int main(int argc, char *argv[]) {
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int rank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
int nCells = args.Input<int>("--nCells", "num cells",2);
int numRefs = args.Input<int>("--numRefs","num adaptive refinements",0);
int numPreRefs = args.Input<int>("--numPreRefs","num preemptive adaptive refinements",0);
int order = args.Input<int>("--order","order of approximation",2);
double eps = args.Input<double>("--epsilon","diffusion parameter",1e-2);
double energyThreshold = args.Input<double>("-energyThreshold","energy thresh for adaptivity", .5);
double rampHeight = args.Input<double>("--rampHeight","ramp height at x = 2", 0.0);
double ipSwitch = args.Input<double>("--ipSwitch","point at which to switch to graph norm", 0.0); // default to 0 to remain on robust norm
bool useAnisotropy = args.Input<bool>("--useAnisotropy","aniso flag ", false);
int H1Order = order+1;
int pToAdd = args.Input<int>("--pToAdd","test space enrichment", 2);
FunctionPtr zero = Function::constant(0.0);
FunctionPtr one = Function::constant(1.0);
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
vector<double> e1,e2;
e1.push_back(1.0);e1.push_back(0.0);
e2.push_back(0.0);e2.push_back(1.0);
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
// first order term with magnitude alpha
double alpha = 0.0;
// confusionBF->addTerm(alpha * u, v);
//////////////////// BUILD MESH ///////////////////////
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);
mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));
MeshInfo meshInfo(mesh); // gets info like cell measure, etc
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
/*
// robust test norm
FunctionPtr C_h = Teuchos::rcp( new EpsilonScaling(eps) );
FunctionPtr invH = Teuchos::rcp(new InvHScaling);
FunctionPtr invSqrtH = Teuchos::rcp(new InvSqrtHScaling);
FunctionPtr sqrtH = Teuchos::rcp(new SqrtHScaling);
FunctionPtr hSwitch = Teuchos::rcp(new HSwitch(ipSwitch,mesh));
ip->addTerm(hSwitch*sqrt(eps) * v->grad() );
ip->addTerm(hSwitch*beta * v->grad() );
ip->addTerm(hSwitch*tau->div() );
// graph norm
ip->addTerm( (one-hSwitch)*((1.0/eps) * tau + v->grad()));
ip->addTerm( (one-hSwitch)*(beta * v->grad() - tau->div()));
// regularizing terms
ip->addTerm(C_h/sqrt(eps) * tau );
ip->addTerm(invSqrtH*v);
*/
// robust test norm
IPPtr robIP = Teuchos::rcp(new IP);
FunctionPtr C_h = Teuchos::rcp( new EpsilonScaling(eps) );
FunctionPtr invH = Teuchos::rcp(new InvHScaling);
FunctionPtr invSqrtH = Teuchos::rcp(new InvSqrtHScaling);
FunctionPtr sqrtH = Teuchos::rcp(new SqrtHScaling);
FunctionPtr hSwitch = Teuchos::rcp(new HSwitch(ipSwitch,mesh));
robIP->addTerm(sqrt(eps) * v->grad() );
robIP->addTerm(beta * v->grad() );
robIP->addTerm(tau->div() );
// regularizing terms
robIP->addTerm(C_h/sqrt(eps) * tau );
robIP->addTerm(invSqrtH*v);
IPPtr graphIP = confusionBF->graphNorm();
graphIP->addTerm(invSqrtH*v);
// graphIP->addTerm(C_h/sqrt(eps) * tau );
IPPtr switchIP = Teuchos::rcp(new IPSwitcher(robIP,graphIP,ipSwitch)); // rob IP for h>ipSwitch mesh size, graph norm o/w
ip = switchIP;
LinearTermPtr vVecLT = Teuchos::rcp(new LinearTerm);
LinearTermPtr tauVecLT = Teuchos::rcp(new LinearTerm);
vVecLT->addTerm(sqrt(eps)*v->grad());
tauVecLT->addTerm(C_h/sqrt(eps)*tau);
LinearTermPtr restLT = Teuchos::rcp(new LinearTerm);
restLT->addTerm(alpha*v);
restLT->addTerm(invSqrtH*v);
restLT = restLT + beta * v->grad();
restLT = restLT + tau->div();
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = zero;
// f = one;
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr Inflow = Teuchos::rcp(new LeftInflow);
SpatialFilterPtr wallBoundary = Teuchos::rcp(new WallBoundary);//MeshUtilities::rampBoundary(rampHeight);
SpatialFilterPtr freeStream = Teuchos::rcp(new FreeStreamBoundary);
bc->addDirichlet(uhat, wallBoundary, one);
// bc->addDirichlet(uhat, wallBoundary, Teuchos::rcp(new WallSmoothBC(eps)));
bc->addDirichlet(beta_n_u_minus_sigma_n, Inflow, zero);
bc->addDirichlet(beta_n_u_minus_sigma_n, freeStream, zero);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution;
solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
BCPtr nullBC = Teuchos::rcp((BC*)NULL); RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL); IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
mesh->registerSolution(backgroundFlow); // to trigger issue with p-refinements
map<int, Teuchos::RCP<Function> > functionMap; functionMap[u->ID()] = Function::constant(3.14);
backgroundFlow->projectOntoMesh(functionMap);
// lower p to p = 1 at SINGULARITY only
vector<int> ids;
/*
for (int i = 0;i<mesh->numActiveElements();i++){
bool cellIDset = false;
int cellID = mesh->activeElements()[i]->cellID();
int elemOrder = mesh->cellPolyOrder(cellID)-1;
FieldContainer<double> vv(4,2); mesh->verticesForCell(vv, cellID);
bool vertexOnWall = false; bool vertexAtSingularity = false;
for (int j = 0;j<4;j++){
if ((abs(vv(j,0)-.5) + abs(vv(j,1)))<1e-10){
vertexAtSingularity = true;
cellIDset = true;
}
}
if (!vertexAtSingularity && elemOrder<2 && !cellIDset ){
ids.push_back(cellID);
cout << "celliD = " << cellID << endl;
}
}
*/
ids.push_back(1);
ids.push_back(3);
mesh->pRefine(ids); // to put order = 1
return 0;
LinearTermPtr residual = rhs->linearTermCopy();
residual->addTerm(-confusionBF->testFunctional(solution));
RieszRepPtr rieszResidual = Teuchos::rcp(new RieszRep(mesh, ip, residual));
rieszResidual->computeRieszRep();
FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,rieszResidual));
FunctionPtr e_tau = Teuchos::rcp(new RepFunction(tau,rieszResidual));
map<int,FunctionPtr> errRepMap;
errRepMap[v->ID()] = e_v;
errRepMap[tau->ID()] = e_tau;
FunctionPtr errTau = tauVecLT->evaluate(errRepMap,false);
FunctionPtr errV = vVecLT->evaluate(errRepMap,false);
FunctionPtr errRest = restLT->evaluate(errRepMap,false);
FunctionPtr xErr = (errTau->x())*(errTau->x()) + (errV->dx())*(errV->dx());
FunctionPtr yErr = (errTau->y())*(errTau->y()) + (errV->dy())*(errV->dy());
FunctionPtr restErr = errRest*errRest;
RefinementStrategy refinementStrategy( solution, energyThreshold );
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// PRE REFINEMENTS
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
if (rank==0){
cout << "Number of pre-refinements = " << numPreRefs << endl;
}
for (int i =0;i<=numPreRefs;i++){
vector<ElementPtr> elems = mesh->activeElements();
vector<ElementPtr>::iterator elemIt;
vector<int> wallCells;
for (elemIt=elems.begin();elemIt != elems.end();elemIt++){
int cellID = (*elemIt)->cellID();
int numSides = mesh->getElement(cellID)->numSides();
FieldContainer<double> vertices(numSides,2); //for quads
mesh->verticesForCell(vertices, cellID);
bool cellIDset = false;
for (int j = 0;j<numSides;j++){
if ((abs(vertices(j,0)-.5)<1e-7) && (abs(vertices(j,1))<1e-7) && !cellIDset){ // if at singularity, i.e. if a vertex is (1,0)
wallCells.push_back(cellID);
cellIDset = true;
}
}
}
if (i<numPreRefs){
refinementStrategy.refineCells(wallCells);
}
}
double minSideLength = meshInfo.getMinCellSideLength() ;
double minCellMeasure = meshInfo.getMinCellMeasure() ;
if (rank==0){
cout << "after prerefs, sqrt min cell measure = " << sqrt(minCellMeasure) << ", min side length = " << minSideLength << endl;
}
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
VTKExporter exporter(solution, mesh, varFactory);
for (int refIndex=0;refIndex<numRefs;refIndex++){
if (rank==0){
cout << "on ref index " << refIndex << endl;
}
rieszResidual->computeRieszRep(); // in preparation to get anisotropy
vector<int> cellIDs;
refinementStrategy.getCellsAboveErrorThreshhold(cellIDs);
map<int,double> energyError = solution->energyError();
map<int,double> xErrMap = xErr->cellIntegrals(cellIDs,mesh,5,true);
map<int,double> yErrMap = yErr->cellIntegrals(cellIDs,mesh,5,true);
map<int,double> restErrMap = restErr->cellIntegrals(cellIDs,mesh,5,true);
for (vector<ElementPtr>::iterator elemIt = mesh->activeElements().begin();elemIt!=mesh->activeElements().end();elemIt++){
int cellID = (*elemIt)->cellID();
double err = xErrMap[cellID]+ yErrMap[cellID] + restErrMap[cellID];
// if (rank==0)
// cout << "err thru LT = " << sqrt(err) << ", while energy err = " << energyError[cellID] << endl;
}
/*
map<int,double> ratio,xErr,yErr;
vector<ElementPtr> elems = mesh->activeElements();
for (vector<ElementPtr>::iterator elemIt = elems.begin();elemIt!=elems.end();elemIt++){
int cellID = (*elemIt)->cellID();
ratio[cellID] = 0.0;
xErr[cellID] = 0.0;
yErr[cellID] = 0.0;
if (std::find(cellIDs.begin(),cellIDs.end(),cellID)!=cellIDs.end()){ // if this cell is above energy thresh
ratio[cellID] = yErrMap[cellID]/xErrMap[cellID];
xErr[cellID] = xErrMap[cellID];
yErr[cellID] = yErrMap[cellID];
}
}
FunctionPtr ratioFxn = Teuchos::rcp(new EnergyErrorFunction(ratio));
FunctionPtr xErrFxn = Teuchos::rcp(new EnergyErrorFunction(xErr));
FunctionPtr yErrFxn = Teuchos::rcp(new EnergyErrorFunction(yErr));
exporter.exportFunction(ratioFxn, string("ratio")+oss.str());
exporter.exportFunction(xErrFxn, string("xErr")+oss.str());
exporter.exportFunction(yErrFxn, string("yErr")+oss.str());
*/
if (useAnisotropy){
refinementStrategy.refine(rank==0,xErrMap,yErrMap); //anisotropic refinements
}else{
refinementStrategy.refine(rank==0); // no anisotropy
}
// lower p to p = 1 at SINGULARITY only
vector<int> ids;
for (int i = 0;i<mesh->numActiveElements();i++){
int cellID = mesh->activeElements()[i]->cellID();
int elemOrder = mesh->cellPolyOrder(cellID)-1;
FieldContainer<double> vv(4,2); mesh->verticesForCell(vv, cellID);
bool vertexOnWall = false; bool vertexAtSingularity = false;
for (int j = 0;j<4;j++){
if ((abs(vv(j,0)-.5) + abs(vv(j,1)))<1e-10)
vertexAtSingularity = true;
}
if (!vertexAtSingularity && elemOrder<2){
ids.push_back(cellID);
}
}
mesh->pRefine(ids); // to put order = 1
/*
if (elemOrder>1){
if (vertexAtSingularity){
vector<int> ids;
ids.push_back(cellID);
mesh->pRefine(ids,1-(elemOrder-1)); // to put order = 1
// mesh->pRefine(ids); // to put order = 1
if (rank==0)
cout << "p unrefining elem with elemOrder = " << elemOrder << endl;
}
}else{
if (!vertexAtSingularity){
vector<int> ids;
ids.push_back(cellID);
mesh->pRefine(ids,2-elemOrder);
}
}
*/
double minSideLength = meshInfo.getMinCellSideLength() ;
if (rank==0)
cout << "minSideLength is " << minSideLength << endl;
solution->condensedSolve();
std::ostringstream oss;
oss << refIndex;
}
// final solve on final mesh
solution->setWriteMatrixToFile(true,"K.mat");
solution->condensedSolve();
////////////////////////////////////////////////////////////////////////////////////////////////////////////
// CHECK CONDITIONING
////////////////////////////////////////////////////////////////////////////////////////////////////////////
bool checkConditioning = true;
if (checkConditioning){
double minSideLength = meshInfo.getMinCellSideLength() ;
StandardAssembler assembler(solution);
double maxCond = 0.0;
int maxCellID = 0;
for (int i = 0;i<mesh->numActiveElements();i++){
int cellID = mesh->getActiveElement(i)->cellID();
FieldContainer<double> ipMat = assembler.getIPMatrix(mesh->getElement(cellID));
double cond = SerialDenseWrapper::getMatrixConditionNumber(ipMat);
if (cond>maxCond){
maxCond = cond;
maxCellID = cellID;
}
}
if (rank==0){
cout << "cell ID " << maxCellID << " has minCellLength " << minSideLength << " and condition estimate " << maxCond << endl;
}
string ipMatName = string("ipMat.mat");
ElementPtr maxCondElem = mesh->getElement(maxCellID);
FieldContainer<double> ipMat = assembler.getIPMatrix(maxCondElem);
SerialDenseWrapper::writeMatrixToMatlabFile(ipMatName,ipMat);
}
//////////////////// print to file ///////////////////////
if (rank==0){
exporter.exportSolution(string("robustIP"));
cout << endl;
}
return 0;
}
bool LinearTermTests::testRieszInversionAsProjection()
{
bool success = true;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr tau = varFactory->testVar("\\tau", HDIV);
VarPtr v = varFactory->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory->traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory->fieldVar("u");
VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
double eps = .01;
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = 2;
int pToAdd = 2;
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 1.0;
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 nCells = 2;
int horizontalCells = nCells, verticalCells = nCells;
// create a new mesh:
MeshPtr myMesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells, confusionBF, H1Order, H1Order+pToAdd);
ElementTypePtr elemType = myMesh->getElement(0)->elementType();
BasisCachePtr basisCache = Teuchos::rcp(new BasisCache(elemType, myMesh));
vector<GlobalIndexType> cellIDs = myMesh->cellIDsOfTypeGlobal(elemType);
bool createSideCacheToo = true;
basisCache->setPhysicalCellNodes(myMesh->physicalCellNodesGlobal(elemType), cellIDs, createSideCacheToo);
LinearTermPtr integrand = Teuchos::rcp(new LinearTerm); // residual
FunctionPtr x = Function::xn(1);
FunctionPtr y = Function::yn(1);
FunctionPtr testFxn1 = x;
FunctionPtr testFxn2 = y;
FunctionPtr fxnToProject = x * y + 1.0;
integrand->addTerm(fxnToProject * v);
IPPtr ip_L2 = Teuchos::rcp(new IP);
ip_L2->addTerm(v);
ip_L2->addTerm(tau);
Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(myMesh, ip_L2, integrand));
riesz->computeRieszRep();
FunctionPtr rieszFxn = RieszRep::repFunction(v,riesz);
int numCells = basisCache->getPhysicalCubaturePoints().dimension(0);
int numPts = basisCache->getPhysicalCubaturePoints().dimension(1);
FieldContainer<double> valProject( numCells, numPts );
FieldContainer<double> valExpected( numCells, numPts );
rieszFxn->values(valProject,basisCache);
fxnToProject->values(valExpected,basisCache);
// int rank = Teuchos::GlobalMPISession::getRank();
// if (rank==0) cout << "physicalCubaturePoints:\n" << basisCache->getPhysicalCubaturePoints();
double maxDiff;
double tol = 1e-12;
success = TestSuite::fcsAgree(valProject,valExpected,tol,maxDiff);
if (success==false)
{
cout << "Failed Riesz Inversion Projection test with maxDiff = " << maxDiff << endl;
serializeOutput("valExpected", valExpected);
serializeOutput("valProject", valProject);
serializeOutput("physicalPoints", basisCache->getPhysicalCubaturePoints());
}
return allSuccess(success);
}
int main(int argc, char *argv[]) {
// Process command line arguments
if (argc > 1)
numRefs = atof(argv[1]);
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
FunctionPtr beta = Teuchos::rcp(new Beta());
////////////////////////////////////////////////////////////////////
// DEFINE VARIABLES
////////////////////////////////////////////////////////////////////
// test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// trial variables
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
////////////////////////////////////////////////////////////////////
// CREATE MESH
////////////////////////////////////////////////////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
FieldContainer<double> meshBoundary(4,2);
meshBoundary(0,0) = 0.0; // x1
meshBoundary(0,1) = -2.0; // y1
meshBoundary(1,0) = 4.0;
meshBoundary(1,1) = -2.0;
meshBoundary(2,0) = 4.0;
meshBoundary(2,1) = 2.0;
meshBoundary(3,0) = 0.0;
meshBoundary(3,1) = 2.0;
int horizontalCells = 4, verticalCells = 4;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
confusionBF, H1Order, H1Order+pToAdd, false);
////////////////////////////////////////////////////////////////////
// INITIALIZE BACKGROUND FLOW FUNCTIONS
////////////////////////////////////////////////////////////////////
BCPtr nullBC = Teuchos::rcp((BC*)NULL);
RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr prevTimeFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
SolutionPtr flowResidual = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
FunctionPtr u_prev_time = Teuchos::rcp( new PreviousSolutionFunction(prevTimeFlow, u) );
// ==================== SET INITIAL GUESS ==========================
double u_free = 0.0;
double sigma1_free = 0.0;
double sigma2_free = 0.0;
map<int, Teuchos::RCP<Function> > functionMap;
functionMap[u->ID()] = Teuchos::rcp( new ConstantScalarFunction(u_free) );
functionMap[sigma1->ID()] = Teuchos::rcp( new ConstantScalarFunction(sigma1_free) );
functionMap[sigma2->ID()] = Teuchos::rcp( new ConstantScalarFunction(sigma2_free) );
prevTimeFlow->projectOntoMesh(functionMap);
// ==================== END SET INITIAL GUESS ==========================
////////////////////////////////////////////////////////////////////
// DEFINE BILINEAR FORM
////////////////////////////////////////////////////////////////////
// tau terms:
confusionBF->addTerm(sigma1 / epsilon, tau->x());
confusionBF->addTerm(sigma2 / epsilon, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(-uhat, tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( beta * u, - v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
////////////////////////////////////////////////////////////////////
// TIMESTEPPING TERMS
////////////////////////////////////////////////////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
double dt = 0.25;
FunctionPtr invDt = Teuchos::rcp(new ScalarParamFunction(1.0/dt));
if (rank==0){
cout << "Timestep dt = " << dt << endl;
}
if (transient)
{
confusionBF->addTerm( u, invDt*v );
rhs->addTerm( u_prev_time * invDt * v );
}
////////////////////////////////////////////////////////////////////
// DEFINE INNER PRODUCT
////////////////////////////////////////////////////////////////////
// mathematician's norm
IPPtr mathIP = Teuchos::rcp(new IP());
mathIP->addTerm(tau);
mathIP->addTerm(tau->div());
mathIP->addTerm(v);
mathIP->addTerm(v->grad());
// quasi-optimal norm
IPPtr qoptIP = Teuchos::rcp(new IP);
qoptIP->addTerm( v );
qoptIP->addTerm( tau / epsilon + v->grad() );
qoptIP->addTerm( beta * v->grad() - tau->div() );
// robust test norm
IPPtr robIP = Teuchos::rcp(new IP);
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
if (!enforceLocalConservation)
{
robIP->addTerm( ip_scaling * v );
if (transient)
robIP->addTerm( invDt * v );
}
robIP->addTerm( sqrt(epsilon) * v->grad() );
// Weight these two terms for inflow
FunctionPtr ip_weight = Teuchos::rcp( new IPWeight() );
robIP->addTerm( ip_weight * beta * v->grad() );
robIP->addTerm( ip_weight * tau->div() );
robIP->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (enforceLocalConservation)
robIP->addZeroMeanTerm( v );
////////////////////////////////////////////////////////////////////
// DEFINE RHS
////////////////////////////////////////////////////////////////////
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
////////////////////////////////////////////////////////////////////
// DEFINE BC
////////////////////////////////////////////////////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
// Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
SpatialFilterPtr lBoundary = Teuchos::rcp( new LeftBoundary );
SpatialFilterPtr tbBoundary = Teuchos::rcp( new TopBottomBoundary );
SpatialFilterPtr rBoundary = Teuchos::rcp( new RightBoundary );
FunctionPtr u0 = Teuchos::rcp( new ZeroBC );
FunctionPtr u_inlet = Teuchos::rcp( new InletBC );
// FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
bc->addDirichlet(beta_n_u_minus_sigma_n, lBoundary, u_inlet);
bc->addDirichlet(beta_n_u_minus_sigma_n, tbBoundary, u0);
bc->addDirichlet(uhat, rBoundary, u0);
// pc->addConstraint(beta_n_u_minus_sigma_n - uhat == u0, rBoundary);
////////////////////////////////////////////////////////////////////
// CREATE SOLUTION OBJECT
////////////////////////////////////////////////////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) );
// solution->setFilter(pc);
// ==================== Enforce Local Conservation ==================
if (enforceLocalConservation) {
if (transient)
{
FunctionPtr conserved_rhs = u_prev_time * invDt;
LinearTermPtr conserved_quantity = invDt * u;
LinearTermPtr flux_part = Teuchos::rcp(new LinearTerm(-1.0, beta_n_u_minus_sigma_n));
conserved_quantity->addTerm(flux_part, true);
// conserved_quantity = conserved_quantity - beta_n_u_minus_sigma_n;
solution->lagrangeConstraints()->addConstraint(conserved_quantity == conserved_rhs);
}
else
{
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero);
}
}
// ==================== Register Solutions ==========================
mesh->registerSolution(solution);
mesh->registerSolution(prevTimeFlow); // u_t(i-1)
mesh->registerSolution(flowResidual); // u_t(i-1)
double energyThreshold = 0.25; // for mesh refinements
Teuchos::RCP<RefinementStrategy> refinementStrategy;
refinementStrategy = Teuchos::rcp(new RefinementStrategy(solution,energyThreshold));
////////////////////////////////////////////////////////////////////
// PSEUDO-TIME SOLVE STRATEGY
////////////////////////////////////////////////////////////////////
double time_tol = 1e-8;
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
double L2_time_residual = 1e7;
int timestepCount = 0;
if (!transient)
numTimeSteps = 1;
while((L2_time_residual > time_tol) && (timestepCount < numTimeSteps))
{
solution->solve(false);
// subtract solutions to get residual
flowResidual->setSolution(solution); // reset previous time solution to current time sol
flowResidual->addSolution(prevTimeFlow, -1.0);
double L2u = flowResidual->L2NormOfSolutionGlobal(u->ID());
double L2sigma1 = flowResidual->L2NormOfSolutionGlobal(sigma1->ID());
double L2sigma2 = flowResidual->L2NormOfSolutionGlobal(sigma2->ID());
L2_time_residual = sqrt(L2u*L2u + L2sigma1*L2sigma1 + L2sigma2*L2sigma2);
cout << endl << "Timestep: " << timestepCount << ", dt = " << dt << ", Time residual = " << L2_time_residual << endl;
if (rank == 0)
{
stringstream outfile;
if (transient)
outfile << "TransientConfusion_" << refIndex << "_" << timestepCount;
else
outfile << "TransientConfusion_" << refIndex;
solution->writeToVTK(outfile.str(), 5);
}
//////////////////////////////////////////////////////////////////////////
// Check conservation by testing against one
//////////////////////////////////////////////////////////////////////////
VarPtr testOne = varFactory.testVar("1", CONSTANT_SCALAR);
// Create a fake bilinear form for the testing
BFPtr fakeBF = Teuchos::rcp( new BF(varFactory) );
// Define our mass flux
FunctionPtr flux_current_time = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_minus_sigma_n) );
FunctionPtr delta_u = Teuchos::rcp( new PreviousSolutionFunction(flowResidual, u) );
LinearTermPtr surfaceFlux = -1.0 * flux_current_time * testOne;
LinearTermPtr volumeChange = invDt * delta_u * testOne;
LinearTermPtr massFluxTerm;
if (transient)
{
massFluxTerm = volumeChange;
// massFluxTerm->addTerm(surfaceFlux);
}
else
{
massFluxTerm = surfaceFlux;
}
// cout << "surface case = " << surfaceFlux->summands()[0].first->boundaryValueOnly() << " volume case = " << volumeChange->summands()[0].first->boundaryValueOnly() << endl;
// FunctionPtr massFlux= Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_minus_sigma_n) );
// LinearTermPtr massFluxTerm = massFlux * testOne;
Teuchos::RCP<shards::CellTopology> quadTopoPtr = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ));
DofOrderingFactory dofOrderingFactory(fakeBF);
int fakeTestOrder = H1Order;
DofOrderingPtr testOrdering = dofOrderingFactory.testOrdering(fakeTestOrder, *quadTopoPtr);
int testOneIndex = testOrdering->getDofIndex(testOne->ID(),0);
vector< ElementTypePtr > elemTypes = mesh->elementTypes(); // global element types
map<int, double> massFluxIntegral; // cellID -> integral
double maxMassFluxIntegral = 0.0;
double totalMassFlux = 0.0;
double totalAbsMassFlux = 0.0;
for (vector< ElementTypePtr >::iterator elemTypeIt = elemTypes.begin(); elemTypeIt != elemTypes.end(); elemTypeIt++)
{
ElementTypePtr elemType = *elemTypeIt;
vector< ElementPtr > elems = mesh->elementsOfTypeGlobal(elemType);
vector<int> cellIDs;
for (int i=0; i<elems.size(); i++) {
cellIDs.push_back(elems[i]->cellID());
}
FieldContainer<double> physicalCellNodes = mesh->physicalCellNodesGlobal(elemType);
BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(elemType,mesh) );
basisCache->setPhysicalCellNodes(physicalCellNodes,cellIDs,true); // true: create side caches
FieldContainer<double> cellMeasures = basisCache->getCellMeasures();
FieldContainer<double> fakeRHSIntegrals(elems.size(),testOrdering->totalDofs());
massFluxTerm->integrate(fakeRHSIntegrals,testOrdering,basisCache,true); // true: force side evaluation
for (int i=0; i<elems.size(); i++) {
int cellID = cellIDs[i];
// pick out the ones for testOne:
massFluxIntegral[cellID] = fakeRHSIntegrals(i,testOneIndex);
}
// find the largest:
for (int i=0; i<elems.size(); i++) {
int cellID = cellIDs[i];
maxMassFluxIntegral = max(abs(massFluxIntegral[cellID]), maxMassFluxIntegral);
}
for (int i=0; i<elems.size(); i++) {
int cellID = cellIDs[i];
maxMassFluxIntegral = max(abs(massFluxIntegral[cellID]), maxMassFluxIntegral);
totalMassFlux += massFluxIntegral[cellID];
totalAbsMassFlux += abs( massFluxIntegral[cellID] );
}
}
// Print results from processor with rank 0
if (rank == 0)
{
cout << "largest mass flux: " << maxMassFluxIntegral << endl;
cout << "total mass flux: " << totalMassFlux << endl;
cout << "sum of mass flux absolute value: " << totalAbsMassFlux << endl;
}
prevTimeFlow->setSolution(solution); // reset previous time solution to current time sol
timestepCount++;
}
if (refIndex < numRefs){
if (rank==0){
cout << "Performing refinement number " << refIndex << endl;
}
refinementStrategy->refine(rank==0);
// RESET solution every refinement - make sure discretization error doesn't creep in
// prevTimeFlow->projectOntoMesh(functionMap);
}
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
int polyOrder = 3;
int pToAdd = 2; // for tests
// define our manufactured solution or problem bilinear form:
double epsilon = 1e-2;
bool useTriangles = false;
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 1.0;
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 = polyOrder + 1;
int horizontalCells = 1, verticalCells = 1;
double energyThreshold = 0.2; // for mesh refinements
double nonlinearStepSize = 0.5;
double nonlinearRelativeEnergyTolerance = 0.015; // used to determine convergence of the nonlinear solution
////////////////////////////////////////////////////////////////////
// SET UP PROBLEM
////////////////////////////////////////////////////////////////////
Teuchos::RCP<BurgersBilinearForm> oldBurgersBF = Teuchos::rcp(new BurgersBilinearForm(epsilon));
// new-style bilinear form definition
VarFactory varFactory;
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_hat = varFactory.fluxVar("\\widehat{\\beta_n u - \\sigma_n}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
VarPtr tau = varFactory.testVar("\\tau",HDIV);
VarPtr v = varFactory.testVar("v",HGRAD);
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(quadPoints, horizontalCells, verticalCells, bf, H1Order, H1Order+pToAdd, useTriangles);
mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));
Teuchos::RCP<Solution> backgroundFlow = Teuchos::rcp(new Solution(mesh, Teuchos::rcp((BC*)NULL) , Teuchos::rcp((RHS*)NULL), Teuchos::rcp((DPGInnerProduct*)NULL))); // create null solution
oldBurgersBF->setBackgroundFlow(backgroundFlow);
// tau parts:
// 1/eps (sigma, tau)_K + (u, div tau)_K - (u_hat, tau_n)_dK
bf->addTerm(sigma1 / epsilon, tau->x());
bf->addTerm(sigma2 / epsilon, tau->y());
bf->addTerm(u, tau->div());
bf->addTerm( - uhat, tau->dot_normal() );
vector<double> e1(2); // (1,0)
e1[0] = 1;
vector<double> e2(2); // (0,1)
e2[1] = 1;
FunctionPtr u_prev = Teuchos::rcp( new PreviousSolutionFunction(backgroundFlow, u) );
FunctionPtr beta = e1 * u_prev + Teuchos::rcp( new ConstantVectorFunction( e2 ) );
// v:
// (sigma, grad v)_K - (sigma_hat_n, v)_dK - (u, beta dot grad v) + (u_hat * n dot beta, v)_dK
bf->addTerm( sigma1, v->dx() );
bf->addTerm( sigma2, v->dy() );
bf->addTerm( -u, beta * v->grad());
bf->addTerm( beta_n_u_minus_sigma_hat, v);
// ==================== SET INITIAL GUESS ==========================
mesh->registerSolution(backgroundFlow);
map<int, Teuchos::RCP<AbstractFunction> > functionMap;
functionMap[BurgersBilinearForm::U] = Teuchos::rcp(new InitialGuess());
functionMap[BurgersBilinearForm::SIGMA_1] = Teuchos::rcp(new ZeroFunction());
functionMap[BurgersBilinearForm::SIGMA_2] = Teuchos::rcp(new ZeroFunction());
backgroundFlow->projectOntoMesh(functionMap);
// ==================== END SET INITIAL GUESS ==========================
// compare stiffness matrices for first linear step:
int trialOrder = 1;
pToAdd = 0;
int testOrder = trialOrder + pToAdd;
CellTopoPtr quadTopoPtr = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ));
DofOrderingFactory dofOrderingFactory(bf);
DofOrderingPtr testOrdering = dofOrderingFactory.testOrdering(testOrder, *quadTopoPtr);
DofOrderingPtr trialOrdering = dofOrderingFactory.trialOrdering(trialOrder, *quadTopoPtr);
int numCells = 1;
// just use testOrdering for both trial and test spaces (we only use to define BasisCache)
ElementTypePtr elemType = Teuchos::rcp( new ElementType(trialOrdering, testOrdering, quadTopoPtr) );
BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(elemType) );
quadPoints.resize(1,quadPoints.dimension(0),quadPoints.dimension(1));
basisCache->setPhysicalCellNodes(quadPoints,vector<int>(1),true); // true: do create side cache
FieldContainer<double> cellSideParities(numCells,quadTopoPtr->getSideCount());
cellSideParities.initialize(1.0); // not worried here about neighbors actually having opposite parity -- just want the two BF implementations to agree...
FieldContainer<double> expectedValues(numCells, testOrdering->totalDofs(), trialOrdering->totalDofs() );
FieldContainer<double> actualValues(numCells, testOrdering->totalDofs(), trialOrdering->totalDofs() );
oldBurgersBF->stiffnessMatrix(expectedValues, elemType, cellSideParities, basisCache);
bf->stiffnessMatrix(actualValues, elemType, cellSideParities, basisCache);
// compare beta's as well
FieldContainer<double> expectedBeta = oldBurgersBF->getBeta(basisCache);
Teuchos::Array<int> dim;
expectedBeta.dimensions(dim);
FieldContainer<double> actualBeta(dim);
beta->values(actualBeta,basisCache);
double tol = 1e-14;
double maxDiff;
if (rank == 0)
{
if ( ! TestSuite::fcsAgree(expectedBeta,actualBeta,tol,maxDiff) )
{
cout << "Test failed: old Burgers beta differs from new; maxDiff " << maxDiff << ".\n";
cout << "Old beta: \n" << expectedBeta;
cout << "New beta: \n" << actualBeta;
}
else
{
cout << "Old and new Burgers beta agree!!\n";
}
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old Burgers stiffness differs from new; maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "TrialDofOrdering: \n" << *trialOrdering;
cout << "TestDofOrdering:\n" << *testOrdering;
}
else
{
cout << "Old and new Burgers stiffness agree!!\n";
}
}
// define our inner product:
// Teuchos::RCP<BurgersInnerProduct> ip = Teuchos::rcp( new BurgersInnerProduct( bf, mesh ) );
// function to scale the squared guy by epsilon/h
FunctionPtr epsilonOverHScaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
IPPtr ip = Teuchos::rcp( new IP );
ip->addTerm(tau);
ip->addTerm(tau->div());
ip->addTerm( epsilonOverHScaling * v );
ip->addTerm( sqrt(sqrt(epsilon)) * v->grad() );
ip->addTerm( beta * v->grad() );
// use old IP instead, for now...
Teuchos::RCP<BurgersInnerProduct> oldIP = Teuchos::rcp( new BurgersInnerProduct( oldBurgersBF, mesh ) );
expectedValues.resize(numCells, testOrdering->totalDofs(), testOrdering->totalDofs() );
actualValues.resize (numCells, testOrdering->totalDofs(), testOrdering->totalDofs() );
BasisCachePtr ipBasisCache = Teuchos::rcp( new BasisCache(elemType, true) ); // true: test vs. test
ipBasisCache->setPhysicalCellNodes(quadPoints,vector<int>(1),false); // false: don't create side cache
oldIP->computeInnerProductMatrix(expectedValues,testOrdering,ipBasisCache);
ip->computeInnerProductMatrix(actualValues,testOrdering,ipBasisCache);
tol = 1e-14;
maxDiff = 0.0;
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old inner product differs from new IP; maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New IP: \n" << actualValues;
cout << "testOrdering: \n" << *testOrdering;
}
else
{
cout << "Old inner product and new IP agree!!\n";
}
}
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
// the RHS as implemented by BurgersProblem divides the first component of beta by 2.0
// so we follow that. I've not done the math; just imitating the code...
Teuchos::RCP<RHSEasy> otherRHS = Teuchos::rcp( new RHSEasy );
vector<double> e1_div2 = e1;
e1_div2[0] /= 2.0;
FunctionPtr rhsBeta = (e1_div2 * beta * e1 + Teuchos::rcp( new ConstantVectorFunction( e2 ) )) * u_prev;
otherRHS->addTerm( rhsBeta * v->grad() - u_prev * tau->div() );
Teuchos::RCP<BurgersProblem> problem = Teuchos::rcp( new BurgersProblem(oldBurgersBF) );
expectedValues.resize(numCells, testOrdering->totalDofs() );
actualValues.resize (numCells, testOrdering->totalDofs() );
problem->integrateAgainstStandardBasis(expectedValues,testOrdering,basisCache);
otherRHS->integrateAgainstStandardBasis(actualValues,testOrdering,basisCache);
tol = 1e-14;
maxDiff = 0.0;
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old RHS differs from new (\"otherRHS\"); maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "testOrdering: \n" << *testOrdering;
}
else
{
cout << "Old and new RHS (\"otherRHS\") agree!!\n";
}
}
FunctionPtr u_prev_squared_div2 = 0.5 * u_prev * u_prev;
rhs->addTerm( (e1 * u_prev_squared_div2 + e2 * u_prev) * v->grad() - u_prev * tau->div());
if (! functionsAgree(e2 * u_prev,
Teuchos::rcp( new ConstantVectorFunction( e2 ) ) * u_prev,
basisCache) )
{
cout << "two like functions differ...\n";
}
FunctionPtr e1_f = Teuchos::rcp( new ConstantVectorFunction( e1 ) );
FunctionPtr e2_f = Teuchos::rcp( new ConstantVectorFunction( e2 ) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction( 1.0 ) );
if (! functionsAgree( Teuchos::rcp( new ProductFunction(e1_f, (e1_f + e2_f)) ), // e1_f * (e1_f + e2_f)
one,
basisCache) )
{
cout << "two like functions differ...\n";
}
if (! functionsAgree(u_prev_squared_div2,
(e1_div2 * beta) * u_prev,
basisCache) )
{
cout << "two like functions differ...\n";
}
if (! functionsAgree(e1 * u_prev_squared_div2,
(e1_div2 * beta * e1) * u_prev,
basisCache) )
{
cout << "two like functions differ...\n";
}
if (! functionsAgree(e1 * u_prev_squared_div2 + e2 * u_prev,
(e1_div2 * beta * e1 + Teuchos::rcp( new ConstantVectorFunction( e2 ) )) * u_prev,
basisCache) )
{
cout << "two like functions differ...\n";
}
problem->integrateAgainstStandardBasis(expectedValues,testOrdering,basisCache);
rhs->integrateAgainstStandardBasis(actualValues,testOrdering,basisCache);
tol = 1e-14;
maxDiff = 0.0;
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old RHS differs from new (\"rhs\"); maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "testOrdering: \n" << *testOrdering;
}
else
{
cout << "Old and new RHS (\"rhs\") agree!!\n";
}
}
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new TopBoundary );
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new NegatedSpatialFilter(outflowBoundary) );
Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp(new PenaltyConstraints);
LinearTermPtr sigma_hat = beta * uhat->times_normal() - beta_n_u_minus_sigma_hat;
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
pc->addConstraint(sigma_hat==zero,outflowBoundary);
FunctionPtr u0 = Teuchos::rcp( new U0 );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
Teuchos::RCP<BCEasy> inflowBC = Teuchos::rcp( new BCEasy );
FunctionPtr u0_squared_div_2 = 0.5 * u0 * u0;
inflowBC->addDirichlet(beta_n_u_minus_sigma_hat,inflowBoundary, ( e1 * u0_squared_div_2 + e2 * u0) * n );
// create a solution object
Teuchos::RCP<Solution> solution = Teuchos::rcp(new Solution(mesh, inflowBC, rhs, ip));
mesh->registerSolution(solution);
solution->setFilter(pc);
// old penalty filter:
Teuchos::RCP<LocalStiffnessMatrixFilter> penaltyBC = Teuchos::rcp(new PenaltyMethodFilter(problem));
// solution->setFilter(penaltyBC);
// compare old and new filters
elemType = mesh->getElement(0)->elementType();
trialOrdering = elemType->trialOrderPtr;
testOrdering = elemType->testOrderPtr;
// stiffness
expectedValues.resize(numCells, trialOrdering->totalDofs(), trialOrdering->totalDofs() );
actualValues.resize (numCells, trialOrdering->totalDofs(), trialOrdering->totalDofs() );
expectedValues.initialize(0.0);
actualValues.initialize(0.0);
// load
FieldContainer<double> expectedLoad(numCells, trialOrdering->totalDofs() );
FieldContainer<double> actualLoad(numCells, trialOrdering->totalDofs() );
penaltyBC->filter(expectedValues,expectedLoad,basisCache,mesh,problem);
pc->filter(actualValues,actualLoad,basisCache,mesh,problem);
maxDiff = 0.0;
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old penalty stiffness differs from new; maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "trialOrdering: \n" << *trialOrdering;
}
else
{
cout << "Old and new penalty stiffness agree!!\n";
}
}
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedLoad,actualLoad,tol,maxDiff) )
{
cout << "Test failed: old penalty load differs from new; maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "trialOrdering: \n" << *trialOrdering;
}
else
{
cout << "Old and new penalty load agree!!\n";
}
}
// define refinement strategy:
Teuchos::RCP<RefinementStrategy> refinementStrategy = Teuchos::rcp(new RefinementStrategy(solution,energyThreshold));
// =================== END INITIALIZATION CODE ==========================
// refine the spectral mesh, for comparability with the original Burgers' driver
mesh->hRefine(vector<int>(1),RefinementPattern::regularRefinementPatternQuad());
int numRefs = 5;
Teuchos::RCP<NonlinearStepSize> stepSize = Teuchos::rcp(new NonlinearStepSize(nonlinearStepSize));
Teuchos::RCP<NonlinearSolveStrategy> solveStrategy = Teuchos::rcp(
new NonlinearSolveStrategy(backgroundFlow, solution, stepSize, nonlinearRelativeEnergyTolerance)
);
for (int refIndex=0; refIndex<numRefs; refIndex++)
{
solveStrategy->solve(rank==0);
refinementStrategy->refine(rank==0); // print to console on rank 0
}
// one more nonlinear solve on refined mesh
int numNRSteps = 5;
for (int i=0; i<numNRSteps; i++)
{
solution->solve(false);
backgroundFlow->addSolution(solution,1.0);
}
if (rank==0)
{
backgroundFlow->writeFieldsToFile(BurgersBilinearForm::U, "u_ref.m");
backgroundFlow->writeFieldsToFile(BurgersBilinearForm::SIGMA_1, "sigmax.m");
backgroundFlow->writeFieldsToFile(BurgersBilinearForm::SIGMA_2, "sigmay.m");
solution->writeFluxesToFile(BurgersBilinearForm::U_HAT, "du_hat_ref.dat");
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("uhat");
VarPtr sigma_n = varFactory.fluxVar("fhat");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("sigma1");
VarPtr sigma2 = varFactory.fieldVar("sigma2");
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma1, tau->x());
bf->addTerm(sigma2, tau->y());
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma1, v->dx() );
bf->addTerm( sigma2, v->dy() );
bf->addTerm( -sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = bf->graphNorm();
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(1.0) );
rhs->addTerm( f * v );
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
SpatialFilterPtr inflow = Teuchos::rcp( new Inflow );
bc->addDirichlet(uhat, inflow, zero);
SpatialFilterPtr leadingWedge = Teuchos::rcp( new LeadingWedge );
bc->addDirichlet(uhat, leadingWedge, zero);
SpatialFilterPtr trailingWedge = Teuchos::rcp( new TrailingWedge );
bc->addDirichlet(sigma_n, trailingWedge, zero);
// bc->addDirichlet(uhat, trailingWedge, zero);
SpatialFilterPtr top = Teuchos::rcp( new Top );
bc->addDirichlet(uhat, top, zero);
SpatialFilterPtr outflow = Teuchos::rcp( new Outflow );
bc->addDirichlet(uhat, outflow, zero);
//////////////////// BUILD MESH ///////////////////////
bool allQuads = true;
int H1Order = 3, pToAdd = 2;
// define nodes for mesh
vector< FieldContainer<double> > vertices;
FieldContainer<double> pt(2);
vector< vector<int> > elementIndices;
vector<int> q(4);
vector<int> t(3);
if (allQuads)
{
pt(0) = -halfwidth;
pt(1) = -1;
vertices.push_back(pt);
pt(0) = 0;
pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = -1;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = 0;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth;
pt(1) = halfwidth;
vertices.push_back(pt);
q[0] = 0;
q[1] = 1;
q[2] = 4;
q[3] = 5;
elementIndices.push_back(q);
q[0] = 1;
q[1] = 2;
q[2] = 3;
q[3] = 4;
elementIndices.push_back(q);
}
else
{
pt(0) = -halfwidth;
pt(1) = -1;
vertices.push_back(pt);
pt(0) = 0;
pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = -1;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = 0;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth;
pt(1) = 0;
vertices.push_back(pt);
t[0] = 0;
t[1] = 1;
t[2] = 7;
elementIndices.push_back(t);
t[0] = 1;
t[1] = 2;
t[2] = 3;
elementIndices.push_back(t);
q[0] = 1;
q[1] = 3;
q[2] = 4;
q[3] = 5;
elementIndices.push_back(q);
q[0] = 7;
q[1] = 1;
q[2] = 5;
q[3] = 6;
elementIndices.push_back(q);
}
Teuchos::RCP<Mesh> mesh = Teuchos::rcp( new Mesh(vertices, elementIndices, bf, H1Order, pToAdd) );
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
solution->setFilter(pc);
if (enforceLocalConservation)
{
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(sigma_n == zero);
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
solution->solve(false);
if (rank==0)
{
stringstream outfile;
outfile << "poissonwedge_" << refIndex;
solution->writeToVTK(outfile.str());
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma_n) );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
}
if (refIndex < numRefs)
{
// refinementStrategy.refine(rank==0); // print to console on rank 0
vector<int> cellsToRefine;
vector<int> cells_h;
vector<int> cells_p;
refinementStrategy.getCellsAboveErrorThreshhold(cellsToRefine);
for (int i=0; i < cellsToRefine.size(); i++)
if (sqrt(mesh->getCellMeasure(cellsToRefine[i])) < 1e-3)
{
int pOrder = mesh->cellPolyOrder(cellsToRefine[i]);
if (allQuads)
cells_p.push_back(cellsToRefine[i]);
else if (pOrder < 8)
cells_p.push_back(cellsToRefine[i]);
else
cout << "Reached cell size and polynomial order limits" << endl;
// cells_h.push_back(cellsToRefine[i]);
}
else
cells_h.push_back(cellsToRefine[i]);
refinementStrategy.pRefineCells(mesh, cells_p);
refinementStrategy.hRefineCells(mesh, cells_h);
}
}
return 0;
}
int main(int argc, char *argv[]) {
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
bool useCompliantGraphNorm = false;
bool enforceOneIrregularity = true;
bool writeStiffnessMatrices = false;
bool writeWorstCaseGramMatrices = false;
int numRefs = 10;
// problem parameters:
double eps = 1e-8;
vector<double> beta_const;
beta_const.push_back(2.0);
beta_const.push_back(1.0);
int k = 2, delta_k = 2;
Teuchos::CommandLineProcessor cmdp(false,true); // false: don't throw exceptions; true: do return errors for unrecognized options
cmdp.setOption("polyOrder",&k,"polynomial order for field variable u");
cmdp.setOption("delta_k", &delta_k, "test space polynomial order enrichment");
cmdp.setOption("numRefs",&numRefs,"number of refinements");
cmdp.setOption("eps", &eps, "epsilon");
if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL) {
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return -1;
}
int H1Order = k + 1;
if (rank==0) {
string normChoice = useCompliantGraphNorm ? "unit-compliant graph norm" : "standard graph norm";
cout << "Using " << normChoice << "." << endl;
cout << "eps = " << eps << endl;
cout << "numRefs = " << numRefs << endl;
cout << "p = " << k << endl;
}
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u;
if (useCompliantGraphNorm) {
u = varFactory.fieldVar("u",HGRAD);
} else {
u = varFactory.fieldVar("u");
}
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(-uhat, tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( beta_const * u, - v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// mathematician's norm
IPPtr mathIP = Teuchos::rcp(new IP());
mathIP->addTerm(tau);
mathIP->addTerm(tau->div());
mathIP->addTerm(v);
mathIP->addTerm(v->grad());
// quasi-optimal norm
IPPtr qoptIP = Teuchos::rcp(new IP);
if (!useCompliantGraphNorm) {
qoptIP->addTerm( tau / eps + v->grad() );
qoptIP->addTerm( beta_const * v->grad() - tau->div() );
qoptIP->addTerm( v );
} else {
FunctionPtr h = Teuchos::rcp( new hFunction );
// here, we're aiming at optimality in 1/h^2 |u|^2 + 1/eps^2 |sigma|^2
qoptIP->addTerm( tau + eps * v->grad() );
qoptIP->addTerm( h * beta_const * v->grad() - tau->div() );
qoptIP->addTerm(v);
qoptIP->addTerm(tau);
}
//////////////////// SPECIFY RHS ///////////////////////
RHSPtr rhs = RHS::rhs();
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
BCPtr bc = BC::bc();
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary );
FunctionPtr u0 = Teuchos::rcp( new U0 );
bc->addDirichlet(uhat, outflowBoundary, u0);
bc->addDirichlet(uhat, inflowBoundary, u0);
// Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp(new PenaltyConstraints);
// pc->addConstraint(uhat==u0,inflowBoundary);
//////////////////// BUILD MESH ///////////////////////
// create a new mesh on a single-cell, unit square domain
Teuchos::RCP<Mesh> mesh = MeshFactory::quadMeshMinRule(confusionBF, H1Order, delta_k);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, qoptIP) );
// solution->setFilter(pc);
double energyThreshold = 0.2; // for mesh refinements
bool useRieszRepBasedRefStrategy = true;
if (rank==0) {
if (useRieszRepBasedRefStrategy) {
cout << "using RieszRep-based refinement strategy.\n";
} else {
cout << "using solution-based refinement strategy.\n";
}
}
Teuchos::RCP<RefinementStrategy> refinementStrategy;
if (!useRieszRepBasedRefStrategy) {
refinementStrategy = Teuchos::rcp( new RefinementStrategy( solution, energyThreshold ) );
} else {
LinearTermPtr residual = confusionBF->testFunctional(solution) - rhs->linearTerm();
refinementStrategy = Teuchos::rcp( new RefinementStrategy( mesh, residual, qoptIP, energyThreshold ) );
}
refinementStrategy->setReportPerCellErrors(true);
refinementStrategy->setEnforceOneIrregularity(enforceOneIrregularity);
for (int refIndex=0; refIndex<numRefs; refIndex++){
if (writeStiffnessMatrices) {
string stiffnessFile = fileNameForRefinement("confusion_stiffness", refIndex);
solution->setWriteMatrixToFile(true, stiffnessFile);
}
solution->solve();
if (writeWorstCaseGramMatrices) {
string gramFile = fileNameForRefinement("confusion_gram", refIndex);
bool jacobiScaling = true;
double condNum = MeshUtilities::computeMaxLocalConditionNumber(qoptIP, mesh, jacobiScaling, gramFile);
if (rank==0) {
cout << "estimated worst-case Gram matrix condition number: " << condNum << endl;
cout << "putative worst-case Gram matrix written to file " << gramFile << endl;
}
}
if (refIndex == numRefs-1) { // write out second-to-last mesh
if (rank==0)
GnuPlotUtil::writeComputationalMeshSkeleton("confusionMesh", mesh, true);
}
refinementStrategy->refine(rank==0); // print to console on rank 0
}
if (writeStiffnessMatrices) {
string stiffnessFile = fileNameForRefinement("confusion_stiffness", numRefs);
solution->setWriteMatrixToFile(true, stiffnessFile);
}
if (writeWorstCaseGramMatrices) {
string gramFile = fileNameForRefinement("confusion_gram", numRefs);
bool jacobiScaling = true;
double condNum = MeshUtilities::computeMaxLocalConditionNumber(qoptIP, mesh, jacobiScaling, gramFile);
if (rank==0) {
cout << "estimated worst-case Gram matrix condition number: " << condNum << endl;
cout << "putative worst-case Gram matrix written to file " << gramFile << endl;
}
}
// one more solve on the final refined mesh:
solution->solve();
#ifdef HAVE_EPETRAEXT_HDF5
ostringstream dir_name;
dir_name << "confusion_eps" << eps;
HDF5Exporter exporter(mesh,dir_name.str());
exporter.exportSolution(solution, varFactory, 0);
if (rank==0) cout << "wrote solution to " << dir_name.str() << endl;
#endif
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
vector<double> beta_const;
beta_const.push_back(1.0);
beta_const.push_back(0.0);
// FunctionPtr beta = Teuchos::rcp(new Beta());
double eps = 1e-2;
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(-uhat, tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( beta_const * u, - v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// mathematician's norm
IPPtr mathIP = Teuchos::rcp(new IP());
mathIP->addTerm(tau);
mathIP->addTerm(tau->div());
mathIP->addTerm(v);
mathIP->addTerm(v->grad());
// quasi-optimal norm
IPPtr qoptIP = Teuchos::rcp(new IP);
qoptIP->addTerm( v );
qoptIP->addTerm( tau / eps + v->grad() );
qoptIP->addTerm( beta_const * v->grad() - tau->div() );
// robust test norm
IPPtr robIP = Teuchos::rcp(new IP);
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(eps) );
if (enforceLocalConservation)
{
robIP->addZeroMeanTerm( v );
}
else
{
robIP->addTerm( ip_scaling * v );
}
robIP->addTerm( sqrt(eps) * v->grad() );
robIP->addTerm( beta_const * v->grad() );
robIP->addTerm( tau->div() );
robIP->addTerm( ip_scaling/sqrt(eps) * tau );
//////////////////// SPECIFY RHS ///////////////////////
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = zero;
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
// SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
// SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary );
SpatialFilterPtr inflowTop = Teuchos::rcp(new InflowLshapeTop);
SpatialFilterPtr inflowBot = Teuchos::rcp(new InflowLshapeBottom);
SpatialFilterPtr LshapeBot1 = Teuchos::rcp(new LshapeBottom1);
SpatialFilterPtr LshapeBot2 = Teuchos::rcp(new LshapeBottom2);
SpatialFilterPtr Top = Teuchos::rcp(new LshapeTop);
SpatialFilterPtr Out = Teuchos::rcp(new LshapeOutflow);
FunctionPtr u0 = Teuchos::rcp( new U0 );
bc->addDirichlet(uhat, LshapeBot1, u0);
bc->addDirichlet(uhat, LshapeBot2, u0);
bc->addDirichlet(uhat, Top, u0);
bc->addDirichlet(uhat, Out, u0);
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
// bc->addDirichlet(uhat, inflowBot, u0);
FunctionPtr u0Top = Teuchos::rcp(new ParabolicProfile);
FunctionPtr u0Bot = Teuchos::rcp(new LinearProfile);
bc->addDirichlet(beta_n_u_minus_sigma_n, inflowTop, beta_const*n*u0Top);
// bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBot, beta_const*n*u0Bot);
bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBot, beta_const*n*zero);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = 2, pToAdd = 2;
/*
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 1.0;
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 horizontalCells = 1, verticalCells = 1;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
confusionBF, H1Order, H1Order+pToAdd);
*/
Teuchos::RCP<Mesh> mesh;
// L-shaped domain for double ramp problem
FieldContainer<double> A(2), B(2), C(2), D(2), E(2), F(2), G(2), H(2);
A(0) = 0.0;
A(1) = 0.5;
B(0) = 0.0;
B(1) = 1.0;
C(0) = 0.5;
C(1) = 1.0;
D(0) = 1.0;
D(1) = 1.0;
E(0) = 1.0;
E(1) = 0.5;
F(0) = 1.0;
F(1) = 0.0;
G(0) = 0.5;
G(1) = 0.0;
H(0) = 0.5;
H(1) = 0.5;
vector<FieldContainer<double> > vertices;
vertices.push_back(A);
int A_index = 0;
vertices.push_back(B);
int B_index = 1;
vertices.push_back(C);
int C_index = 2;
vertices.push_back(D);
int D_index = 3;
vertices.push_back(E);
int E_index = 4;
vertices.push_back(F);
int F_index = 5;
vertices.push_back(G);
int G_index = 6;
vertices.push_back(H);
int H_index = 7;
vector< vector<int> > elementVertices;
vector<int> el1, el2, el3, el4, el5;
// left patch:
el1.push_back(A_index);
el1.push_back(H_index);
el1.push_back(C_index);
el1.push_back(B_index);
// top right:
el2.push_back(H_index);
el2.push_back(E_index);
el2.push_back(D_index);
el2.push_back(C_index);
// bottom right:
el3.push_back(G_index);
el3.push_back(F_index);
el3.push_back(E_index);
el3.push_back(H_index);
elementVertices.push_back(el1);
elementVertices.push_back(el2);
elementVertices.push_back(el3);
mesh = Teuchos::rcp( new Mesh(vertices, elementVertices, confusionBF, H1Order, pToAdd) );
//////////////////// SOLVE & REFINE ///////////////////////
// Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, qoptIP) );
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) );
// solution->setFilter(pc);
if (enforceLocalConservation)
{
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero);
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
int numRefs = 8;
for (int refIndex=0; refIndex<numRefs; refIndex++)
{
solution->solve(false);
refinementStrategy.refine(rank==0); // print to console on rank 0
}
// one more solve on the final refined mesh:
solution->solve(false);
if (rank==0)
{
solution->writeToVTK("step.vtu",min(H1Order+1,4));
solution->writeFluxesToFile(uhat->ID(), "uhat.dat");
cout << "wrote files: u.m, uhat.dat\n";
}
return 0;
}
bool ScratchPadTests::testResidualMemoryError()
{
int rank = Teuchos::GlobalMPISession::getRank();
double tol = 1e-11;
bool success = true;
int nCells = 2;
double eps = 1e-2;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr tau = varFactory->testVar("\\tau", HDIV);
VarPtr v = varFactory->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory->traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory->fieldVar("u");
VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// robust test norm
IPPtr robIP = Teuchos::rcp(new IP);
robIP->addTerm(tau);
robIP->addTerm(tau->div());
robIP->addTerm(v->grad());
robIP->addTerm(v);
//////////////////// SPECIFY RHS ///////////////////////
FunctionPtr zero = Function::constant(0.0);
FunctionPtr one = Function::constant(1.0);
RHSPtr rhs = RHS::rhs();
FunctionPtr f = zero;
// FunctionPtr f = one;
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
BCPtr bc = BC::bc();
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new LRInflowSquareBoundary );
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new LROutflowSquareBoundary);
FunctionPtr n = Function::normal();
vector<double> e1,e2;
e1.push_back(1.0);
e1.push_back(0.0);
e2.push_back(0.0);
e2.push_back(1.0);
bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, beta*n*one);
bc->addDirichlet(uhat, outflowBoundary, zero);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int order = 2;
int H1Order = order+1;
int pToAdd = 2;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);
// mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution;
solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) );
solution->solve(false);
mesh->registerSolution(solution);
double energyErr1 = solution->energyErrorTotal();
LinearTermPtr residual = rhs->linearTermCopy();
residual->addTerm(-confusionBF->testFunctional(solution));
RieszRepPtr rieszResidual = Teuchos::rcp(new RieszRep(mesh, robIP, residual));
rieszResidual->computeRieszRep();
FunctionPtr e_v = RieszRep::repFunction(v,rieszResidual);
FunctionPtr e_tau = RieszRep::repFunction(tau,rieszResidual);
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
refinementStrategy.refine();
solution->solve(false);
double energyErr2 = solution->energyErrorTotal();
// if energy error rises
if (energyErr1 < energyErr2)
{
if (rank==0)
cout << "energy error increased from " << energyErr1 << " to " << energyErr2 << " after refinement.\n";
success = false;
}
return success;
}
void FunctionTests::setup()
{
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr tau = varFactory->testVar("\\tau", HDIV);
VarPtr v = varFactory->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory->traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory->fieldVar("u");
VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");
vector<double> beta_const;
beta_const.push_back(2.0);
beta_const.push_back(1.0);
double eps = 1e-2;
// standard confusion bilinear form
_confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
_confusionBF->addTerm(sigma1 / eps, tau->x());
_confusionBF->addTerm(sigma2 / eps, tau->y());
_confusionBF->addTerm(u, tau->div());
_confusionBF->addTerm(-uhat, tau->dot_normal());
// v terms:
_confusionBF->addTerm( sigma1, v->dx() );
_confusionBF->addTerm( sigma2, v->dy() );
_confusionBF->addTerm( beta_const * u, - v->grad() );
_confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = -1.0; // x1
quadPoints(0,1) = -1.0; // y1
quadPoints(1,0) = 1.0;
quadPoints(1,1) = -1.0;
quadPoints(2,0) = 1.0;
quadPoints(2,1) = 1.0;
quadPoints(3,0) = -1.0;
quadPoints(3,1) = 1.0;
int H1Order = 1, pToAdd = 0;
int horizontalCells = 1, verticalCells = 1;
// create a pointer to a new mesh:
_spectralConfusionMesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
_confusionBF, H1Order, H1Order+pToAdd);
// some 2D test points:
// setup test points:
static const int NUM_POINTS_1D = 10;
double x[NUM_POINTS_1D] = {-1.0,-0.8,-0.6,-.4,-.2,0,0.2,0.4,0.6,0.8};
double y[NUM_POINTS_1D] = {-0.8,-0.6,-.4,-.2,0,0.2,0.4,0.6,0.8,1.0};
_testPoints = FieldContainer<double>(NUM_POINTS_1D*NUM_POINTS_1D,2);
for (int i=0; i<NUM_POINTS_1D; i++)
{
for (int j=0; j<NUM_POINTS_1D; j++)
{
_testPoints(i*NUM_POINTS_1D + j, 0) = x[i];
_testPoints(i*NUM_POINTS_1D + j, 1) = y[j];
}
}
_elemType = _spectralConfusionMesh->getElementType(0);
vector<GlobalIndexType> cellIDs;
GlobalIndexType cellID = 0;
cellIDs.push_back(cellID);
_basisCache = Teuchos::rcp( new BasisCache( _elemType, _spectralConfusionMesh ) );
_basisCache->setRefCellPoints(_testPoints);
_basisCache->setPhysicalCellNodes( _spectralConfusionMesh->physicalCellNodesForCell(cellID), cellIDs, true );
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
int polyOrder = 2;
// define our manufactured solution or problem bilinear form:
double epsilon = 1e-3;
bool useTriangles = false;
int pToAdd = 2;
int nCells = 2;
if ( argc > 1)
{
nCells = atoi(argv[1]);
if (rank==0)
{
cout << "numCells = " << nCells << endl;
}
}
int numSteps = 20;
if ( argc > 2)
{
numSteps = atoi(argv[2]);
if (rank==0)
{
cout << "num NR steps = " << numSteps << endl;
}
}
int useHessian = 0; // defaults to "not use"
if ( argc > 3)
{
useHessian = atoi(argv[3]);
if (rank==0)
{
cout << "useHessian = " << useHessian << endl;
}
}
int thresh = numSteps; // threshhold for when to apply linesearch/hessian
if ( argc > 4)
{
thresh = atoi(argv[4]);
if (rank==0)
{
cout << "thresh = " << thresh << endl;
}
}
int H1Order = polyOrder + 1;
double energyThreshold = 0.2; // for mesh refinements
double nonlinearStepSize = 0.5;
double nonlinearRelativeEnergyTolerance = 1e-8; // used to determine convergence of the nonlinear solution
////////////////////////////////////////////////////////////////////
// DEFINE VARIABLES
////////////////////////////////////////////////////////////////////
// new-style bilinear form definition
VarFactory varFactory;
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_hat = varFactory.fluxVar("\\widehat{\\beta_n u - \\sigma_n}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
VarPtr tau = varFactory.testVar("\\tau",HDIV);
VarPtr v = varFactory.testVar("v",HGRAD);
BFPtr bf = Teuchos::rcp( new BF(varFactory) ); // initialize bilinear form
////////////////////////////////////////////////////////////////////
// CREATE MESH
////////////////////////////////////////////////////////////////////
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells, bf, H1Order, H1Order+pToAdd);
mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));
////////////////////////////////////////////////////////////////////
// INITIALIZE BACKGROUND FLOW FUNCTIONS
////////////////////////////////////////////////////////////////////
BCPtr nullBC = Teuchos::rcp((BC*)NULL);
RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC,
nullRHS, nullIP) );
vector<double> e1(2); // (1,0)
e1[0] = 1;
vector<double> e2(2); // (0,1)
e2[1] = 1;
FunctionPtr u_prev = Teuchos::rcp( new PreviousSolutionFunction(backgroundFlow, u) );
FunctionPtr beta = e1 * u_prev + Teuchos::rcp( new ConstantVectorFunction( e2 ) );
////////////////////////////////////////////////////////////////////
// DEFINE BILINEAR FORM
////////////////////////////////////////////////////////////////////
// tau parts:
// 1/eps (sigma, tau)_K + (u, div tau)_K - (u_hat, tau_n)_dK
bf->addTerm(sigma1 / epsilon, tau->x());
bf->addTerm(sigma2 / epsilon, tau->y());
bf->addTerm(u, tau->div());
bf->addTerm( - uhat, tau->dot_normal() );
// v:
// (sigma, grad v)_K - (sigma_hat_n, v)_dK - (u, beta dot grad v) + (u_hat * n dot beta, v)_dK
bf->addTerm( sigma1, v->dx() );
bf->addTerm( sigma2, v->dy() );
bf->addTerm( -u, beta * v->grad());
bf->addTerm( beta_n_u_minus_sigma_hat, v);
// ==================== SET INITIAL GUESS ==========================
mesh->registerSolution(backgroundFlow);
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr u0 = Teuchos::rcp( new U0 );
map<int, Teuchos::RCP<Function> > functionMap;
functionMap[u->ID()] = u0;
functionMap[sigma1->ID()] = zero;
functionMap[sigma2->ID()] = zero;
backgroundFlow->projectOntoMesh(functionMap);
// ==================== END SET INITIAL GUESS ==========================
////////////////////////////////////////////////////////////////////
// DEFINE INNER PRODUCT
////////////////////////////////////////////////////////////////////
// function to scale the squared guy by epsilon/h
FunctionPtr epsilonOverHScaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
IPPtr ip = Teuchos::rcp( new IP );
ip->addTerm( epsilonOverHScaling * (1.0/sqrt(epsilon))* tau);
ip->addTerm( tau->div());
// ip->addTerm( epsilonOverHScaling * v );
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
ip->addTerm(v->grad());
// ip->addTerm( beta * v->grad() );
////////////////////////////////////////////////////////////////////
// DEFINE RHS
////////////////////////////////////////////////////////////////////
RHSPtr rhs = RHS::rhs();
FunctionPtr u_prev_squared_div2 = 0.5 * u_prev * u_prev;
rhs->addTerm((e1 * u_prev_squared_div2 + e2 * u_prev) * v->grad() - u_prev * tau->div());
////////////////////////////////////////////////////////////////////
// DEFINE DIRICHLET BC
////////////////////////////////////////////////////////////////////
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new TopBoundary);
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new NegatedSpatialFilter(outflowBoundary) );
BCPtr inflowBC = BC::bc();
FunctionPtr u0_squared_div_2 = 0.5 * u0 * u0;
inflowBC->addDirichlet(beta_n_u_minus_sigma_hat,inflowBoundary,
( e1 * u0_squared_div_2 + e2 * u0) * n );
////////////////////////////////////////////////////////////////////
// CREATE SOLUTION OBJECT
////////////////////////////////////////////////////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp(new Solution(mesh, inflowBC, rhs, ip));
mesh->registerSolution(solution);
////////////////////////////////////////////////////////////////////
// WARNING: UNFINISHED HESSIAN BIT
////////////////////////////////////////////////////////////////////
VarFactory hessianVars = varFactory.getBubnovFactory(VarFactory::BUBNOV_TRIAL);
VarPtr du = hessianVars.test(u->ID());
BFPtr hessianBF = Teuchos::rcp( new BF(hessianVars) ); // initialize bilinear form
// FunctionPtr e_v = Function::constant(1.0); // dummy error rep function for now - should do nothing
FunctionPtr u_current = Teuchos::rcp( new PreviousSolutionFunction(solution, u) );
FunctionPtr sig1_prev = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma1) );
FunctionPtr sig2_prev = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma2) );
FunctionPtr sig_prev = (e1*sig1_prev + e2*sig2_prev);
FunctionPtr fnhat = Teuchos::rcp(new PreviousSolutionFunction(solution,beta_n_u_minus_sigma_hat));
FunctionPtr uhat_prev = Teuchos::rcp(new PreviousSolutionFunction(solution,uhat));
LinearTermPtr residual = Teuchos::rcp(new LinearTerm);// residual
residual->addTerm(fnhat*v - (e1 * (u_prev_squared_div2 - sig1_prev) + e2 * (u_prev - sig2_prev)) * v->grad());
residual->addTerm((1/epsilon)*sig_prev * tau + u_prev * tau->div() - uhat_prev*tau->dot_normal());
LinearTermPtr Bdu = Teuchos::rcp(new LinearTerm);// residual
Bdu->addTerm( u_current*tau->div() - u_current*(beta*v->grad()));
Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ip, residual));
Teuchos::RCP<RieszRep> duRiesz = Teuchos::rcp(new RieszRep(mesh, ip, Bdu));
riesz->computeRieszRep();
FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,riesz));
e_v->writeValuesToMATLABFile(mesh, "e_v.m");
FunctionPtr posErrPart = Teuchos::rcp(new PositivePart(e_v->dx()));
hessianBF->addTerm(e_v->dx()*u,du);
// hessianBF->addTerm(posErrPart*u,du);
Teuchos::RCP<HessianFilter> hessianFilter = Teuchos::rcp(new HessianFilter(hessianBF));
if (useHessian)
{
solution->setWriteMatrixToFile(true,"hessianStiffness.dat");
}
else
{
solution->setWriteMatrixToFile(true,"stiffness.dat");
}
Teuchos::RCP< LineSearchStep > LS_Step = Teuchos::rcp(new LineSearchStep(riesz));
ofstream out;
out.open("Burgers.txt");
double NL_residual = 9e99;
for (int i = 0; i<numSteps; i++)
{
solution->solve(false); // do one solve to initialize things...
double stepLength = 1.0;
stepLength = LS_Step->stepSize(backgroundFlow,solution, NL_residual);
if (useHessian)
{
solution->setFilter(hessianFilter);
}
backgroundFlow->addSolution(solution,stepLength);
NL_residual = LS_Step->getNLResidual();
if (rank==0)
{
cout << "NL residual after adding = " << NL_residual << " with step size " << stepLength << endl;
out << NL_residual << endl; // saves initial NL error
}
}
out.close();
////////////////////////////////////////////////////////////////////
// DEFINE REFINEMENT STRATEGY
////////////////////////////////////////////////////////////////////
Teuchos::RCP<RefinementStrategy> refinementStrategy;
refinementStrategy = Teuchos::rcp(new RefinementStrategy(solution,energyThreshold));
int numRefs = 0;
Teuchos::RCP<NonlinearStepSize> stepSize = Teuchos::rcp(new NonlinearStepSize(nonlinearStepSize));
Teuchos::RCP<NonlinearSolveStrategy> solveStrategy;
solveStrategy = Teuchos::rcp( new NonlinearSolveStrategy(backgroundFlow, solution, stepSize,
nonlinearRelativeEnergyTolerance));
////////////////////////////////////////////////////////////////////
// SOLVE
////////////////////////////////////////////////////////////////////
for (int refIndex=0; refIndex<numRefs; refIndex++)
{
solveStrategy->solve(rank==0); // print to console on rank 0
refinementStrategy->refine(rank==0); // print to console on rank 0
}
// solveStrategy->solve(rank==0);
if (rank==0)
{
backgroundFlow->writeToVTK("Burgers.vtu",min(H1Order+1,4));
solution->writeFluxesToFile(uhat->ID(), "burgers.dat");
cout << "wrote solution files" << endl;
}
return 0;
}
int main(int argc, char *argv[]) {
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
choice::Args args( argc, argv );
int rank = 0;
int numProcs = 1;
#endif
int nCells = args.Input<int>("--nCells", "num cells",2);
int numRefs = args.Input<int>("--numRefs","num adaptive refinements",0);
double eps = args.Input<double>("--epsilon","diffusion parameter",1e-2);
double energyThreshold = args.Input<double>("--energyThreshold","adaptivity thresh",.5);
if (rank==0){
cout << "nCells = " << nCells << ", numRefs = " << numRefs << ", eps = " << eps << endl;
}
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// quasi-optimal norm
IPPtr qoptIP = Teuchos::rcp(new IP);
qoptIP->addTerm( v );
qoptIP->addTerm( tau / eps + v->grad() );
qoptIP->addTerm( beta * v->grad() - tau->div() );
// robust test norm
IPPtr robIP = Teuchos::rcp(new IP);
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(eps) );
FunctionPtr invSqrtH = Teuchos::rcp(new InvSqrtHScaling);
robIP->addTerm( ip_scaling * v);
robIP->addTerm( ip_scaling/sqrt(eps) * tau );
robIP->addTerm( sqrt(eps) * v->grad() );
robIP->addTerm( beta * v->grad() );
robIP->addTerm( tau->div() );
/*
robIP->addTerm(v);
robIP->addTerm(v->grad());
robIP->addTerm(tau->div());
robIP->addTerm(invSqrtH*tau);
*/
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling ); // see what effect this has
// robIP->addZeroMeanTerm( h2_scaling*v );
//////////////////// SPECIFY RHS ///////////////////////
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
// FunctionPtr f = zero;
// rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
// SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary(beta) );
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary);
FunctionPtr u_exact = Teuchos::rcp( new Uex(eps,0) );
FunctionPtr sig1_exact = Teuchos::rcp( new Uex(eps,1) );
FunctionPtr sig2_exact = Teuchos::rcp( new Uex(eps,2) );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
vector<double> e1(2); // (1,0)
vector<double> e2(2); // (0,1)
e1[0] = 1;
e2[1] = 1;
FunctionPtr sigma = sig1_exact*e1 + sig2_exact*e2;
bc->addDirichlet(uhat, outflowBoundary, zero);
bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, beta*n*u_exact-sigma*n);
// bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, beta*n*u_exact); // ignoring sigma
FunctionPtr u_disc = Teuchos::rcp( new Udisc );
// bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, beta*n*u_disc);
// bc->addDirichlet(uhat, inflowBoundary, u_exact);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = 2, pToAdd = 3;
int horizontalCells = nCells, verticalCells = nCells;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution;
solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) );
// solution = Teuchos::rcp( new Solution(mesh, bc, rhs, qoptIP) );
if (enforceLocalConservation) {
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero);
}
RefinementStrategy refinementStrategy( solution, energyThreshold );
ofstream convOut;
stringstream convOutFile;
convOutFile << "erickson_conv_" << round(-log(eps)/log(10.0)) <<".txt";
convOut.open(convOutFile.str().c_str());
for (int refIndex=0; refIndex < numRefs; refIndex++){
solution->condensedSolve(false);
// solution->solve(false);
double quadTol = 1e-7;
int cubEnrich = 25;
FunctionPtr u_soln = Teuchos::rcp( new PreviousSolutionFunction(solution, u) );
FunctionPtr sigma1_soln = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma1) );
FunctionPtr sigma2_soln = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma2) );
FunctionPtr u_diff = (u_soln - u_exact)*(u_soln - u_exact);
FunctionPtr sig1_diff = (sigma1_soln - sig1_exact)*(sigma1_soln - sig1_exact);
FunctionPtr sig2_diff = (sigma2_soln - sig2_exact)*(sigma2_soln - sig2_exact);
double u_L2_error = u_diff->integrate(mesh,cubEnrich);
double sigma_L2_error = sig1_diff->integrate(mesh,cubEnrich) + sig2_diff->integrate(mesh,cubEnrich);
double L2_error = sqrt(u_L2_error + sigma_L2_error);
double energy_error = solution->energyErrorTotal();
u_soln->writeValuesToMATLABFile(mesh, "u_soln.m");
u_diff->writeValuesToMATLABFile(mesh, "u_diff.m");
u_exact->writeValuesToMATLABFile(mesh, "u_exact.m");
sig1_exact->writeValuesToMATLABFile(mesh, "s1_exact.m");
sig2_exact->writeValuesToMATLABFile(mesh, "s2_exact.m");
convOut << mesh->numGlobalDofs() << " " << L2_error << " " << energy_error << endl;
if (rank==0){
cout << "L2 error = " << L2_error << ", energy error = " << energy_error << ", ratio = " << L2_error/energy_error << endl;
cout << "u squared L2 error = " << u_L2_error << ", sigma squared l2 error = " << sigma_L2_error << ", num dofs = " << mesh->numGlobalDofs() << endl;
}
refinementStrategy.refine(rank==0); // print to console on rank 0
}
convOut.close();
// one more solve on the final refined mesh:
solution->condensedSolve(false);
VTKExporter exporter(solution, mesh, varFactory);
if (rank==0){
exporter.exportSolution("robustIP");
cout << endl;
}
return 0;
/*
// determine trialIDs
vector< int > trialIDs = mesh->bilinearForm()->trialIDs();
vector< int > fieldIDs;
vector< int > fluxIDs;
vector< int >::iterator idIt;
for (idIt = trialIDs.begin();idIt!=trialIDs.end();idIt++){
int trialID = *(idIt);
if (!mesh->bilinearForm()->isFluxOrTrace(trialID)){ // if field
fieldIDs.push_back(trialID);
} else {
fluxIDs.push_back(trialID);
}
}
int numFieldInds = 0;
map<int,vector<int> > globalFluxInds; // from cellID to localDofInd vector
map<int,vector<int> > globalFieldInds; // from cellID to localDofInd vector
map<int,vector<int> > localFieldInds; // from cellID to localDofInd vector
map<int,vector<int> > localFluxInds; // from cellID to localDofInd vector
set<int> allFluxInds; // unique set of all flux inds
mesh->getDofIndices(allFluxInds,globalFluxInds,globalFieldInds,localFluxInds,localFieldInds);
if (rank==0){
vector< ElementPtr > activeElems = mesh->activeElements();
vector< ElementPtr >::iterator elemIt;
cout << "num flux dofs = " << allFluxInds.size() << endl;
cout << "num field dofs = " << mesh->numFieldDofs() << endl;
cout << "num flux dofs = " << mesh->numFluxDofs() << endl;
elemIt = activeElems.begin();
int cellID = (*elemIt)->cellID();
cout << "num LOCAL field dofs = " << localFieldInds[cellID].size() << endl;
ofstream fieldInds;
fieldInds.open("fieldInds.dat");
for (elemIt = activeElems.begin();elemIt!=activeElems.end();elemIt++){
int cellID = (*elemIt)->cellID();
vector<int> inds = globalFieldInds[cellID];
vector<int> locFieldInds = localFieldInds[cellID];
cout << "local field inds for cell ID " << cellID << endl;
for (int i = 0;i<inds.size();++i){
fieldInds << inds[i]+1 << endl;
cout << locFieldInds[i] << endl;
}
vector<int> finds = globalFluxInds[cellID];
vector<int> locFluxInds = localFluxInds[cellID];
cout << "local flux inds for cell ID " << cellID << endl;
for (int i = 0;i<finds.size();++i){
cout << locFluxInds[i] << endl;
}
cout << "global flux inds for cell ID " << cellID << endl;
for (int i = 0;i<finds.size();++i){
cout << globalFluxInds[cellID][i] << endl;
}
}
fieldInds.close();
ofstream fluxInds;
fluxInds.open("fluxInds.dat");
set<int>::iterator fluxIt;
for (fluxIt = allFluxInds.begin();fluxIt!=allFluxInds.end();fluxIt++){
fluxInds << (*fluxIt)+1 << endl; // offset by 1 for matlab
}
fluxInds.close();
}
return 0;
*/
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
vector<double> beta_const;
double c = sqrt(1.25);
beta_const.push_back(1.0/c);
beta_const.push_back(.5/c);
// FunctionPtr beta = Teuchos::rcp(new Beta());
double eps = 1e-3;
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(-uhat, tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( beta_const * u, - v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// quasi-optimal norm
IPPtr qoptIP = Teuchos::rcp(new IP);
qoptIP->addTerm( v );
qoptIP->addTerm( tau / eps + v->grad() );
qoptIP->addTerm( beta_const * v->grad() - tau->div() );
// robust test norm
IPPtr robIP = Teuchos::rcp(new IP);
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(eps) );
if (enforceLocalConservation)
{
robIP->addZeroMeanTerm( v );
}
else
{
robIP->addTerm( ip_scaling * v );
}
robIP->addTerm( sqrt(eps) * v->grad() );
bool useNewBC = false;
FunctionPtr weight = Teuchos::rcp( new SqrtWeight(eps) );
if (useNewBC)
{
robIP->addTerm( beta_const * v->grad() );
robIP->addTerm( tau->div() );
robIP->addTerm( ip_scaling/sqrt(eps) * tau );
}
else
{
robIP->addTerm( weight * beta_const * v->grad() );
robIP->addTerm( weight * tau->div() );
robIP->addTerm( weight * ip_scaling/sqrt(eps) * tau );
}
//////////////////// SPECIFY RHS ///////////////////////
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = zero;
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary );
FunctionPtr u0 = Teuchos::rcp( new U0 );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
bc->addDirichlet(uhat, outflowBoundary, zero);
if (useNewBC)
{
bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, beta_const*n*u0);
}
else
{
SpatialFilterPtr inflowBot = Teuchos::rcp( new InflowSquareBot );
SpatialFilterPtr inflowLeft = Teuchos::rcp( new InflowSquareLeft );
bc->addDirichlet(beta_n_u_minus_sigma_n, inflowLeft, beta_const*n*u0);
bc->addDirichlet(uhat, inflowBot, u0);
}
// Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp(new PenaltyConstraints);
// pc->addConstraint(uhat==u0,inflowBoundary);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = 2, pToAdd = 2;
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 1.0;
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 nCells = 2;
int horizontalCells = nCells, verticalCells = nCells;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
confusionBF, H1Order, H1Order+pToAdd);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) );
// solution->setFilter(pc);
if (enforceLocalConservation)
{
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero);
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
int numRefs = 9;
for (int refIndex=0; refIndex<numRefs; refIndex++)
{
solution->solve(false);
refinementStrategy.refine(rank==0); // print to console on rank 0
}
// one more solve on the final refined mesh:
solution->solve(false);
if (rank==0)
{
solution->writeToVTK("Hughes.vtu",min(H1Order+1,4));
solution->writeFluxesToFile(uhat->ID(), "uhat.dat");
cout << "wrote files: u.m, uhat.dat\n";
}
return 0;
}
// tests to make sure that the rieszNorm computed via matrices is the same as the one computed thru direct integration
bool ScratchPadTests::testRieszIntegration()
{
double tol = 1e-11;
bool success = true;
int nCells = 2;
double eps = .25;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr tau = varFactory->testVar("\\tau", HDIV);
VarPtr v = varFactory->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory->traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory->fieldVar("u");
VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// robust test norm
IPPtr ip = Teuchos::rcp(new IP);
// just H1 projection
ip->addTerm(v->grad());
ip->addTerm(v);
ip->addTerm(tau);
ip->addTerm(tau->div());
//////////////////// SPECIFY RHS AND HELPFUL FUNCTIONS ///////////////////////
FunctionPtr n = Function::normal();
vector<double> e1,e2;
e1.push_back(1.0);
e1.push_back(0.0);
e2.push_back(0.0);
e2.push_back(1.0);
FunctionPtr one = Function::constant(1.0);
FunctionPtr zero = Function::constant(0.0);
RHSPtr rhs = RHS::rhs();
FunctionPtr f = one;
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
BCPtr bc = BC::bc();
SpatialFilterPtr squareBoundary = Teuchos::rcp( new SquareBoundary );
bc->addDirichlet(uhat, squareBoundary, zero);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int order = 2;
int H1Order = order+1;
int pToAdd = 2;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);
//////////////////// SOLVE & REFINE ///////////////////////
LinearTermPtr lt = Teuchos::rcp(new LinearTerm);
FunctionPtr fxn = Function::xn(1); // fxn = x
lt->addTerm(fxn*v + fxn->grad()*v->grad());
lt->addTerm(fxn*tau->x() + fxn*tau->y() + (fxn->dx() + fxn->dy())*tau->div());
Teuchos::RCP<RieszRep> rieszLT = Teuchos::rcp(new RieszRep(mesh, ip, lt));
rieszLT->computeRieszRep();
double rieszNorm = rieszLT->getNorm();
FunctionPtr e_v = RieszRep::repFunction(v,rieszLT);
FunctionPtr e_tau = RieszRep::repFunction(tau,rieszLT);
map<int,FunctionPtr> repFxns;
repFxns[v->ID()] = e_v;
repFxns[tau->ID()] = e_tau;
double integratedNorm = sqrt((lt->evaluate(repFxns,false))->integrate(mesh,5,true));
success = abs(rieszNorm-integratedNorm)<tol;
if (success==false)
{
cout << "Failed testRieszIntegration; riesz norm is computed to be = " << rieszNorm << ", while using integration it's computed to be " << integratedNorm << endl;
return success;
}
return success;
}
bool LinearTermTests::testMixedTermConsistency()
{
bool success = true;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr tau = varFactory->testVar("\\tau", HDIV);
VarPtr v = varFactory->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory->traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory->fieldVar("u");
VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
double eps = .01;
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = 1;
int pToAdd = 1;
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 1.0;
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 nCells = 1;
int horizontalCells = nCells, verticalCells = nCells;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> myMesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
confusionBF, H1Order, H1Order+pToAdd);
ElementTypePtr elemType = myMesh->getElement(0)->elementType();
// DofOrderingPtr testOrder = elemType->testOrderPtr;
BasisCachePtr basisCache = Teuchos::rcp(new BasisCache(elemType, myMesh, true));
LinearTermPtr integrandIBP = Teuchos::rcp(new LinearTerm);// residual
vector<double> e1(2); // (1,0)
vector<double> e2(2); // (0,1)
e1[0] = 1;
e2[1] = 1;
FunctionPtr n = Function::normal();
FunctionPtr X = Function::xn(1);
FunctionPtr Y = Function::yn(1);
FunctionPtr testFxn1 = X;
FunctionPtr testFxn2 = Y;
FunctionPtr divTestFxn = testFxn1->dx() + testFxn2->dy();
FunctionPtr vectorTest = testFxn1*e1 + testFxn2*e2;
integrandIBP->addTerm(vectorTest*n*v + -vectorTest*v->grad()); // boundary term
// define dummy IP to initialize riesz rep class, but just integrate RHS
IPPtr dummyIP = Teuchos::rcp(new IP);
dummyIP->addTerm(v);
Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(myMesh, dummyIP, integrandIBP));
map<GlobalIndexType,FieldContainer<double> > rieszRHS = riesz->integrateFunctional();
set<GlobalIndexType> cellIDs = myMesh->cellIDsInPartition();
for (set<GlobalIndexType>::iterator cellIDIt=cellIDs.begin(); cellIDIt !=cellIDs.end(); cellIDIt++)
{
GlobalIndexType cellID = *cellIDIt;
ElementTypePtr elemTypePtr = myMesh->getElementType(cellID);
DofOrderingPtr testOrderingPtr = elemTypePtr->testOrderPtr;
int numTestDofs = testOrderingPtr->totalDofs();
BasisCachePtr basisCache = BasisCache::basisCacheForCell(myMesh, cellID, true);
FieldContainer<double> rhsIBPValues(1,numTestDofs);
integrandIBP->integrate(rhsIBPValues, testOrderingPtr, basisCache);
FieldContainer<double> rieszValues(1,numTestDofs);
(riesz->getFunctional())->integrate(rieszValues, testOrderingPtr, basisCache);
double maxDiff;
double tol = 1e-13;
FieldContainer<double> rhsIBPVals(numTestDofs);
for (int i = 0; i< numTestDofs; i++)
{
rhsIBPVals(i) = rhsIBPValues(0,i);
// cout << "riesz rhs values = " << rieszRHS[cellID](i) << ", rhsIBPValues = " << rhsIBPVals(i) << ", riesz returned values = " << rieszValues(0,i) << endl;
}
bool fcsAgree = TestSuite::fcsAgree(rieszRHS[cellID],rhsIBPVals,tol,maxDiff);
if (!fcsAgree)
{
success=false;
cout << "Failed mixed term consistency test with maxDiff = " << maxDiff << " on cellID " << cellID<< endl;
}
}
return allSuccess(success);
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int rank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
int nCells = args.Input<int>("--nCells", "num cells",2);
int numRefs = args.Input<int>("--numRefs","num adaptive refinements",0);
int numPreRefs = args.Input<int>("--numPreRefs","num preemptive adaptive refinements",0);
int order = args.Input<int>("--order","order of approximation",2);
double eps = args.Input<double>("--epsilon","diffusion parameter",1e-2);
double energyThreshold = args.Input<double>("-energyThreshold","energy thresh for adaptivity", .5);
double rampHeight = args.Input<double>("--rampHeight","ramp height at x = 2", 0.0);
bool useAnisotropy = args.Input<bool>("--useAnisotropy","aniso flag ", false);
FunctionPtr zero = Function::constant(0.0);
FunctionPtr one = Function::constant(1.0);
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
vector<double> e1,e2;
e1.push_back(1.0);
e1.push_back(0.0);
e2.push_back(0.0);
e2.push_back(1.0);
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
// first order term with magnitude alpha
double alpha = 0.0;
confusionBF->addTerm(alpha * u, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// robust test norm
IPPtr robIP = Teuchos::rcp(new IP);
FunctionPtr C_h = Teuchos::rcp( new EpsilonScaling(eps) );
FunctionPtr invH = Teuchos::rcp(new InvHScaling);
FunctionPtr invSqrtH = Teuchos::rcp(new InvSqrtHScaling);
FunctionPtr sqrtH = Teuchos::rcp(new SqrtHScaling);
robIP->addTerm(v*alpha);
robIP->addTerm(invSqrtH*v);
// robIP->addTerm(v);
robIP->addTerm(sqrt(eps) * v->grad() );
robIP->addTerm(beta * v->grad() );
robIP->addTerm(tau->div() );
robIP->addTerm(C_h/sqrt(eps) * tau );
LinearTermPtr vVecLT = Teuchos::rcp(new LinearTerm);
LinearTermPtr tauVecLT = Teuchos::rcp(new LinearTerm);
vVecLT->addTerm(sqrt(eps)*v->grad());
tauVecLT->addTerm(C_h/sqrt(eps)*tau);
LinearTermPtr restLT = Teuchos::rcp(new LinearTerm);
restLT->addTerm(alpha*v);
restLT->addTerm(invSqrtH*v);
restLT = restLT + beta * v->grad();
restLT = restLT + tau->div();
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = zero;
// f = one;
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
// SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
// SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary);
// bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, zero);
// bc->addDirichlet(uhat, outflowBoundary, zero);
SpatialFilterPtr rampInflow = Teuchos::rcp(new LeftInflow);
SpatialFilterPtr rampBoundary = MeshUtilities::rampBoundary(rampHeight);
SpatialFilterPtr freeStream = Teuchos::rcp(new FreeStreamBoundary);
SpatialFilterPtr outflowBoundary = Teuchos::rcp(new OutflowBoundary);
bc->addDirichlet(uhat, rampBoundary, one);
// bc->addDirichlet(uhat, outflowBoundary, one);
bc->addDirichlet(beta_n_u_minus_sigma_n, rampInflow, zero);
bc->addDirichlet(beta_n_u_minus_sigma_n, freeStream, zero);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = order+1;
int pToAdd = 2;
// create a pointer to a new mesh:
// Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildRampMesh(rampHeight,confusionBF, H1Order, H1Order+pToAdd);
mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution;
solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) );
// solution->solve(false);
solution->condensedSolve();
LinearTermPtr residual = rhs->linearTermCopy();
residual->addTerm(-confusionBF->testFunctional(solution));
RieszRepPtr rieszResidual = Teuchos::rcp(new RieszRep(mesh, robIP, residual));
rieszResidual->computeRieszRep();
FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,rieszResidual));
FunctionPtr e_tau = Teuchos::rcp(new RepFunction(tau,rieszResidual));
map<int,FunctionPtr> errRepMap;
errRepMap[v->ID()] = e_v;
errRepMap[tau->ID()] = e_tau;
FunctionPtr errTau = tauVecLT->evaluate(errRepMap,false);
FunctionPtr errV = vVecLT->evaluate(errRepMap,false);
FunctionPtr errRest = restLT->evaluate(errRepMap,false);
FunctionPtr xErr = (errTau->x())*(errTau->x()) + (errV->dx())*(errV->dx());
FunctionPtr yErr = (errTau->y())*(errTau->y()) + (errV->dy())*(errV->dy());
FunctionPtr restErr = errRest*errRest;
RefinementStrategy refinementStrategy( solution, energyThreshold );
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// PRE REFINEMENTS
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
if (rank==0)
{
cout << "Number of pre-refinements = " << numPreRefs << endl;
}
for (int i =0; i<=numPreRefs; i++)
{
vector<ElementPtr> elems = mesh->activeElements();
vector<ElementPtr>::iterator elemIt;
vector<int> wallCells;
for (elemIt=elems.begin(); elemIt != elems.end(); elemIt++)
{
int cellID = (*elemIt)->cellID();
int numSides = mesh->getElement(cellID)->numSides();
FieldContainer<double> vertices(numSides,2); //for quads
mesh->verticesForCell(vertices, cellID);
bool cellIDset = false;
for (int j = 0; j<numSides; j++)
{
if ((abs(vertices(j,0)-1.0)<1e-7) && (abs(vertices(j,1))<1e-7) && !cellIDset) // if at singularity, i.e. if a vertex is (1,0)
{
wallCells.push_back(cellID);
cellIDset = true;
}
}
}
if (i<numPreRefs)
{
refinementStrategy.refineCells(wallCells);
}
}
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
VTKExporter exporter(solution, mesh, varFactory);
for (int refIndex=0; refIndex<numRefs; refIndex++)
{
if (rank==0)
{
cout << "on ref index " << refIndex << endl;
}
rieszResidual->computeRieszRep(); // in preparation to get anisotropy
vector<int> cellIDs;
refinementStrategy.getCellsAboveErrorThreshhold(cellIDs);
map<int,double> energyError = solution->energyError();
map<int,double> xErrMap = xErr->cellIntegrals(cellIDs,mesh,5,true);
map<int,double> yErrMap = yErr->cellIntegrals(cellIDs,mesh,5,true);
map<int,double> restErrMap = restErr->cellIntegrals(cellIDs,mesh,5,true);
for (vector<ElementPtr>::iterator elemIt = mesh->activeElements().begin(); elemIt!=mesh->activeElements().end(); elemIt++)
{
int cellID = (*elemIt)->cellID();
double err = xErrMap[cellID]+ yErrMap[cellID] + restErrMap[cellID];
if (rank==0)
cout << "err thru LT = " << sqrt(err) << ", while energy err = " << energyError[cellID] << endl;
}
map<int,double> ratio,xErr,yErr;
vector<ElementPtr> elems = mesh->activeElements();
for (vector<ElementPtr>::iterator elemIt = elems.begin(); elemIt!=elems.end(); elemIt++)
{
int cellID = (*elemIt)->cellID();
ratio[cellID] = 0.0;
xErr[cellID] = 0.0;
yErr[cellID] = 0.0;
if (std::find(cellIDs.begin(),cellIDs.end(),cellID)!=cellIDs.end()) // if this cell is above energy thresh
{
ratio[cellID] = yErrMap[cellID]/xErrMap[cellID];
xErr[cellID] = xErrMap[cellID];
yErr[cellID] = yErrMap[cellID];
}
}
FunctionPtr ratioFxn = Teuchos::rcp(new EnergyErrorFunction(ratio));
FunctionPtr xErrFxn = Teuchos::rcp(new EnergyErrorFunction(xErr));
FunctionPtr yErrFxn = Teuchos::rcp(new EnergyErrorFunction(yErr));
std::ostringstream oss;
oss << refIndex;
exporter.exportFunction(ratioFxn, string("ratio")+oss.str());
exporter.exportFunction(xErrFxn, string("xErr")+oss.str());
exporter.exportFunction(yErrFxn, string("yErr")+oss.str());
if (useAnisotropy)
{
refinementStrategy.refine(rank==0,xErrMap,yErrMap); //anisotropic refinements
}
else
{
refinementStrategy.refine(rank==0); // no anisotropy
}
solution->condensedSolve();
}
// final solve on final mesh
solution->condensedSolve();
//////////////////// print to file ///////////////////////
FunctionPtr orderFxn = Teuchos::rcp(new MeshPolyOrderFunction(mesh));
std::ostringstream oss;
oss << nCells;
if (rank==0)
{
exporter.exportSolution(string("robustIP")+oss.str());
exporter.exportFunction(orderFxn, "meshOrder");
cout << endl;
}
return 0;
}
// tests Riesz inversion by integration by parts
bool LinearTermTests::testRieszInversion()
{
bool success = true;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr tau = varFactory->testVar("\\tau", HDIV);
VarPtr v = varFactory->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory->traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory->fieldVar("u");
VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
double eps = .01;
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = 1;
int pToAdd = 1;
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 1.0;
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 nCells = 1;
int horizontalCells = nCells, verticalCells = nCells;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> myMesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
confusionBF, H1Order, H1Order+pToAdd);
ElementTypePtr elemType = myMesh->getElement(0)->elementType();
BasisCachePtr basisCache = Teuchos::rcp(new BasisCache(elemType, myMesh));
vector<GlobalIndexType> cellIDs;
vector<ElementPtr> elems = myMesh->activeElements();
vector<ElementPtr>::iterator elemIt;
for (elemIt=elems.begin(); elemIt!=elems.end(); elemIt++)
{
int cellID = (*elemIt)->cellID();
cellIDs.push_back(cellID);
}
bool createSideCacheToo = true;
basisCache->setPhysicalCellNodes(myMesh->physicalCellNodesGlobal(elemType), cellIDs, createSideCacheToo);
LinearTermPtr integrand = Teuchos::rcp(new LinearTerm);// residual
LinearTermPtr integrandIBP = Teuchos::rcp(new LinearTerm);// residual
vector<double> e1(2); // (1,0)
vector<double> e2(2); // (0,1)
e1[0] = 1;
e2[1] = 1;
FunctionPtr n = Function::normal();
FunctionPtr X = Function::xn(1);
FunctionPtr Y = Function::yn(1);
FunctionPtr testFxn1 = X;
FunctionPtr testFxn2 = Y;
FunctionPtr divTestFxn = testFxn1->dx() + testFxn2->dy();
FunctionPtr vectorTest = testFxn1*e1 + testFxn2*e2;
integrand->addTerm(divTestFxn*v);
integrandIBP->addTerm(vectorTest*n*v - vectorTest*v->grad()); // boundary term
IPPtr sobolevIP = Teuchos::rcp(new IP);
sobolevIP->addTerm(v);
sobolevIP->addTerm(tau);
Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(myMesh, sobolevIP, integrand));
// riesz->setPrintOption(true);
riesz->computeRieszRep();
Teuchos::RCP<RieszRep> rieszIBP = Teuchos::rcp(new RieszRep(myMesh, sobolevIP, integrandIBP));
riesz->setFunctional(integrandIBP);
// rieszIBP->setPrintOption(true);
rieszIBP->computeRieszRep();
FunctionPtr rieszOrigFxn = RieszRep::repFunction(v,riesz);
FunctionPtr rieszIBPFxn = RieszRep::repFunction(v,rieszIBP);
int numCells = basisCache->getPhysicalCubaturePoints().dimension(0);
int numPts = basisCache->getPhysicalCubaturePoints().dimension(1);
FieldContainer<double> valOriginal( numCells, numPts);
FieldContainer<double> valIBP( numCells, numPts);
rieszOrigFxn->values(valOriginal,basisCache);
rieszIBPFxn->values(valIBP,basisCache);
double maxDiff;
double tol = 1e-14;
success = TestSuite::fcsAgree(valOriginal,valIBP,tol,maxDiff);
if (success==false)
{
cout << "Failed TestRieszInversion with maxDiff = " << maxDiff << endl;
}
return success;
}
// tests to make sure the energy error calculated thru direct integration works for vector valued test functions too
bool ScratchPadTests::testLTResidual()
{
double tol = 1e-11;
int rank = Teuchos::GlobalMPISession::getRank();
bool success = true;
int nCells = 2;
double eps = .1;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr tau = varFactory->testVar("\\tau", HDIV);
VarPtr v = varFactory->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory->traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory->fieldVar("u");
VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// robust test norm
IPPtr ip = Teuchos::rcp(new IP);
// choose the mesh-independent norm even though it may have boundary layers
ip->addTerm(v->grad());
ip->addTerm(v);
ip->addTerm(tau);
ip->addTerm(tau->div());
//////////////////// SPECIFY RHS AND HELPFUL FUNCTIONS ///////////////////////
FunctionPtr n = Function::normal();
vector<double> e1,e2;
e1.push_back(1.0);
e1.push_back(0.0);
e2.push_back(0.0);
e2.push_back(1.0);
FunctionPtr one = Function::constant(1.0);
FunctionPtr zero = Function::constant(0.0);
RHSPtr rhs = RHS::rhs();
FunctionPtr f = one; // if this is set to zero instead, we pass the test (a clue?)
rhs->addTerm( f * v );
//////////////////// CREATE BCs ///////////////////////
BCPtr bc = BC::bc();
SpatialFilterPtr squareBoundary = Teuchos::rcp( new SquareBoundary );
bc->addDirichlet(uhat, squareBoundary, one);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int order = 2;
int H1Order = order+1;
int pToAdd = 2;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution;
solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
solution->solve(false);
double energyError = solution->energyErrorTotal();
LinearTermPtr residual = rhs->linearTermCopy();
residual->addTerm(-confusionBF->testFunctional(solution),true);
// FunctionPtr uh = Function::solution(uhat,solution);
// FunctionPtr fn = Function::solution(beta_n_u_minus_sigma_n,solution);
// FunctionPtr uF = Function::solution(u,solution);
// FunctionPtr sigma = e1*Function::solution(sigma1,solution)+e2*Function::solution(sigma2,solution);
// residual->addTerm(- (fn*v - uh*tau->dot_normal()));
// residual->addTerm(- (uF*(tau->div() - beta*v->grad()) + sigma*((1/eps)*tau + v->grad())));
// residual->addTerm(-(fn*v - uF*beta*v->grad() + sigma*v->grad())); // just v portion
// residual->addTerm(uh*tau->dot_normal() - uF*tau->div() - sigma*((1/eps)*tau)); // just tau portion
Teuchos::RCP<RieszRep> rieszResidual = Teuchos::rcp(new RieszRep(mesh, ip, residual));
rieszResidual->computeRieszRep();
double energyErrorLT = rieszResidual->getNorm();
int cubEnrich = 0;
bool testVsTest = true;
FunctionPtr e_v = RieszRep::repFunction(v,rieszResidual);
FunctionPtr e_tau = RieszRep::repFunction(tau,rieszResidual);
// experiment by Nate: manually specify the error (this appears to produce identical results, as it should)
// FunctionPtr err = e_v * e_v + e_tau * e_tau + e_v->grad() * e_v->grad() + e_tau->div() * e_tau->div();
map<int,FunctionPtr> errFxns;
errFxns[v->ID()] = e_v;
errFxns[tau->ID()] = e_tau;
LinearTermPtr ipAtErrFxns = ip->evaluate(errFxns);
FunctionPtr err = ip->evaluate(errFxns)->evaluate(errFxns);
double energyErrorIntegrated = sqrt(err->integrate(mesh,cubEnrich,testVsTest));
// check that energy error computed thru Solution and through rieszRep are the same
bool success1 = abs(energyError-energyErrorLT)<tol;
// checks that matrix-computed and integrated errors are the same
bool success2 = abs(energyErrorLT-energyErrorIntegrated)<tol;
success = success1==true && success2==true;
if (!success)
{
if (rank==0)
cout << "Failed testLTResidual; energy error = " << energyError << ", while linearTerm error is computed to be " << energyErrorLT << ", and when computing through integration of the Riesz rep function, error = " << energyErrorIntegrated << endl;
}
// VTKExporter exporter(solution, mesh, varFactory);
// exporter.exportSolution("testLTRes");
// cout << endl;
return success;
}