bool FunctionTests::testBasisSumFunction()
{
bool success = true;
// on a single-element mesh, the BasisSumFunction should be identical to
// the Solution with those coefficients
// define a new mesh: more interesting if we're not on the ref cell
int spaceDim = 2;
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 2.0;
quadPoints(1,1) = 0.0;
quadPoints(2,0) = 1.0;
quadPoints(2,1) = 1.0;
quadPoints(3,0) = 0.0;
quadPoints(3,1) = 1.0;
int H1Order = 1, pToAdd = 0;
int horizontalCells = 1, verticalCells = 1;
// create a pointer to a new mesh:
MeshPtr spectralConfusionMesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
_confusionBF, H1Order, H1Order+pToAdd);
BCPtr bc = BC::bc();
SolutionPtr soln = Teuchos::rcp( new Solution(spectralConfusionMesh, bc) );
soln->initializeLHSVector();
int cellID = 0;
double tol = 1e-16; // overly restrictive, just for now.
DofOrderingPtr trialSpace = spectralConfusionMesh->getElementType(cellID)->trialOrderPtr;
set<int> trialIDs = trialSpace->getVarIDs();
BasisCachePtr volumeCache = BasisCache::basisCacheForCell(spectralConfusionMesh, cellID);
for (set<int>::iterator trialIt=trialIDs.begin(); trialIt != trialIDs.end(); trialIt++)
{
int trialID = *trialIt;
const vector<int>* sidesForVar = &trialSpace->getSidesForVarID(trialID);
bool boundaryValued = sidesForVar->size() != 1;
// note that for volume trialIDs, sideIndex = 0, and numSides = 1…
for (vector<int>::const_iterator sideIt = sidesForVar->begin(); sideIt != sidesForVar->end(); sideIt++)
{
int sideIndex = *sideIt;
BasisCachePtr sideCache = volumeCache->getSideBasisCache(sideIndex);
BasisPtr basis = trialSpace->getBasis(trialID, sideIndex);
int basisCardinality = basis->getCardinality();
for (int basisOrdinal = 0; basisOrdinal<basisCardinality; basisOrdinal++)
{
FieldContainer<double> basisCoefficients(basisCardinality);
basisCoefficients(basisOrdinal) = 1.0;
soln->setSolnCoeffsForCellID(basisCoefficients, cellID, trialID, sideIndex);
VarPtr v = Var::varForTrialID(trialID, spectralConfusionMesh->bilinearForm());
FunctionPtr solnFxn = Function::solution(v, soln, false);
FunctionPtr basisSumFxn = Teuchos::rcp( new BasisSumFunction(basis, basisCoefficients, Teuchos::rcp((BasisCache*)NULL), OP_VALUE, boundaryValued) );
if (!boundaryValued)
{
double l2diff = (solnFxn - basisSumFxn)->l2norm(spectralConfusionMesh);
// cout << "l2diff = " << l2diff << endl;
if (l2diff > tol)
{
success = false;
cout << "testBasisSumFunction: l2diff of " << l2diff << " exceeds tol of " << tol << endl;
cout << "l2norm of basisSumFxn: " << basisSumFxn->l2norm(spectralConfusionMesh) << endl;
cout << "l2norm of solnFxn: " << solnFxn->l2norm(spectralConfusionMesh) << endl;
}
l2diff = (solnFxn->dx() - basisSumFxn->dx())->l2norm(spectralConfusionMesh);
// cout << "l2diff = " << l2diff << endl;
if (l2diff > tol)
{
success = false;
cout << "testBasisSumFunction: l2diff of dx() " << l2diff << " exceeds tol of " << tol << endl;
cout << "l2norm of basisSumFxn->dx(): " << basisSumFxn->dx()->l2norm(spectralConfusionMesh) << endl;
cout << "l2norm of solnFxn->dx(): " << solnFxn->dx()->l2norm(spectralConfusionMesh) << endl;
}
// test that the restriction to a side works
int numSides = volumeCache->cellTopology()->getSideCount();
for (int i=0; i<numSides; i++)
{
BasisCachePtr mySideCache = volumeCache->getSideBasisCache(i);
if (! solnFxn->equals(basisSumFxn, mySideCache, tol))
{
success = false;
cout << "testBasisSumFunction: on side 0, l2diff of " << l2diff << " exceeds tol of " << tol << endl;
reportFunctionValueDifferences(solnFxn, basisSumFxn, mySideCache, tol);
}
if (! solnFxn->grad(spaceDim)->equals(basisSumFxn->grad(spaceDim), mySideCache, tol))
{
success = false;
cout << "testBasisSumFunction: on side 0, l2diff of dx() " << l2diff << " exceeds tol of " << tol << endl;
reportFunctionValueDifferences(solnFxn->grad(spaceDim), basisSumFxn->grad(spaceDim), mySideCache, tol);
}
}
}
else
{
FieldContainer<double> cellIntegral(1);
// compute l2 diff of integral along the one side where we can legitimately assert equality:
FunctionPtr diffFxn = solnFxn - basisSumFxn;
(diffFxn*diffFxn)->integrate(cellIntegral, sideCache);
double l2diff = sqrt(cellIntegral(0));
if (l2diff > tol)
{
success = false;
cout << "testBasisSumFunction: on side " << sideIndex << ", l2diff of " << l2diff << " exceeds tol of " << tol << endl;
int numCubPoints = sideCache->getPhysicalCubaturePoints().dimension(1);
FieldContainer<double> solnFxnValues(1,numCubPoints);
FieldContainer<double> basisFxnValues(1,numCubPoints);
solnFxn->values(solnFxnValues, sideCache);
basisSumFxn->values(basisFxnValues, sideCache);
cout << "solnFxnValues:\n" << solnFxnValues;
cout << "basisFxnValues:\n" << basisFxnValues;
}
else
{
// cout << "testBasisSumFunction: on side " << sideIndex << ", l2diff of " << l2diff << " is within tol of " << tol << endl;
}
}
}
}
}
return success;
}
bool ScratchPadTests::testGalerkinOrthogonality()
{
double tol = 1e-11;
bool success = true;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr v = varFactory->testVar("v", HGRAD);
vector<double> beta;
beta.push_back(1.0);
beta.push_back(1.0);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// robust test norm
IPPtr ip = Teuchos::rcp(new IP);
ip->addTerm(v);
ip->addTerm(beta*v->grad());
// define trial variables
VarPtr beta_n_u = varFactory->fluxVar("\\widehat{\\beta \\cdot n }");
VarPtr u = varFactory->fieldVar("u");
//////////////////// BUILD MESH ///////////////////////
BFPtr convectionBF = Teuchos::rcp( new BF(varFactory) );
FunctionPtr n = Function::normal();
// v terms:
convectionBF->addTerm( -u, beta * v->grad() );
convectionBF->addTerm( beta_n_u, v);
// define nodes for mesh
int order = 2;
int H1Order = order+1;
int pToAdd = 1;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(4, convectionBF, H1Order, H1Order+pToAdd);
//////////////////// SOLVE ///////////////////////
RHSPtr rhs = RHS::rhs();
BCPtr bc = BC::bc();
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new NegatedSpatialFilter(inflowBoundary) );
FunctionPtr uIn;
uIn = Teuchos::rcp(new Uinflow); // uses a discontinuous piecewise-constant basis function on left and bottom sides of square
bc->addDirichlet(beta_n_u, inflowBoundary, beta*n*uIn);
Teuchos::RCP<Solution> solution;
solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
solution->solve(false);
FunctionPtr uFxn = Function::solution(u, solution);
FunctionPtr fnhatFxn = Function::solution(beta_n_u,solution);
// make residual for riesz representation function
LinearTermPtr residual = Teuchos::rcp(new LinearTerm);// residual
FunctionPtr parity = Function::sideParity();
residual->addTerm(-fnhatFxn*v + (beta*uFxn)*v->grad());
Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ip, residual));
riesz->computeRieszRep();
map<int,FunctionPtr> err_rep_map;
err_rep_map[v->ID()] = RieszRep::repFunction(v,riesz);
//////////////////// GET BOUNDARY CONDITION DATA ///////////////////////
FieldContainer<GlobalIndexType> bcGlobalIndices;
FieldContainer<double> bcGlobalValues;
mesh->boundary().bcsToImpose(bcGlobalIndices,bcGlobalValues,*(solution->bc()), NULL);
set<int> bcInds;
for (int i=0; i<bcGlobalIndices.dimension(0); i++)
{
bcInds.insert(bcGlobalIndices(i));
}
//////////////////// CHECK GALERKIN ORTHOGONALITY ///////////////////////
BCPtr nullBC;
RHSPtr nullRHS;
IPPtr nullIP;
SolutionPtr solnPerturbation = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
map< int, vector<DofInfo> > infoMap = constructGlobalDofToLocalDofInfoMap(mesh);
for (map< int, vector<DofInfo> >::iterator mapIt = infoMap.begin();
mapIt != infoMap.end(); mapIt++)
{
int dofIndex = mapIt->first;
vector< DofInfo > dofInfoVector = mapIt->second; // all the local dofs that map to dofIndex
// create perturbation in direction du
solnPerturbation->clear(); // clear all solns
// set each corresponding local dof to 1.0
for (vector< DofInfo >::iterator dofInfoIt = dofInfoVector.begin();
dofInfoIt != dofInfoVector.end(); dofInfoIt++)
{
DofInfo info = *dofInfoIt;
FieldContainer<double> solnCoeffs(info.basisCardinality);
solnCoeffs(info.basisOrdinal) = 1.0;
solnPerturbation->setSolnCoeffsForCellID(solnCoeffs, info.cellID, info.trialID, info.sideIndex);
}
// solnPerturbation->setSolnCoeffForGlobalDofIndex(1.0,dofIndex);
LinearTermPtr b_du = convectionBF->testFunctional(solnPerturbation);
FunctionPtr gradient = b_du->evaluate(err_rep_map, TestingUtilities::isFluxOrTraceDof(mesh,dofIndex)); // use boundary part only if flux
double grad = gradient->integrate(mesh,10);
if (!TestingUtilities::isFluxOrTraceDof(mesh,dofIndex) && abs(grad)>tol) // if we're not single-precision zero FOR FIELDS
{
// int cellID = mesh->getGlobalToLocalMap()[dofIndex].first;
cout << "Failed testGalerkinOrthogonality() for fields with diff " << abs(grad) << " at dof " << dofIndex << "; info:" << endl;
cout << dofInfoString(infoMap[dofIndex]);
success = false;
}
}
FieldContainer<double> errorJumps(mesh->numGlobalDofs()); //initialized to zero
// just test fluxes ON INTERNAL SKELETON here
set<GlobalIndexType> activeCellIDs = mesh->getActiveCellIDsGlobal();
for (GlobalIndexType activeCellID : activeCellIDs)
{
ElementPtr elem = mesh->getElement(activeCellID);
for (int sideIndex = 0; sideIndex < 4; sideIndex++)
{
ElementTypePtr elemType = elem->elementType();
vector<int> localDofIndices = elemType->trialOrderPtr->getDofIndices(beta_n_u->ID(), sideIndex);
for (int i = 0; i<localDofIndices.size(); i++)
{
int globalDofIndex = mesh->globalDofIndex(elem->cellID(), localDofIndices[i]);
vector< DofInfo > dofInfoVector = infoMap[globalDofIndex];
solnPerturbation->clear();
TestingUtilities::setSolnCoeffForGlobalDofIndex(solnPerturbation,1.0,globalDofIndex);
// also add in BCs
for (int i = 0; i<bcGlobalIndices.dimension(0); i++)
{
TestingUtilities::setSolnCoeffForGlobalDofIndex(solnPerturbation,bcGlobalValues(i),bcGlobalIndices(i));
}
LinearTermPtr b_du = convectionBF->testFunctional(solnPerturbation);
FunctionPtr gradient = b_du->evaluate(err_rep_map, TestingUtilities::isFluxOrTraceDof(mesh,globalDofIndex)); // use boundary part only if flux
double jump = gradient->integrate(mesh,10);
errorJumps(globalDofIndex) += jump;
}
}
}
for (int i = 0; i<mesh->numGlobalDofs(); i++)
{
if (abs(errorJumps(i))>tol)
{
cout << "Failing Galerkin orthogonality test for fluxes with diff " << errorJumps(i) << " at dof " << i << endl;
cout << dofInfoString(infoMap[i]);
success = false;
}
}
return success;
}
