAS);
for (int cellIndex=0; cellIndex<numCells; cellIndex++){
for (int testDofIndex=0; testDofIndex<numDofs2; testDofIndex++){
int localTestDof = trialOrderPtr->getDofIndex(testTrialID, testDofIndex, sideIndex);
localRHSVector(cellIndex,localTestDof) += penaltyParameter*unweightedRHSVector(cellIndex,testDofIndex);
}
}
}
}
}
}
