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 commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
int norm = args.Input<int>("--norm", "0 = graph\n 1 = robust\n 2 = coupled robust");
// Optional arguments (have defaults)
int uniformRefinements = args.Input("--uniformRefinements", "number of uniform refinements", 0);
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation", false);
double radius = args.Input("--r", "cylinder radius", 0.6);
int Re = args.Input("--Re", "Reynolds number", 1);
int maxNewtonIterations = args.Input("--maxIterations", "maximum number of Newton iterations", 1);
int polyOrder = args.Input("--polyOrder", "polynomial order for field variables", 2);
int deltaP = args.Input("--deltaP", "how much to enrich test space", 2);
// string saveFile = args.Input<string>("--meshSaveFile", "file to which to save refinement history", "");
// string replayFile = args.Input<string>("--meshLoadFile", "file with refinement history to replay", "");
args.Process();
//////////////////// PROBLEM DEFINITIONS ///////////////////////
int H1Order = polyOrder+1;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau1 = varFactory.testVar("tau1", HDIV);
VarPtr tau2 = varFactory.testVar("tau2", HDIV);
VarPtr v1 = varFactory.testVar("v1", HGRAD);
VarPtr v2 = varFactory.testVar("v2", HGRAD);
VarPtr vc = varFactory.testVar("vc", HGRAD);
// define trial variables
VarPtr u1 = varFactory.fieldVar("u1");
VarPtr u2 = varFactory.fieldVar("u2");
VarPtr p = varFactory.fieldVar("p");
VarPtr u1hat = varFactory.traceVar("u1hat");
VarPtr u2hat = varFactory.traceVar("u2hat");
VarPtr t1hat = varFactory.fluxVar("t1hat");
VarPtr t2hat = varFactory.fluxVar("t2hat");
VarPtr sigma1 = varFactory.fieldVar("sigma1", VECTOR_L2);
VarPtr sigma2 = varFactory.fieldVar("sigma2", VECTOR_L2);
//////////////////// BUILD MESH ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshFactory::shiftedHemkerMesh(-1, 3, 2, radius, bf, H1Order, deltaP);
////////////////////////////////////////////////////////////////////
// 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 u1_prev = Function::solution(u1, backgroundFlow);
FunctionPtr u2_prev = Function::solution(u2, backgroundFlow);
FunctionPtr sigma1_prev = Function::solution(sigma1, backgroundFlow);
FunctionPtr sigma2_prev = Function::solution(sigma2, backgroundFlow);
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
FunctionPtr beta = e1 * u1_prev + e2 * u2_prev;
// ==================== SET INITIAL GUESS ==========================
map<int, Teuchos::RCP<Function> > functionMap;
functionMap[u1->ID()] = one;
functionMap[u2->ID()] = zero;
functionMap[sigma1->ID()] = Function::vectorize(zero,zero);
functionMap[sigma2->ID()] = Function::vectorize(zero,zero);
functionMap[p->ID()] = zero;
backgroundFlow->projectOntoMesh(functionMap);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
// // stress equation
bf->addTerm( sigma1, tau1 );
bf->addTerm( sigma2, tau2 );
bf->addTerm( u1, tau1->div() );
bf->addTerm( u2, tau2->div() );
bf->addTerm( -u1hat, tau1->dot_normal() );
bf->addTerm( -u2hat, tau2->dot_normal() );
// momentum equation
// bf->addTerm( Function::xPart(sigma1_prev)*u1, v1 );
// bf->addTerm( Function::yPart(sigma1_prev)*u2, v1 );
// bf->addTerm( Function::xPart(sigma2_prev)*u1, v2 );
// bf->addTerm( Function::yPart(sigma2_prev)*u2, v2 );
// bf->addTerm( beta*sigma1, v1);
// bf->addTerm( beta*sigma2, v2);
bf->addTerm( 1./Re*sigma1, v1->grad() );
bf->addTerm( 1./Re*sigma2, v2->grad() );
bf->addTerm( t1hat, v1);
bf->addTerm( t2hat, v2);
bf->addTerm( -p, v1->dx() );
bf->addTerm( -p, v2->dy() );
// continuity equation
bf->addTerm( -u1, vc->dx() );
bf->addTerm( -u2, vc->dy() );
bf->addTerm( u1hat, vc->times_normal_x() );
bf->addTerm( u2hat, vc->times_normal_y() );
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
// stress equation
rhs->addTerm( -sigma1_prev * tau1 );
rhs->addTerm( -sigma2_prev * tau2 );
rhs->addTerm( -u1_prev * tau1->div() );
rhs->addTerm( -u2_prev * tau2->div() );
// momentum equation
// rhs->addTerm( -beta*sigma1_prev * v1 );
// rhs->addTerm( -beta*sigma2_prev * v2 );
rhs->addTerm( -1./Re*sigma1_prev * v1->grad() );
rhs->addTerm( -1./Re*sigma2_prev * v2->grad() );
// continuity equation
rhs->addTerm( u1_prev * vc->dx() );
rhs->addTerm( u2_prev * vc->dy() );
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
if (norm == 0)
{
ip = bf->graphNorm();
}
else if (norm == 1)
{
// ip = bf->l2Norm();
}
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr left = Teuchos::rcp( new ConstantXBoundary(-1) );
SpatialFilterPtr right = Teuchos::rcp( new ConstantXBoundary(3) );
SpatialFilterPtr top = Teuchos::rcp( new ConstantYBoundary(1) );
SpatialFilterPtr bottom = Teuchos::rcp( new ConstantYBoundary(-1) );
SpatialFilterPtr circle = Teuchos::rcp( new CircleBoundary(radius) );
FunctionPtr boundaryU1 = Teuchos::rcp( new BoundaryU1 );
bc->addDirichlet(u1hat, left, boundaryU1);
bc->addDirichlet(u2hat, left, zero);
bc->addDirichlet(u1hat, right, boundaryU1);
bc->addDirichlet(u2hat, right, zero);
bc->addDirichlet(u1hat, top, zero);
bc->addDirichlet(u2hat, top, zero);
bc->addDirichlet(u1hat, bottom, zero);
bc->addDirichlet(u2hat, bottom, zero);
bc->addDirichlet(u1hat, circle, zero);
bc->addDirichlet(u2hat, circle, zero);
// zero mean constraint on pressure
bc->addZeroMeanConstraint(p);
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
if (enforceLocalConservation)
{
solution->lagrangeConstraints()->addConstraint(u1hat->times_normal_x() + u2hat->times_normal_y() == zero);
}
// ==================== Register Solutions ==========================
mesh->registerSolution(solution);
mesh->registerSolution(backgroundFlow);
// Teuchos::RCP< RefinementHistory > refHistory = Teuchos::rcp( new RefinementHistory );
// mesh->registerObserver(refHistory);
//////////////////// SOLVE & REFINE ///////////////////////
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(backgroundFlow, mesh, varFactory);
ofstream errOut;
ofstream fluxOut;
if (commRank == 0)
{
errOut.open("stokeshemker_err.txt");
fluxOut.open("stokeshemker_flux.txt");
}
errOut.precision(15);
fluxOut.precision(15);
// Cell IDs for flux calculations
vector< pair<ElementPtr, int> > cellFace0;
vector< pair<ElementPtr, int> > cellFace1;
vector< pair<ElementPtr, int> > cellFace2;
vector< pair<ElementPtr, int> > cellFace3;
vector< pair<ElementPtr, int> > cellFace4;
cellFace0.push_back(make_pair(mesh->getElement(12), 3));
cellFace0.push_back(make_pair(mesh->getElement(13), 3));
cellFace0.push_back(make_pair(mesh->getElement(14), 3));
cellFace0.push_back(make_pair(mesh->getElement(15), 3));
cellFace1.push_back(make_pair(mesh->getElement(12), 1));
cellFace1.push_back(make_pair(mesh->getElement(13), 1));
cellFace1.push_back(make_pair(mesh->getElement(14), 1));
cellFace1.push_back(make_pair(mesh->getElement(15), 1));
cellFace2.push_back(make_pair(mesh->getElement(11), 1));
cellFace2.push_back(make_pair(mesh->getElement(2 ), 0));
cellFace2.push_back(make_pair(mesh->getElement(5 ), 2));
cellFace2.push_back(make_pair(mesh->getElement(16), 1));
cellFace3.push_back(make_pair(mesh->getElement(9 ), 3));
cellFace3.push_back(make_pair(mesh->getElement(8 ), 3));
cellFace3.push_back(make_pair(mesh->getElement(19), 3));
cellFace3.push_back(make_pair(mesh->getElement(18), 3));
cellFace4.push_back(make_pair(mesh->getElement(9 ), 1));
cellFace4.push_back(make_pair(mesh->getElement(8 ), 1));
cellFace4.push_back(make_pair(mesh->getElement(19), 1));
cellFace4.push_back(make_pair(mesh->getElement(18), 1));
// // for loading refinement history
// if (replayFile.length() > 0) {
// RefinementHistory refHistory;
// replayFile = replayFile;
// refHistory.loadFromFile(replayFile);
// refHistory.playback(mesh);
// int numElems = mesh->numActiveElements();
// if (commRank==0){
// double minSideLength = meshInfo.getMinCellSideLength() ;
// cout << "after replay, num elems = " << numElems << " and min side length = " << minSideLength << endl;
// }
// }
for (int i = 0; i < uniformRefinements; i++)
refinementStrategy.hRefineUniformly(mesh);
double nonlinearRelativeEnergyTolerance = 1e-5; // used to determine convergence of the nonlinear solution
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
double L2Update = 1e10;
int iterCount = 0;
while (L2Update > nonlinearRelativeEnergyTolerance && iterCount < maxNewtonIterations)
{
solution->solve(false);
double u1L2Update = solution->L2NormOfSolutionGlobal(u1->ID());
double u2L2Update = solution->L2NormOfSolutionGlobal(u2->ID());
L2Update = sqrt(u1L2Update*u1L2Update + u2L2Update*u2L2Update);
double energy_error = solution->energyErrorTotal();
// Check local conservation
if (commRank == 0)
{
FunctionPtr n = Function::normal();
FunctionPtr u1_prev = Function::solution(u1hat, solution);
FunctionPtr u2_prev = Function::solution(u2hat, solution);
FunctionPtr flux = u1_prev*n->x() + u2_prev*n->y();
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, mesh);
// cout << "Mass flux: Largest Local = " << fluxImbalances[0]
// << ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
errOut << mesh->numGlobalDofs() << " " << energy_error << " "
<< fluxImbalances[0] << " " << fluxImbalances[1] << " " << fluxImbalances[2] << endl;
double massFlux0 = computeFluxOverElementSides(u1_prev, mesh, cellFace0);
double massFlux1 = computeFluxOverElementSides(u1_prev, mesh, cellFace1);
double massFlux2 = computeFluxOverElementSides(u1_prev, mesh, cellFace2);
double massFlux3 = computeFluxOverElementSides(u1_prev, mesh, cellFace3);
double massFlux4 = computeFluxOverElementSides(u1_prev, mesh, cellFace4);
fluxOut << massFlux0 << " " << massFlux1 << " " << massFlux2 << " " << massFlux3 << " " << massFlux4 << " " << endl;
cout << "Total mass flux = " << massFlux0 << " " << massFlux1 << " " << massFlux2 << " " << massFlux3 << " " << massFlux4 << " " << endl;
// if (saveFile.length() > 0) {
// std::ostringstream oss;
// oss << string(saveFile) << refIndex ;
// cout << "on refinement " << refIndex << " saving mesh file to " << oss.str() << endl;
// refHistory->saveToFile(oss.str());
// }
}
// line search algorithm
double alpha = 1.0;
// bool useLineSearch = false;
// int posEnrich = 5; // amount of enriching of grid points on which to ensure positivity
// if (useLineSearch){ // to enforce positivity of density rho
// double lineSearchFactor = .5; double eps = .001; // arbitrary
// FunctionPtr rhoTemp = Function::solution(rho,backgroundFlow) + alpha*Function::solution(rho,solution) - Function::constant(eps);
// FunctionPtr eTemp = Function::solution(e,backgroundFlow) + alpha*Function::solution(e,solution) - Function::constant(eps);
// bool rhoIsPositive = rhoTemp->isPositive(mesh,posEnrich);
// bool eIsPositive = eTemp->isPositive(mesh,posEnrich);
// int iter = 0; int maxIter = 20;
// while (!(rhoIsPositive && eIsPositive) && iter < maxIter){
// alpha = alpha*lineSearchFactor;
// rhoTemp = Function::solution(rho,backgroundFlow) + alpha*Function::solution(rho,solution);
// eTemp = Function::solution(e,backgroundFlow) + alpha*Function::solution(e,solution);
// rhoIsPositive = rhoTemp->isPositive(mesh,posEnrich);
// eIsPositive = eTemp->isPositive(mesh,posEnrich);
// iter++;
// }
// if (commRank==0 && alpha < 1.0){
// cout << "line search factor alpha = " << alpha << endl;
// }
// }
backgroundFlow->addSolution(solution, alpha, false, true);
iterCount++;
// if (commRank == 0)
// cout << "L2 Norm of Update = " << L2Update << endl;
}
if (commRank == 0)
cout << endl;
if (commRank == 0)
{
stringstream outfile;
outfile << "stokeshemker" << uniformRefinements << "_" << refIndex;
exporter.exportSolution(outfile.str());
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
if (commRank == 0)
{
errOut.close();
fluxOut.close();
}
return 0;
}
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;
}
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 commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
double epsilon = args.Input<double>("--epsilon", "diffusion parameter");
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation");
int norm = args.Input<int>("--norm", "0 = graph\n 1 = robust\n 2 = modified robust");
// Optional arguments (have defaults)
halfwidth = args.Input("--halfwidth", "half the width of the wedge", 0.5);
bool allQuads = args.Input("--allQuads", "use only quads in mesh", false);
bool zeroL2 = args.Input("--zeroL2", "take L2 term on v in robust norm to zero", enforceLocalConservation);
args.Process();
//////////////////// 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 beta_n_u_minus_sigma_n = varFactory.fluxVar("fhat");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma = varFactory.fieldVar("sigma", VECTOR_L2);
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma / epsilon, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( beta * u, - v->grad() );
bf->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
// Graph norm
if (norm == 0)
{
ip = bf->graphNorm();
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
ip->addZeroMeanTerm( h2_scaling*v );
}
// Robust norm
else if (norm == 1)
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
if (!zeroL2)
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
// Weight these two terms for inflow
ip->addTerm( beta * v->grad() );
ip->addTerm( tau->div() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (zeroL2)
ip->addZeroMeanTerm( h2_scaling*v );
}
// Modified robust norm
else if (norm == 2)
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
if (!zeroL2)
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
ip->addTerm( tau->div() - beta*v->grad() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (zeroL2)
ip->addZeroMeanTerm( h2_scaling*v );
}
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
SpatialFilterPtr inflow = Teuchos::rcp( new Inflow );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
bc->addDirichlet(beta_n_u_minus_sigma_n, inflow, zero);
SpatialFilterPtr leadingWedge = Teuchos::rcp( new LeadingWedge );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
bc->addDirichlet(uhat, leadingWedge, one);
SpatialFilterPtr trailingWedge = Teuchos::rcp( new TrailingWedge );
bc->addDirichlet(beta_n_u_minus_sigma_n, trailingWedge, beta*n*one);
// bc->addDirichlet(uhat, trailingWedge, one);
SpatialFilterPtr top = Teuchos::rcp( new Top );
bc->addDirichlet(uhat, top, zero);
// bc->addDirichlet(beta_n_u_minus_sigma_n, top, zero);
SpatialFilterPtr outflow = Teuchos::rcp( new Outflow );
pc->addConstraint(beta*uhat->times_normal() - beta_n_u_minus_sigma_n == zero, outflow);
//////////////////// BUILD MESH ///////////////////////
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(beta_n_u_minus_sigma_n == zero);
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(solution, mesh, varFactory);
ofstream errOut;
if (commRank == 0)
errOut.open("singularwedge_err.txt");
for (int refIndex=0; refIndex<=numRefs; refIndex++){
solution->solve(false);
double energy_error = solution->energyErrorTotal();
if (commRank==0){
stringstream outfile;
outfile << "singularwedge_" << refIndex;
exporter.exportSolution(outfile.str());
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_minus_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;
errOut << mesh->numGlobalDofs() << " " << energy_error << " "
<< fluxImbalances[0] << " " << fluxImbalances[1] << " " << fluxImbalances[2] << endl;
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
if (commRank == 0)
errOut.close();
return 0;
}
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 commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
double epsilon = args.Input<double>("--epsilon", "diffusion parameter");
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation");
int norm = args.Input<int>("--norm", "0 = graph\n 1 = robust\n 2 = modified robust");
// Optional arguments (have defaults)
bool zeroL2 = args.Input("--zeroL2", "take L2 term on v in robust norm to zero", false);
args.Process();
//////////////////// 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 sigma = varFactory.fieldVar("sigma", VECTOR_L2);
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma / epsilon, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( beta * u, - v->grad() );
bf->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
if (norm == 0)
{
ip = bf->graphNorm();
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
ip->addZeroMeanTerm( h2_scaling*v );
}
// Robust norm
else if (norm == 1)
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
if (!zeroL2)
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
// Weight these two terms for inflow
ip->addTerm( beta * v->grad() );
ip->addTerm( tau->div() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (zeroL2)
ip->addZeroMeanTerm( h2_scaling*v );
}
// Modified robust norm
else if (norm == 2)
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
// FunctionPtr ip_weight = Teuchos::rcp( new IPWeight() );
if (!zeroL2)
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
ip->addTerm( beta * v->grad() );
ip->addTerm( tau->div() - beta*v->grad() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (zeroL2)
ip->addZeroMeanTerm( h2_scaling*v );
}
// // robust test norm
// IPPtr robIP = Teuchos::rcp(new IP);
// FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
// if (!enforceLocalConservation)
// robIP->addTerm( ip_scaling * 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 );
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
SpatialFilterPtr lBoundary = Teuchos::rcp( new LeftBoundary );
SpatialFilterPtr tbBoundary = Teuchos::rcp( new TopBottomBoundary );
SpatialFilterPtr rBoundary = Teuchos::rcp( new RightBoundary );
// SpatialFilterPtr leftCircleBoundary = Teuchos::rcp( new LeftCircleBoundary );
// SpatialFilterPtr rightCircleBoundary = Teuchos::rcp( new RightCircleBoundary );
SpatialFilterPtr circleBoundary = Teuchos::rcp( new CircleBoundary );
bc->addDirichlet(beta_n_u_minus_sigma_n, lBoundary, zero);
bc->addDirichlet(beta_n_u_minus_sigma_n, tbBoundary, zero);
pc->addConstraint(beta*uhat->times_normal() - beta_n_u_minus_sigma_n == zero, rBoundary);
// bc->addDirichlet(uhat, leftCircleBoundary, one);
// bc->addDirichlet(beta_n_u_minus_sigma_n, rightCircleBoundary, beta*n*one);
bc->addDirichlet(uhat, circleBoundary, one);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = 3, pToAdd = 2;
Teuchos::RCP<Mesh> mesh;
mesh = MeshFactory::shiftedHemkerMesh(-3, 9, 6, 1, bf, H1Order, pToAdd);
// mesh = BuildHemkerMesh(bf, nseg, circleMesh, triangulateMesh, 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(beta_n_u_minus_sigma_n == zero);
}
double energyThreshold = 0.25; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
Teuchos::RCP<RefinementHistory> refHistory = Teuchos::rcp( new RefinementHistory );
mesh->registerObserver(refHistory);
#ifdef saveVTK
VTKExporter exporter(solution, mesh, varFactory);
#endif
ofstream errOut;
if (commRank == 0)
errOut.open("hemker_err.txt");
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
solution->solve(false);
double energy_error = solution->energyErrorTotal();
if (commRank==0)
{
stringstream outfile;
outfile << "hemker_" << refIndex;
#ifdef saveVTK
exporter.exportSolution(outfile.str());
#endif
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_minus_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;
errOut << mesh->numGlobalDofs() << " " << energy_error << " "
<< fluxImbalances[0] << " " << fluxImbalances[1] << " " << fluxImbalances[2] << endl;
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
if (commRank == 0)
errOut.close();
return 0;
}
int main(int argc, char *argv[])
{
#ifdef ENABLE_INTEL_FLOATING_POINT_EXCEPTIONS
cout << "NOTE: enabling floating point exceptions for divide by zero.\n";
_MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() & ~_MM_MASK_INVALID);
#endif
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
int rank = Teuchos::GlobalMPISession::getRank();
Teuchos::CommandLineProcessor cmdp(false,true); // false: don't throw exceptions; true: do return errors for unrecognized options
const static double PI = 3.141592653589793238462;
bool useCondensedSolve = true; // condensed solve not yet compatible with minimum rule meshes
int k = 2; // poly order for u in every direction, including temporal
int numCells = 32; // in x, y
int numTimeCells = 1;
int numTimeSlabs = -1;
int numFrames = 201;
int delta_k = 3; // test space enrichment: should be 3 for 3D
int maxRefinements = 0; // maximum # of refinements on each time slab
bool useMumpsIfAvailable = true;
bool useConstantConvection = false;
double refinementTolerance = 0.1;
int checkPointFrequency = 50; // output solution and mesh every 50 time slabs
int previousSolutionTimeSlabNumber = -1;
string previousSolutionFile = "";
string previousMeshFile = "";
cmdp.setOption("polyOrder",&k,"polynomial order for field variable u");
cmdp.setOption("delta_k", &delta_k, "test space polynomial order enrichment");
cmdp.setOption("numCells",&numCells,"number of cells in x and y directions");
cmdp.setOption("numTimeCells",&numTimeCells,"number of time axis cells");
cmdp.setOption("numTimeSlabs",&numTimeSlabs,"number of time slabs");
cmdp.setOption("numFrames",&numFrames,"number of frames for export");
cmdp.setOption("useConstantConvection", "useVariableConvection", &useConstantConvection);
cmdp.setOption("useCondensedSolve", "useUncondensedSolve", &useCondensedSolve, "use static condensation to reduce the size of the global solve");
cmdp.setOption("useMumps", "useKLU", &useMumpsIfAvailable, "use MUMPS (if available)");
cmdp.setOption("refinementTolerance", &refinementTolerance, "relative error beyond which to stop refining");
cmdp.setOption("maxRefinements", &maxRefinements, "maximum # of refinements on each time slab");
cmdp.setOption("previousSlabNumber", &previousSolutionTimeSlabNumber, "time slab number of previous solution");
cmdp.setOption("previousSolution", &previousSolutionFile, "file with previous solution");
cmdp.setOption("previousMesh", &previousMeshFile, "file with previous mesh");
if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL)
{
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return -1;
}
int H1Order = k + 1;
VarFactory varFactory;
// traces:
VarPtr qHat = varFactory.fluxVar("\\widehat{q}");
// fields:
VarPtr u = varFactory.fieldVar("u", L2);
// test functions:
VarPtr v = varFactory.testVar("v", HGRAD);
FunctionPtr x = Function::xn(1);
FunctionPtr y = Function::yn(1);
FunctionPtr c;
if (useConstantConvection)
{
c = Function::vectorize(Function::constant(0.5), Function::constant(0.5), Function::constant(1.0));
}
else
{
c = Function::vectorize(y-0.5, 0.5-x, Function::constant(1.0));
}
FunctionPtr n = Function::normal();
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
bf->addTerm( u, c * v->grad());
bf->addTerm(qHat, v);
double width = 2.0, height = 2.0;
int horizontalCells = numCells, verticalCells = numCells;
int depthCells = numTimeCells;
double x0 = -0.5;
double y0 = -0.5;
double t0 = 0;
double totalTime = 2.0 * PI;
vector<double> frameTimes;
for (int i=0; i<numFrames; i++)
{
frameTimes.push_back((totalTime*i) / (numFrames-1));
}
if (numTimeSlabs==-1)
{
// want the number of grid points in temporal direction to be about 2000. The temporal length is 2 * PI
numTimeSlabs = (int) 2000 / k;
}
double timeLengthPerSlab = totalTime / numTimeSlabs;
if (rank==0)
{
cout << "solving on " << numCells << " x " << numCells << " x " << numTimeCells << " mesh " << "of order " << k << ".\n";
cout << "numTimeSlabs: " << numTimeSlabs << endl;
}
SpatialFilterPtr inflowFilter = Teuchos::rcp( new InflowFilterForClockwisePlanarRotation (x0,x0+width,y0,y0+height,0.5,0.5));
vector<double> dimensions;
dimensions.push_back(width);
dimensions.push_back(height);
dimensions.push_back(timeLengthPerSlab);
vector<int> elementCounts(3);
elementCounts[0] = horizontalCells;
elementCounts[1] = verticalCells;
elementCounts[2] = depthCells;
vector<double> origin(3);
origin[0] = x0;
origin[1] = y0;
origin[2] = t0;
Teuchos::RCP<Solver> solver = Teuchos::rcp( new KluSolver );
#ifdef HAVE_AMESOS_MUMPS
if (useMumpsIfAvailable) solver = Teuchos::rcp( new MumpsSolver );
#endif
// double errorPercentage = 0.5; // for mesh refinements: ask to refine elements that account for 80% of the error in each step
// Teuchos::RCP<RefinementStrategy> refinementStrategy;
// refinementStrategy = Teuchos::rcp( new ErrorPercentageRefinementStrategy( soln, errorPercentage ));
if (maxRefinements != 0)
{
cout << "Warning: maxRefinements is not 0, but the slice exporter implicitly assumes there won't be any refinements.\n";
}
MeshPtr mesh;
MeshPtr prevMesh;
SolutionPtr prevSoln;
mesh = MeshFactory::rectilinearMesh(bf, dimensions, elementCounts, H1Order, delta_k, origin);
if (rank==0) cout << "Initial mesh has " << mesh->getTopology()->activeCellCount() << " active (leaf) cells " << "and " << mesh->globalDofCount() << " degrees of freedom.\n";
FunctionPtr sideParity = Function::sideParity();
int lastFrameOutputted = -1;
SolutionPtr soln;
IPPtr ip;
ip = bf->graphNorm();
FunctionPtr u0 = Teuchos::rcp( new Cone_U0(0.0, 0.25, 0.1, 1.0, false) );
BCPtr bc = BC::bc();
bc->addDirichlet(qHat, inflowFilter, Function::zero()); // zero BCs enforced at the inflow boundary.
bc->addDirichlet(qHat, SpatialFilter::matchingZ(t0), u0);
MeshPtr initialMesh = mesh;
int startingSlabNumber;
if (previousSolutionTimeSlabNumber != -1)
{
startingSlabNumber = previousSolutionTimeSlabNumber + 1;
if (rank==0) cout << "Loading mesh from " << previousMeshFile << endl;
prevMesh = MeshFactory::loadFromHDF5(bf, previousMeshFile);
prevSoln = Solution::solution(mesh, bc, RHS::rhs(), ip); // include BC and IP objects for sake of condensed dof interpreter setup...
prevSoln->setUseCondensedSolve(useCondensedSolve);
if (rank==0) cout << "Loading solution from " << previousSolutionFile << endl;
prevSoln->loadFromHDF5(previousSolutionFile);
double tn = (previousSolutionTimeSlabNumber+1) * timeLengthPerSlab;
origin[2] = tn;
mesh = MeshFactory::rectilinearMesh(bf, dimensions, elementCounts, H1Order, delta_k, origin);
FunctionPtr q_prev = Function::solution(qHat, prevSoln);
FunctionPtr q_transfer = Teuchos::rcp( new MeshTransferFunction(-q_prev, prevMesh, mesh, tn) ); // negate because the normals go in opposite directions
bc = BC::bc();
bc->addDirichlet(qHat, inflowFilter, Function::zero()); // zero BCs enforced at the inflow boundary.
bc->addDirichlet(qHat, SpatialFilter::matchingZ(tn), q_transfer);
double t_slab_final = (previousSolutionTimeSlabNumber+1) * timeLengthPerSlab;
int frameOrdinal = 0;
while (frameTimes[frameOrdinal] < t_slab_final)
{
lastFrameOutputted = frameOrdinal++;
}
}
else
{
startingSlabNumber = 0;
}
#ifdef HAVE_EPETRAEXT_HDF5
ostringstream dir_name;
dir_name << "spacetime_slice_convectingCone_k" << k << "_startSlab" << startingSlabNumber;
map<GlobalIndexType,GlobalIndexType> cellMap;
MeshPtr meshSlice = MeshTools::timeSliceMesh(initialMesh, 0, cellMap, H1Order);
HDF5Exporter sliceExporter(meshSlice,dir_name.str());
#endif
soln = Solution::solution(mesh, bc, RHS::rhs(), ip);
soln->setUseCondensedSolve(useCondensedSolve);
for(int timeSlab = startingSlabNumber; timeSlab<numTimeSlabs; timeSlab++)
{
double energyThreshold = 0.2; // for mesh refinements: ask to refine elements that account for 80% of the error in each step
Teuchos::RCP<RefinementStrategy> refinementStrategy;
refinementStrategy = Teuchos::rcp( new RefinementStrategy( soln, energyThreshold ));
FunctionPtr u_spacetime = Function::solution(u, soln);
double relativeEnergyError;
int refNumber = 0;
// {
// // DEBUGGING: just to try running the time slicing:
// double t_slab_final = (timeStep+1) * timeLengthPerSlab;
// int frameOrdinal = lastFrameOutputted + 1;
// while (frameTimes[frameOrdinal] < t_slab_final) {
// FunctionPtr u_spacetime = Function::solution(u, soln);
// ostringstream dir_name;
// dir_name << "spacetime_slice_convectingCone_k" << k;
// MeshTools::timeSliceExport(dir_name.str(), mesh, u_spacetime, frameTimes[frameOrdinal], "u_slice");
//
// cout << "Exported frame " << frameOrdinal << ", t=" << frameTimes[frameOrdinal] << endl;
// frameOrdinal++;
// }
// }
do
{
soln->solve(solver);
soln->reportTimings();
#ifdef HAVE_EPETRAEXT_HDF5
ostringstream dir_name;
dir_name << "spacetime_convectingCone_k" << k << "_t" << timeSlab;
HDF5Exporter exporter(soln->mesh(),dir_name.str());
exporter.exportSolution(soln, varFactory);
if (rank==0) cout << "Exported HDF solution for time slab to directory " << dir_name.str() << endl;
// string u_name = "u_spacetime";
// exporter.exportFunction(u_spacetime, u_name);
ostringstream file_name;
file_name << dir_name.str();
bool saveSolutionAndMeshForThisSlab = ((timeSlab + 1) % checkPointFrequency == 0); // +1 so that first output is nth, not first
if (saveSolutionAndMeshForThisSlab)
{
dir_name << ".soln";
soln->saveToHDF5(dir_name.str());
if (rank==0) cout << endl << "wrote " << dir_name.str() << endl;
file_name << ".mesh";
soln->mesh()->saveToHDF5(file_name.str());
}
#endif
FunctionPtr u_soln = Function::solution(u, soln);
double solnNorm = u_soln->l2norm(mesh);
double energyError = soln->energyErrorTotal();
relativeEnergyError = energyError / solnNorm;
if (rank==0)
{
cout << "Relative energy error for refinement " << refNumber++ << ": " << relativeEnergyError << endl;
}
if ((relativeEnergyError > refinementTolerance) && (refNumber < maxRefinements))
{
refinementStrategy->refine();
if (rank==0)
{
cout << "After refinement, mesh has " << mesh->getTopology()->activeCellCount() << " active (leaf) cells " << "and " << mesh->globalDofCount() << " degrees of freedom.\n";
}
}
}
while ((relativeEnergyError > refinementTolerance) && (refNumber < maxRefinements));
double t_slab_final = (timeSlab+1) * timeLengthPerSlab;
int frameOrdinal = lastFrameOutputted + 1;
vector<double> timesForSlab;
while (frameTimes[frameOrdinal] < t_slab_final)
{
double t = frameTimes[frameOrdinal];
if (rank==0) cout << "exporting t=" << t << " on slab " << timeSlab << endl;
FunctionPtr sliceFunction = MeshTools::timeSliceFunction(mesh, cellMap, u_spacetime, t);
sliceExporter.exportFunction(sliceFunction, "u_slice", t);
lastFrameOutputted = frameOrdinal++;
}
// set up next mesh/solution:
FunctionPtr q_prev = Function::solution(qHat, soln);
// cout << "Error in setup of q_prev: simple solution doesn't know about the map from the previous time slab to the current one. (TODO: fix this.)\n";
double tn = (timeSlab+1) * timeLengthPerSlab;
origin[2] = tn;
mesh = MeshFactory::rectilinearMesh(bf, dimensions, elementCounts, H1Order, delta_k, origin);
FunctionPtr q_transfer = Teuchos::rcp( new MeshTransferFunction(-q_prev, soln->mesh(), mesh, tn) ); // negate because the normals go in opposite directions
bc = BC::bc();
bc->addDirichlet(qHat, inflowFilter, Function::zero()); // zero BCs enforced at the inflow boundary.
bc->addDirichlet(qHat, SpatialFilter::matchingZ(tn), q_transfer);
// IMPORTANT: now that we are ready to step to next soln, nullify BC. If we do not do this, then we have an RCP chain
// that extends back to the first time slab, effectively a memory leak.
soln->setBC(BC::bc());
soln = Solution::solution(mesh, bc, RHS::rhs(), ip);
soln->setUseCondensedSolve(useCondensedSolve);
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
#endif
int commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// {
// // 1D tests
// CellTopoPtrLegacy line_2 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >() ) );
// // let's draw a line
// vector<double> v0 = makeVertex(0);
// vector<double> v1 = makeVertex(1);
// vector<double> v2 = makeVertex(2);
// vector< vector<double> > vertices;
// vertices.push_back(v0);
// vertices.push_back(v1);
// vertices.push_back(v2);
// vector<unsigned> line1VertexList;
// vector<unsigned> line2VertexList;
// line1VertexList.push_back(0);
// line1VertexList.push_back(1);
// line2VertexList.push_back(1);
// line2VertexList.push_back(2);
// vector< vector<unsigned> > elementVertices;
// elementVertices.push_back(line1VertexList);
// elementVertices.push_back(line2VertexList);
// vector< CellTopoPtrLegacy > cellTopos;
// cellTopos.push_back(line_2);
// cellTopos.push_back(line_2);
// MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
// MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
// FunctionPtr x = Function::xn(1);
// FunctionPtr function = x;
// FunctionPtr fbdr = Function::restrictToCellBoundary(function);
// vector<FunctionPtr> functions;
// functions.push_back(function);
// functions.push_back(function);
// vector<string> functionNames;
// functionNames.push_back("function1");
// functionNames.push_back("function2");
// // {
// // HDF5Exporter exporter(mesh, "function1", false);
// // exporter.exportFunction(function, "function1");
// // }
// // {
// // HDF5Exporter exporter(mesh, "boundary1", false);
// // exporter.exportFunction(fbdr, "boundary1");
// // }
// // {
// // HDF5Exporter exporter(mesh, "functions1", false);
// // exporter.exportFunction(functions, functionNames);
// // }
// }
{
// 2D tests
// CellTopoPtrLegacy quad_4 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ) );
// CellTopoPtrLegacy tri_3 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() ) );
CellTopoPtr quad_4 = CellTopology::quad();
CellTopoPtr tri_3 = CellTopology::triangle();
// let's draw a little house
vector<double> v0 = makeVertex(-1,0);
vector<double> v1 = makeVertex(1,0);
vector<double> v2 = makeVertex(1,2);
vector<double> v3 = makeVertex(-1,2);
vector<double> v4 = makeVertex(0.0,3);
vector< vector<double> > vertices;
vertices.push_back(v0);
vertices.push_back(v1);
vertices.push_back(v2);
vertices.push_back(v3);
vertices.push_back(v4);
vector<unsigned> quadVertexList;
quadVertexList.push_back(0);
quadVertexList.push_back(1);
quadVertexList.push_back(2);
quadVertexList.push_back(3);
vector<unsigned> triVertexList;
triVertexList.push_back(3);
triVertexList.push_back(2);
triVertexList.push_back(4);
vector< vector<unsigned> > elementVertices;
elementVertices.push_back(quadVertexList);
elementVertices.push_back(triVertexList);
// vector< CellTopoPtrLegacy > cellTopos;
vector< CellTopoPtr> cellTopos;
cellTopos.push_back(quad_4);
cellTopos.push_back(tri_3);
MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr vf = VarFactory::varFactory();
VarPtr tau = vf->testVar("tau", HDIV);
VarPtr v = vf->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = vf->traceVar("uhat");
VarPtr fhat = vf->fluxVar("fhat");
VarPtr u = vf->fieldVar("u");
VarPtr sigma = vf->fieldVar("sigma", VECTOR_L2);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(vf) );
// tau terms:
bf->addTerm(sigma, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( fhat, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = bf->graphNorm();
//////////////////// SPECIFY RHS ///////////////////////
RHSPtr rhs = RHS::rhs();
FunctionPtr one = Function::constant(1.0);
rhs->addTerm( one * v );
//////////////////// CREATE BCs ///////////////////////
BCPtr bc = BC::bc();
FunctionPtr zero = Function::zero();
SpatialFilterPtr entireBoundary = SpatialFilter::allSpace();
bc->addDirichlet(uhat, entireBoundary, zero);
//////////////////// SOLVE & REFINE ///////////////////////
// Output solution
Intrepid::FieldContainer<GlobalIndexType> savedCellPartition;
Teuchos::RCP<Epetra_FEVector> savedLHSVector;
{
//////////////////// BUILD MESH ///////////////////////
int H1Order = 4, pToAdd = 2;
Teuchos::RCP<Mesh> mesh = Teuchos::rcp( new Mesh (meshTopology, bf, H1Order, pToAdd) );
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
solution->solve(false);
RefinementStrategy refinementStrategy( solution, 0.2);
HDF5Exporter exporter(mesh, "Poisson");
// exporter.exportSolution(solution, vf, 0, 2, cellIDToSubdivision(mesh, 4));
exporter.exportSolution(solution, 0, 2);
mesh->saveToHDF5("MeshSave.h5");
solution->saveToHDF5("SolnSave.h5");
solution->save("PoissonProblem");
// int numRefs = 1;
// for (int ref = 1; ref <= numRefs; ref++)
// {
// refinementStrategy.refine(commRank==0);
// solution->solve(false);
// mesh->saveToHDF5("MeshSave.h5");
// solution->saveToHDF5("SolnSave.h5");
// exporter.exportSolution(solution, vf, ref, 2, cellIDToSubdivision(mesh, 4));
// }
mesh->globalDofAssignment()->getPartitions(savedCellPartition);
savedLHSVector = solution->getLHSVector();
}
{
SolutionPtr loadedSolution = Solution::load(bf, "PoissonProblem");
HDF5Exporter exporter(loadedSolution->mesh(), "ProblemLoaded");
// exporter.exportSolution(loadedSolution, vf, 0, 2, cellIDToSubdivision(loadedSolution->mesh(), 4));
exporter.exportSolution(loadedSolution, 0, 2);
}
// {
// MeshPtr loadedMesh = MeshFactory::loadFromHDF5(bf, "Test0.h5");
// Teuchos::RCP<Solution> loadedSolution = Teuchos::rcp( new Solution(loadedMesh, bc, rhs, ip) );
// loadedSolution->solve(false);
// HDF5Exporter exporter(loadedMesh, "MeshLoaded");
// exporter.exportSolution(loadedSolution, vf, 0, 2, cellIDToSubdivision(loadedMesh, 4));
// }
{
MeshPtr loadedMesh = MeshFactory::loadFromHDF5(bf, "MeshSave.h5");
Intrepid::FieldContainer<GlobalIndexType> loadedCellPartition;
loadedMesh->globalDofAssignment()->getPartitions(loadedCellPartition);
if (loadedCellPartition.size() != savedCellPartition.size())
{
cout << "Error: the loaded partition has different size/shape than the saved one.\n";
cout << "loaded size: " << loadedCellPartition.size() << "; saved size: " << savedCellPartition.size() << endl;
}
else
{
bool partitionsMatch = true;
for (int i=0; i<loadedCellPartition.size(); i++)
{
if (loadedCellPartition[i] != savedCellPartition[i])
{
partitionsMatch = false;
break;
}
}
if (partitionsMatch) cout << "Saved and loaded cell partitions match!\n";
else
{
cout << "Saved and loaded cell partitions differ.\n";
cout << "saved:\n" << savedCellPartition;
cout << "loaded:\n" << loadedCellPartition;
}
}
Teuchos::RCP<Solution> loadedSolution = Teuchos::rcp( new Solution(loadedMesh, bc, rhs, ip) );
loadedSolution->loadFromHDF5("SolnSave.h5");
Teuchos::RCP<Epetra_FEVector> loadedLHSVector = loadedSolution->getLHSVector();
if (loadedLHSVector->Map().MinLID() != savedLHSVector->Map().MinLID())
{
cout << "On rank " << commRank << ", loaded min LID = " << loadedLHSVector->Map().MinLID();
cout << ", but saved min LID = " << savedLHSVector->Map().MinLID() << endl;
}
else if (loadedLHSVector->Map().MaxLID() != savedLHSVector->Map().MaxLID())
{
cout << "On rank " << commRank << ", loaded max LID = " << loadedLHSVector->Map().MaxLID();
cout << ", but saved max LID = " << savedLHSVector->Map().MaxLID() << endl;
}
else
{
bool globalIDsMatch = true;
for (int lid = loadedLHSVector->Map().MinLID(); lid <= loadedLHSVector->Map().MaxLID(); lid++)
{
if (loadedLHSVector->Map().GID(lid) != savedLHSVector->Map().GID(lid))
{
globalIDsMatch = false;
}
}
if (! globalIDsMatch)
{
cout << "On rank " << commRank << ", loaded and saved solution vector maps differ in their global IDs.\n";
}
else
{
cout << "On rank " << commRank << ", loaded and saved solution vector maps match in their global IDs.\n";
}
bool entriesMatch = true;
double tol = 1e-16;
if (loadedLHSVector->Map().MinLID() != loadedLHSVector->Map().MaxLID())
{
for (int lid = loadedLHSVector->Map().MinLID(); lid <= loadedLHSVector->Map().MaxLID(); lid++)
{
double loadedValue = (*loadedLHSVector)[0][lid];
double savedValue = (*savedLHSVector)[0][lid];
double diff = abs( loadedValue - savedValue );
if (diff > tol)
{
entriesMatch = false;
cout << "On rank " << commRank << ", loaded and saved solution vectors differ in entry with lid " << lid;
cout << "; loaded value = " << loadedValue << "; saved value = " << savedValue << ".\n";
}
}
if (entriesMatch)
{
cout << "On rank " << commRank << ", loaded and saved solution vectors match!\n";
}
else
{
cout << "On rank " << commRank << ", loaded and saved solution vectors do not match.\n";
}
}
}
HDF5Exporter exporter(loadedMesh, "SolutionLoaded");
// exporter.exportSolution(loadedSolution, vf, 0, 2, cellIDToSubdivision(loadedMesh, 4));
exporter.exportSolution(loadedSolution, 0, 2);
}
}
// {
// // 3D tests
// CellTopoPtrLegacy hex = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Hexahedron<8> >() ));
// // let's draw a little box
// vector<double> v0 = makeVertex(0,0,0);
// vector<double> v1 = makeVertex(1,0,0);
// vector<double> v2 = makeVertex(1,1,0);
// vector<double> v3 = makeVertex(0,1,0);
// vector<double> v4 = makeVertex(0,0,1);
// vector<double> v5 = makeVertex(1,0,1);
// vector<double> v6 = makeVertex(1,1,1);
// vector<double> v7 = makeVertex(0,1,1);
// vector< vector<double> > vertices;
// vertices.push_back(v0);
// vertices.push_back(v1);
// vertices.push_back(v2);
// vertices.push_back(v3);
// vertices.push_back(v4);
// vertices.push_back(v5);
// vertices.push_back(v6);
// vertices.push_back(v7);
// vector<unsigned> hexVertexList;
// hexVertexList.push_back(0);
// hexVertexList.push_back(1);
// hexVertexList.push_back(2);
// hexVertexList.push_back(3);
// hexVertexList.push_back(4);
// hexVertexList.push_back(5);
// hexVertexList.push_back(6);
// hexVertexList.push_back(7);
// // vector<unsigned> triVertexList;
// // triVertexList.push_back(2);
// // triVertexList.push_back(3);
// // triVertexList.push_back(4);
// vector< vector<unsigned> > elementVertices;
// elementVertices.push_back(hexVertexList);
// // elementVertices.push_back(triVertexList);
// vector< CellTopoPtrLegacy > cellTopos;
// cellTopos.push_back(hex);
// // cellTopos.push_back(tri_3);
// MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
// MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
// FunctionPtr x = Function::xn(1);
// FunctionPtr y = Function::yn(1);
// FunctionPtr z = Function::zn(1);
// FunctionPtr function = x + y + z;
// FunctionPtr fbdr = Function::restrictToCellBoundary(function);
// FunctionPtr vect = Function::vectorize(x, y, z);
// vector<FunctionPtr> functions;
// functions.push_back(function);
// functions.push_back(vect);
// vector<string> functionNames;
// functionNames.push_back("function");
// functionNames.push_back("vect");
// // {
// // HDF5Exporter exporter(mesh, "function3", false);
// // exporter.exportFunction(function, "function3");
// // }
// // {
// // HDF5Exporter exporter(mesh, "boundary3", false);
// // exporter.exportFunction(fbdr, "boundary3");
// // }
// // {
// // HDF5Exporter exporter(mesh, "vect3", false);
// // exporter.exportFunction(vect, "vect3");
// // }
// // {
// // HDF5Exporter exporter(mesh, "functions3", false);
// // exporter.exportFunction(functions, functionNames);
// // }
// }
}
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 commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation");
bool steady = args.Input<bool>("--steady", "run steady rather than transient");
// Optional arguments (have defaults)
double dt = args.Input("--dt", "time step", 0.25);
int numTimeSteps = args.Input("--nt", "number of time steps", 20);
halfWidth = args.Input("--halfWidth", "half width of inlet profile", 1.0);
args.Process();
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr beta_n_u_hat = varFactory.fluxVar("\\widehat{\\beta \\cdot n }");
VarPtr u = varFactory.fieldVar("u");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// BUILD MESH ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// define nodes for mesh
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 = 8, verticalCells = 8;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
bf, H1Order, H1Order+pToAdd);
////////////////////////////////////////////////////////////////////
// INITIALIZE 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) );
//////////////////// DEFINE BILINEAR FORM ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr invDt = Teuchos::rcp(new ScalarParamFunction(1.0/dt));
// v terms:
bf->addTerm( beta * u, - v->grad() );
bf->addTerm( beta_n_u_hat, v);
if (!steady)
{
bf->addTerm( u, invDt*v );
rhs->addTerm( u_prev_time * invDt * v );
}
//////////////////// SPECIFY RHS ///////////////////////
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = bf->graphNorm();
// ip->addTerm(v);
// ip->addTerm(beta*v->grad());
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr lBoundary = Teuchos::rcp( new LeftBoundary );
FunctionPtr u1 = Teuchos::rcp( new InletBC );
bc->addDirichlet(beta_n_u_hat, lBoundary, -u1);
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
// ==================== Register Solutions ==========================
mesh->registerSolution(solution);
mesh->registerSolution(prevTimeFlow);
mesh->registerSolution(flowResidual);
// ==================== SET INITIAL GUESS ==========================
double u_free = 0.0;
map<int, Teuchos::RCP<Function> > functionMap;
// functionMap[u->ID()] = Teuchos::rcp( new ConInletBC
functionMap[u->ID()] = Teuchos::rcp( new InletBC );
prevTimeFlow->projectOntoMesh(functionMap);
//////////////////// SOLVE & REFINE ///////////////////////
if (enforceLocalConservation)
{
if (steady)
{
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(beta_n_u_hat == zero);
}
else
{
// FunctionPtr parity = Teuchos::rcp<Function>( new SideParityFunction );
// LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(parity, beta_n_u_minus_sigma_n) );
LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(1.0, beta_n_u_hat) );
LinearTermPtr sourcePart = Teuchos::rcp<LinearTerm>( new LinearTerm(invDt, u) );
conservedQuantity->addTerm(sourcePart, true);
solution->lagrangeConstraints()->addConstraint(conservedQuantity == u_prev_time * invDt);
}
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(solution, mesh, varFactory);
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
if (steady)
{
solution->solve(false);
if (commRank == 0)
{
stringstream outfile;
outfile << "Convection_" << refIndex;
exporter.exportSolution(outfile.str());
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_hat) );
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;
}
}
else
{
int timestepCount = 0;
double time_tol = 1e-8;
double L2_time_residual = 1e9;
// cout << L2_time_residual <<" "<< time_tol << timestepCount << numTimeSteps << endl;
while((L2_time_residual > time_tol) && (timestepCount < numTimeSteps))
{
solution->solve(false);
// Subtract solutions to get residual
flowResidual->setSolution(solution);
flowResidual->addSolution(prevTimeFlow, -1.0);
L2_time_residual = flowResidual->L2NormOfSolutionGlobal(u->ID());
if (commRank == 0)
{
cout << endl << "Timestep: " << timestepCount << ", dt = " << dt << ", Time residual = " << L2_time_residual << endl;
stringstream outfile;
outfile << "TransientConvection_" << refIndex << "-" << timestepCount;
exporter.exportSolution(outfile.str());
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_hat) );
FunctionPtr source = Teuchos::rcp( new PreviousSolutionFunction(flowResidual, u) );
source = -invDt * source;
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, source, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
}
prevTimeFlow->setSolution(solution); // reset previous time solution to current time sol
timestepCount++;
}
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
return 0;
}
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 commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
int norm = args.Input<int>("--norm", "0 = graph\n 1 = robust\n 2 = coupled robust");
// Optional arguments (have defaults)
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation", false);
double Re = args.Input("--Re", "Reynolds number", 40);
double nu = 1./Re;
double lambda = Re/2.-sqrt(Re*Re/4+4*pi*pi);
int maxNewtonIterations = args.Input("--maxIterations", "maximum number of Newton iterations", 20);
int polyOrder = args.Input("--polyOrder", "polynomial order for field variables", 2);
int deltaP = args.Input("--deltaP", "how much to enrich test space", 2);
// string saveFile = args.Input<string>("--meshSaveFile", "file to which to save refinement history", "");
// string replayFile = args.Input<string>("--meshLoadFile", "file with refinement history to replay", "");
args.Process();
// if (commRank==0)
// {
// cout << "saveFile is " << saveFile << endl;
// cout << "loadFile is " << replayFile << endl;
// }
//////////////////// PROBLEM DEFINITIONS ///////////////////////
int H1Order = polyOrder+1;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
// VarPtr tau11 = varFactory.testVar("tau11", HGRAD);
// VarPtr tau12 = varFactory.testVar("tau12", HGRAD);
// VarPtr tau22 = varFactory.testVar("tau22", HGRAD);
VarPtr tau1 = varFactory.testVar("tau1", HDIV);
VarPtr tau2 = varFactory.testVar("tau2", HDIV);
VarPtr v1 = varFactory.testVar("v1", HGRAD);
VarPtr v2 = varFactory.testVar("v2", HGRAD);
VarPtr q = varFactory.testVar("q", HGRAD);
// define trial variables
VarPtr u1 = varFactory.fieldVar("u1");
VarPtr u2 = varFactory.fieldVar("u2");
// VarPtr sigma11 = varFactory.fieldVar("sigma11");
// VarPtr sigma12 = varFactory.fieldVar("sigma12");
// VarPtr sigma22 = varFactory.fieldVar("sigma22");
VarPtr sigma1 = varFactory.fieldVar("sigma1", VECTOR_L2);
VarPtr sigma2 = varFactory.fieldVar("sigma2", VECTOR_L2);
VarPtr u1hat = varFactory.traceVar("u1hat");
VarPtr u2hat = varFactory.traceVar("u2hat");
VarPtr t1hat = varFactory.fluxVar("t1hat");
VarPtr t2hat = varFactory.fluxVar("t2hat");
VarPtr p = varFactory.fieldVar("p");
//////////////////// BUILD MESH ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// define nodes for mesh
FieldContainer<double> meshBoundary(4,2);
double xmin = -0.5;
double xmax = 1.0;
double ymin = -0.5;
double ymax = 1.5;
meshBoundary(0,0) = xmin; // x1
meshBoundary(0,1) = ymin; // y1
meshBoundary(1,0) = xmax;
meshBoundary(1,1) = ymin;
meshBoundary(2,0) = xmax;
meshBoundary(2,1) = ymax;
meshBoundary(3,0) = xmin;
meshBoundary(3,1) = ymax;
int horizontalCells = 6, verticalCells = 8;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
bf, H1Order, H1Order+deltaP);
////////////////////////////////////////////////////////////////////
// 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 u1_prev = Function::solution(u1, backgroundFlow);
FunctionPtr u2_prev = Function::solution(u2, backgroundFlow);
FunctionPtr sigma1_prev = Function::solution(sigma1, backgroundFlow);
FunctionPtr sigma2_prev = Function::solution(sigma2, backgroundFlow);
FunctionPtr p_prev = Function::solution(p, backgroundFlow);
// FunctionPtr sigma11_prev = Function::solution(sigma11, backgroundFlow);
// FunctionPtr sigma12_prev = Function::solution(sigma12, backgroundFlow);
// FunctionPtr sigma22_prev = Function::solution(sigma22, backgroundFlow);
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
FunctionPtr u1Exact = Teuchos::rcp( new ExactU1(lambda) );
FunctionPtr u2Exact = Teuchos::rcp( new ExactU2(lambda) );
// FunctionPtr beta = e1 * u1_prev + e2 * u2_prev;
// ==================== SET INITIAL GUESS ==========================
map<int, Teuchos::RCP<Function> > functionMap;
functionMap[u1->ID()] = u1Exact;
functionMap[u2->ID()] = u2Exact;
// functionMap[sigma1->ID()] = Function::vectorize(zero,zero);
// functionMap[sigma2->ID()] = Function::vectorize(zero,zero);
// functionMap[p->ID()] = zero;
backgroundFlow->projectOntoMesh(functionMap);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
// // stress equation
bf->addTerm( 1./nu*sigma1, tau1 );
bf->addTerm( 1./nu*sigma2, tau2 );
bf->addTerm( u1, tau1->div() );
bf->addTerm( u2, tau2->div() );
bf->addTerm( -u1hat, tau1->dot_normal() );
bf->addTerm( -u2hat, tau2->dot_normal() );
// bf->addTerm( 1./(2*nu)*sigma11, tau11 );
// bf->addTerm( 1./(2*nu)*sigma12, tau12 );
// bf->addTerm( 1./(2*nu)*sigma12, tau12 );
// bf->addTerm( 1./(2*nu)*sigma22, tau22 );
// bf->addTerm( u1, tau11->dx() );
// bf->addTerm( u1, tau12->dy() );
// bf->addTerm( u2, tau12->dx() );
// bf->addTerm( u2, tau22->dy() );
// bf->addTerm( -u1hat, tau11->times_normal_x() );
// bf->addTerm( -u1hat, tau12->times_normal_y() );
// bf->addTerm( -u2hat, tau12->times_normal_x() );
// bf->addTerm( -u2hat, tau22->times_normal_y() );
// momentum equation
bf->addTerm( -2.*u1_prev*u1, v1->dx() );
bf->addTerm( -u2_prev*u1, v1->dy() );
bf->addTerm( -u1_prev*u2, v1->dy() );
bf->addTerm( -u2_prev*u1, v2->dx() );
bf->addTerm( -u1_prev*u2, v1->dy() );
bf->addTerm( -2.*u2_prev*u2, v2->dy() );
bf->addTerm( -p, v1->dx() );
bf->addTerm( -p, v2->dy() );
// bf->addTerm( sigma11, v1->dx() );
// bf->addTerm( sigma12, v1->dy() );
// bf->addTerm( sigma12, v2->dx() );
// bf->addTerm( sigma22, v2->dy() );
bf->addTerm( sigma1, v1->grad() );
bf->addTerm( sigma2, v2->grad() );
bf->addTerm( t1hat, v1);
bf->addTerm( t2hat, v2);
// continuity equation
bf->addTerm( -u1, q->dx() );
bf->addTerm( -u2, q->dy() );
bf->addTerm( u1hat, q->times_normal_x() );
bf->addTerm( u2hat, q->times_normal_y() );
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
// stress equation
rhs->addTerm( -u1_prev * tau1->div() );
rhs->addTerm( -u2_prev * tau2->div() );
// momentum equation
rhs->addTerm( 2.*u1_prev*u1_prev * v1->dx() );
rhs->addTerm( u2_prev*u1_prev * v1->dy() );
rhs->addTerm( u1_prev*u2_prev * v1->dy() );
rhs->addTerm( u2_prev*u1_prev * v2->dx() );
rhs->addTerm( u1_prev*u2_prev * v1->dy() );
rhs->addTerm( 2.*u2_prev*u2_prev * v2->dy() );
// rhs->addTerm( p_prev * v1->dx() );
// rhs->addTerm( p_prev * v2->dy() );
// rhs->addTerm( -sigma1_prev * v1->grad() );
// rhs->addTerm( -sigma2_prev * v2->grad() );
// rhs->addTerm( -sigma11_prev * v1->dx() );
// rhs->addTerm( -sigma12_prev * v1->dy() );
// rhs->addTerm( -sigma12_prev * v2->dx() );
// rhs->addTerm( -sigma22_prev * v2->dy() );
// continuity equation
rhs->addTerm( u1_prev * q->dx() );
rhs->addTerm( u2_prev * q->dy() );
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
if (norm == 0)
{
ip = bf->graphNorm();
}
else if (norm == 1)
{
// ip = bf->l2Norm();
}
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
// Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
SpatialFilterPtr left = Teuchos::rcp( new ConstantXBoundary(-0.5) );
SpatialFilterPtr right = Teuchos::rcp( new ConstantXBoundary(1) );
SpatialFilterPtr top = Teuchos::rcp( new ConstantYBoundary(-0.5) );
SpatialFilterPtr bottom = Teuchos::rcp( new ConstantYBoundary(1.5) );
bc->addDirichlet(u1hat, left, u1Exact);
bc->addDirichlet(u2hat, left, u2Exact);
bc->addDirichlet(u1hat, right, u1Exact);
bc->addDirichlet(u2hat, right, u2Exact);
bc->addDirichlet(u1hat, top, u1Exact);
bc->addDirichlet(u2hat, top, u2Exact);
bc->addDirichlet(u1hat, bottom, u1Exact);
bc->addDirichlet(u2hat, bottom, u2Exact);
// zero mean constraint on pressure
bc->addZeroMeanConstraint(p);
// pc->addConstraint(u1hat*u2hat-t1hat == zero, top);
// pc->addConstraint(u2hat*u2hat-t2hat == zero, top);
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
// solution->setFilter(pc);
// if (enforceLocalConservation) {
// solution->lagrangeConstraints()->addConstraint(u1hat->times_normal_x() + u2hat->times_normal_y() == zero);
// }
// ==================== Register Solutions ==========================
mesh->registerSolution(solution);
mesh->registerSolution(backgroundFlow);
// Teuchos::RCP< RefinementHistory > refHistory = Teuchos::rcp( new RefinementHistory );
// mesh->registerObserver(refHistory);
//////////////////// SOLVE & REFINE ///////////////////////
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(backgroundFlow, mesh, varFactory);
stringstream outfile;
outfile << "kovasznay" << "_" << 0;
exporter.exportSolution(outfile.str());
double nonlinearRelativeEnergyTolerance = 1e-5; // used to determine convergence of the nonlinear solution
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
double L2Update = 1e10;
int iterCount = 0;
while (L2Update > nonlinearRelativeEnergyTolerance && iterCount < maxNewtonIterations)
{
solution->solve(false);
double u1L2Update = solution->L2NormOfSolutionGlobal(u1->ID());
double u2L2Update = solution->L2NormOfSolutionGlobal(u2->ID());
L2Update = sqrt(u1L2Update*u1L2Update + u2L2Update*u2L2Update);
// Check local conservation
if (commRank == 0)
{
cout << "L2 Norm of Update = " << L2Update << endl;
// if (saveFile.length() > 0) {
// std::ostringstream oss;
// oss << string(saveFile) << refIndex ;
// cout << "on refinement " << refIndex << " saving mesh file to " << oss.str() << endl;
// refHistory->saveToFile(oss.str());
// }
}
// line search algorithm
double alpha = 1.0;
backgroundFlow->addSolution(solution, alpha);
iterCount++;
}
if (commRank == 0)
{
stringstream outfile;
outfile << "kovasznay" << "_" << refIndex+1;
exporter.exportSolution(outfile.str());
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
#endif
{
// 1D tests
CellTopoPtr line_2 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >() ) );
// let's draw a line
vector<double> v0 = makeVertex(0);
vector<double> v1 = makeVertex(1);
vector<double> v2 = makeVertex(2);
vector< vector<double> > vertices;
vertices.push_back(v0);
vertices.push_back(v1);
vertices.push_back(v2);
vector<unsigned> line1VertexList;
vector<unsigned> line2VertexList;
line1VertexList.push_back(0);
line1VertexList.push_back(1);
line2VertexList.push_back(1);
line2VertexList.push_back(2);
vector< vector<unsigned> > elementVertices;
elementVertices.push_back(line1VertexList);
elementVertices.push_back(line2VertexList);
vector< CellTopoPtr > cellTopos;
cellTopos.push_back(line_2);
cellTopos.push_back(line_2);
MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
FunctionPtr x = Function::xn(1);
FunctionPtr function = x;
FunctionPtr fbdr = Function::restrictToCellBoundary(function);
vector<FunctionPtr> functions;
functions.push_back(function);
functions.push_back(function);
vector<string> functionNames;
functionNames.push_back("function1");
functionNames.push_back("function2");
{
XDMFExporter exporter(meshTopology, "function1", false);
exporter.exportFunction(function, "function1");
}
{
XDMFExporter exporter(meshTopology, "boundary1", false);
exporter.exportFunction(fbdr, "boundary1");
}
{
XDMFExporter exporter(meshTopology, "functions1", false);
exporter.exportFunction(functions, functionNames);
}
}
{
// 2D tests
CellTopoPtr quad_4 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ) );
CellTopoPtr tri_3 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() ) );
// let's draw a little house
vector<double> v0 = makeVertex(-1,0);
vector<double> v1 = makeVertex(1,0);
vector<double> v2 = makeVertex(1,2);
vector<double> v3 = makeVertex(-1,2);
vector<double> v4 = makeVertex(0.0,3);
vector< vector<double> > vertices;
vertices.push_back(v0);
vertices.push_back(v1);
vertices.push_back(v2);
vertices.push_back(v3);
vertices.push_back(v4);
vector<unsigned> quadVertexList;
quadVertexList.push_back(0);
quadVertexList.push_back(1);
quadVertexList.push_back(2);
quadVertexList.push_back(3);
vector<unsigned> triVertexList;
triVertexList.push_back(3);
triVertexList.push_back(2);
triVertexList.push_back(4);
vector< vector<unsigned> > elementVertices;
elementVertices.push_back(quadVertexList);
elementVertices.push_back(triVertexList);
vector< CellTopoPtr > cellTopos;
cellTopos.push_back(quad_4);
cellTopos.push_back(tri_3);
MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
FunctionPtr x2 = Function::xn(2);
FunctionPtr y2 = Function::yn(2);
FunctionPtr function = x2 + y2;
FunctionPtr vect = Function::vectorize(x2, y2);
FunctionPtr fbdr = Function::restrictToCellBoundary(function);
vector<FunctionPtr> functions;
functions.push_back(function);
functions.push_back(vect);
vector<string> functionNames;
functionNames.push_back("function");
functionNames.push_back("vect");
vector<FunctionPtr> bdrfunctions;
bdrfunctions.push_back(fbdr);
bdrfunctions.push_back(fbdr);
vector<string> bdrfunctionNames;
bdrfunctionNames.push_back("bdr1");
bdrfunctionNames.push_back("bdr2");
map<int, int> cellIDToNum1DPts;
cellIDToNum1DPts[1] = 4;
{
XDMFExporter exporter(meshTopology, "Grid2D", false);
// exporter.exportFunction(function, "function2", 0, 10);
// exporter.exportFunction(vect, "vect2", 1, 10, cellIDToNum1DPts);
// exporter.exportFunction(fbdr, "boundary2", 0);
exporter.exportFunction(functions, functionNames, 1, 10);
}
{
XDMFExporter exporter(meshTopology, "BdrGrid2D", false);
// exporter.exportFunction(function, "function2", 0, 10);
// exporter.exportFunction(vect, "vect2", 1, 10, cellIDToNum1DPts);
// exporter.exportFunction(fbdr, "boundary2", 0);
exporter.exportFunction(bdrfunctions, bdrfunctionNames, 1, 10);
}
//////////////////// 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 fhat = varFactory.fluxVar("fhat");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma = varFactory.fieldVar("sigma", VECTOR_L2);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( fhat, v);
//////////////////// BUILD MESH ///////////////////////
int H1Order = 4, pToAdd = 2;
Teuchos::RCP<Mesh> mesh = Teuchos::rcp( new Mesh (meshTopology, bf, H1Order, pToAdd) );
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = bf->graphNorm();
//////////////////// SPECIFY RHS ///////////////////////
RHSPtr rhs = RHS::rhs();
// Teuchos::RCP<RHS> rhs = Teuchos::rcp( new RHS );
FunctionPtr one = Function::constant(1.0);
rhs->addTerm( one * v );
//////////////////// CREATE BCs ///////////////////////
// Teuchos::RCP<BC> bc = Teuchos::rcp( new BCEasy );
BCPtr bc = BC::bc();
FunctionPtr zero = Function::zero();
SpatialFilterPtr entireBoundary = Teuchos::rcp( new EntireBoundary );
bc->addDirichlet(uhat, entireBoundary, zero);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
solution->solve(false);
RefinementStrategy refinementStrategy( solution, 0.2);
// Output solution
FunctionPtr uSoln = Function::solution(u, solution);
FunctionPtr sigmaSoln = Function::solution(sigma, solution);
FunctionPtr uhatSoln = Function::solution(uhat, solution);
FunctionPtr fhatSoln = Function::solution(fhat, solution);
{
XDMFExporter exporter(meshTopology, "Poisson", false);
exporter.exportFunction(uSoln, "u", 0, 4);
exporter.exportFunction(uSoln, "u", 1, 5);
exporter.exportFunction(uhatSoln, "uhat", 0, 4);
exporter.exportFunction(uhatSoln, "uhat", 1, 5);
// exporter.exportFunction(fhatSoln, "fhat", 0, 4);
// exporter.exportFunction(fhatSoln, "fhat", 1, 5);
}
{
XDMFExporter exporter(meshTopology, "PoissonSolution", false);
exporter.exportSolution(solution, mesh, varFactory, 0, 2, cellIDToSubdivision(mesh, 10));
refinementStrategy.refine(true);
solution->solve(false);
exporter.exportSolution(solution, mesh, varFactory, 1, 2, cellIDToSubdivision(mesh, 10));
}
// exporter.exportFunction(sigmaSoln, "Poisson-s", "sigma", 0, 5);
// exporter.exportFunction(uhatSoln, "Poisson-uhat", "uhat", 1, 6);
}
{
// 3D tests
CellTopoPtr hex = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Hexahedron<8> >() ));
// let's draw a little box
vector<double> v0 = makeVertex(0,0,0);
vector<double> v1 = makeVertex(1,0,0);
vector<double> v2 = makeVertex(1,1,0);
vector<double> v3 = makeVertex(0,1,0);
vector<double> v4 = makeVertex(0,0,1);
vector<double> v5 = makeVertex(1,0,1);
vector<double> v6 = makeVertex(1,1,1);
vector<double> v7 = makeVertex(0,1,1);
vector< vector<double> > vertices;
vertices.push_back(v0);
vertices.push_back(v1);
vertices.push_back(v2);
vertices.push_back(v3);
vertices.push_back(v4);
vertices.push_back(v5);
vertices.push_back(v6);
vertices.push_back(v7);
vector<unsigned> hexVertexList;
hexVertexList.push_back(0);
hexVertexList.push_back(1);
hexVertexList.push_back(2);
hexVertexList.push_back(3);
hexVertexList.push_back(4);
hexVertexList.push_back(5);
hexVertexList.push_back(6);
hexVertexList.push_back(7);
// vector<unsigned> triVertexList;
// triVertexList.push_back(2);
// triVertexList.push_back(3);
// triVertexList.push_back(4);
vector< vector<unsigned> > elementVertices;
elementVertices.push_back(hexVertexList);
// elementVertices.push_back(triVertexList);
vector< CellTopoPtr > cellTopos;
cellTopos.push_back(hex);
// cellTopos.push_back(tri_3);
MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
FunctionPtr x = Function::xn(1);
FunctionPtr y = Function::yn(1);
FunctionPtr z = Function::zn(1);
FunctionPtr function = x + y + z;
FunctionPtr fbdr = Function::restrictToCellBoundary(function);
FunctionPtr vect = Function::vectorize(x, y, z);
vector<FunctionPtr> functions;
functions.push_back(function);
functions.push_back(vect);
vector<string> functionNames;
functionNames.push_back("function");
functionNames.push_back("vect");
{
XDMFExporter exporter(meshTopology, "function3", false);
exporter.exportFunction(function, "function3");
}
{
XDMFExporter exporter(meshTopology, "boundary3", false);
exporter.exportFunction(fbdr, "boundary3");
}
{
XDMFExporter exporter(meshTopology, "vect3", false);
exporter.exportFunction(vect, "vect3");
}
{
XDMFExporter exporter(meshTopology, "functions3", false);
exporter.exportFunction(functions, functionNames);
}
}
}
bool VectorizedBasisTestSuite::testPoisson()
{
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 sigma_n = varFactory->fluxVar("\\widehat{\\sigma_{n}}");
VarPtr u = varFactory->fieldVar("u");
VarPtr sigma = varFactory->fieldVar("\\sigma", VECTOR_L2);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( -sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = bf->graphNorm();
//////////////////// SPECIFY RHS ///////////////////////
RHSPtr rhs = RHS::rhs();
FunctionPtr f = Function::constant(1.0);
rhs->addTerm( f * v );
//////////////////// CREATE BCs ///////////////////////
BCPtr bc = BC::bc();
SpatialFilterPtr boundary = SpatialFilter::allSpace();
FunctionPtr zero = Function::zero();
bc->addDirichlet(uhat, boundary, zero);
//////////////////// BUILD MESH ///////////////////////
int H1Order = 3, pToAdd = 2;
// define nodes for mesh
FieldContainer<double> meshBoundary(4,2);
meshBoundary(0,0) = 0.0; // x1
meshBoundary(0,1) = 0.0; // y1
meshBoundary(1,0) = 1.0;
meshBoundary(1,1) = 0.0;
meshBoundary(2,0) = 1.0;
meshBoundary(2,1) = 1.0;
meshBoundary(3,0) = 0.0;
meshBoundary(3,1) = 1.0;
int horizontalCells = 1, verticalCells = 1;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshFactory::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
bf, H1Order, H1Order+pToAdd, false);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
#ifdef USE_VTK
VTKExporter exporter(solution, mesh, varFactory);
#endif
for (int refIndex=0; refIndex<=4; refIndex++)
{
solution->solve(false);
#ifdef USE_VTK
// output commented out because it's not properly part of the test.
// stringstream outfile;
// outfile << "test_" << refIndex;
// exporter.exportSolution(outfile.str());
#endif
if (refIndex < 4)
refinementStrategy.refine(false); // don't print to console
}
return success;
}
int main(int argc, char *argv[])
{
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
int spaceDim = 2;
#ifdef HAVE_MPI
choice::MpiArgs args( argc, argv );
#else
choice::Args args(argc, argv );
#endif
int minPolyOrder = args.Input<int>("--minPolyOrder", "L^2 (field) minimum polynomial order",0);
int maxPolyOrder = args.Input<int>("--maxPolyOrder", "L^2 (field) maximum polynomial order",1);
int minLogElements = args.Input<int>("--minLogElements", "base 2 log of the minimum number of elements in one mesh direction", 0);
int maxLogElements = args.Input<int>("--maxLogElements", "base 2 log of the maximum number of elements in one mesh direction", 4);
double Re = args.Input<double>("--Re", "Reynolds number", 40);
// bool outputStiffnessMatrix = args.Input<bool>("--writeFinalStiffnessToDisk", "write the final stiffness matrix to disk.", false);
bool computeMaxConditionNumber = args.Input<bool>("--computeMaxConditionNumber", "compute the maximum Gram matrix condition number for final mesh.", false);
int maxIters = args.Input<int>("--maxIters", "maximum number of Newton-Raphson iterations to take to try to match tolerance", 50);
double minL2Increment = args.Input<double>("--NRtol", "Newton-Raphson tolerance, L^2 norm of increment", 1e-12);
string normChoice = args.Input<string>("--norm", "norm choice: graph, compliantGraph, stokesGraph, or stokesCompliantGraph", "graph");
bool useCondensedSolve = args.Input<bool>("--useCondensedSolve", "use static condensation", true);
double dt = args.Input<double>("--timeStep", "time step (0 for none)", 0);
double zmcRho = args.Input<double>("--zmcRho", "zero-mean constraint rho (stabilization parameter)", -1);
// string replayFile = args.Input<string>("--replayFile", "file with refinement history to replay", "");
// string saveFile = args.Input<string>("--saveReplay", "file to which to save refinement history", "");
args.Process();
int pToAdd = 2; // for optimal test function approximation
bool useLineSearch = false;
bool computeRelativeErrors = true; // we'll say false when one of the exact solution components is 0
bool useEnrichedTraces = true; // enriched traces are the right choice, mathematically speaking
BasisFactory::basisFactory()->setUseEnrichedTraces(useEnrichedTraces);
// parse args:
bool useTriangles = false, useGraphNorm = false, useCompliantNorm = false, useStokesCompliantNorm = false, useStokesGraphNorm = false;
if (normChoice=="graph")
{
useGraphNorm = true;
}
else if (normChoice=="compliantGraph")
{
useCompliantNorm = true;
}
else if (normChoice=="stokesGraph")
{
useStokesGraphNorm = true;
}
else if (normChoice=="stokesCompliantGraph")
{
useStokesCompliantNorm = true;
}
else
{
if (rank==0) cout << "unknown norm choice. Exiting.\n";
exit(-1);
}
bool artificialTimeStepping = (dt > 0);
if (rank == 0)
{
cout << "pToAdd = " << pToAdd << endl;
cout << "useTriangles = " << (useTriangles ? "true" : "false") << "\n";
cout << "norm = " << normChoice << endl;
}
// define Kovasznay domain:
FieldContainer<double> quadPointsKovasznay(4,2);
// domain from Cockburn Kanschat for Stokes:
quadPointsKovasznay(0,0) = -0.5; // x1
quadPointsKovasznay(0,1) = 0.0; // y1
quadPointsKovasznay(1,0) = 1.5;
quadPointsKovasznay(1,1) = 0.0;
quadPointsKovasznay(2,0) = 1.5;
quadPointsKovasznay(2,1) = 2.0;
quadPointsKovasznay(3,0) = -0.5;
quadPointsKovasznay(3,1) = 2.0;
// Domain from Evans Hughes for Navier-Stokes:
// quadPointsKovasznay(0,0) = 0.0; // x1
// quadPointsKovasznay(0,1) = -0.5; // y1
// quadPointsKovasznay(1,0) = 1.0;
// quadPointsKovasznay(1,1) = -0.5;
// quadPointsKovasznay(2,0) = 1.0;
// quadPointsKovasznay(2,1) = 0.5;
// quadPointsKovasznay(3,0) = 0.0;
// quadPointsKovasznay(3,1) = 0.5;
// double Re = 10.0; // Cockburn Kanschat Stokes
// double Re = 40.0; // Evans Hughes Navier-Stokes
// double Re = 1000.0;
string formulationTypeStr = "vgp";
FunctionPtr u1_exact, u2_exact, p_exact;
int numCellsFineMesh = 20; // for computing a zero-mean pressure
int H1OrderFineMesh = 5;
// VGPNavierStokesProblem(double Re, Intrepid::FieldContainer<double> &quadPoints, int horizontalCells,
// int verticalCells, int H1Order, int pToAdd,
// TFunctionPtr<double> u1_0, TFunctionPtr<double> u2_0, TFunctionPtr<double> f1, TFunctionPtr<double> f2,
// bool enrichVelocity = false, bool enhanceFluxes = false)
FunctionPtr zero = Function::zero();
VGPNavierStokesProblem zeroProblem = VGPNavierStokesProblem(Re, quadPointsKovasznay,
numCellsFineMesh, numCellsFineMesh,
H1OrderFineMesh, pToAdd,
zero, zero, zero, useCompliantNorm || useStokesCompliantNorm);
VarFactoryPtr varFactory = VGPStokesFormulation::vgpVarFactory();
VarPtr u1_vgp = varFactory->fieldVar(VGP_U1_S);
VarPtr u2_vgp = varFactory->fieldVar(VGP_U2_S);
VarPtr sigma11_vgp = varFactory->fieldVar(VGP_SIGMA11_S);
VarPtr sigma12_vgp = varFactory->fieldVar(VGP_SIGMA12_S);
VarPtr sigma21_vgp = varFactory->fieldVar(VGP_SIGMA21_S);
VarPtr sigma22_vgp = varFactory->fieldVar(VGP_SIGMA22_S);
VarPtr p_vgp = varFactory->fieldVar(VGP_P_S);
VarPtr v1_vgp = varFactory->testVar(VGP_V1_S, HGRAD);
VarPtr v2_vgp = varFactory->testVar(VGP_V2_S, HGRAD);
// if (rank==0) {
// cout << "bilinear form with zero background flow:\n";
// zeroProblem.bf()->printTrialTestInteractions();
// }
VGPStokesFormulation stokesForm(1/Re);
NavierStokesFormulation::setKovasznay(Re, zeroProblem.mesh(), u1_exact, u2_exact, p_exact);
// if (rank==0) cout << "Stokes bilinearForm: " << stokesForm.bf()->displayString() << endl;
map< string, string > convergenceDataForMATLAB; // key: field file name
for (int polyOrder = minPolyOrder; polyOrder <= maxPolyOrder; polyOrder++)
{
int H1Order = polyOrder + 1;
int numCells1D = pow(2.0,minLogElements);
if (rank==0)
{
cout << "L^2 order: " << polyOrder << endl;
cout << "Re = " << Re << endl;
}
int kovasznayCubatureEnrichment = 20; // 20 is better than 10 for accurately measuring error on the coarser meshes.
vector< VGPNavierStokesProblem > problems;
do
{
VGPNavierStokesProblem problem = VGPNavierStokesProblem(Re,quadPointsKovasznay,
numCells1D,numCells1D,
H1Order, pToAdd,
u1_exact, u2_exact, p_exact, useCompliantNorm || useStokesCompliantNorm);
problem.backgroundFlow()->setCubatureEnrichmentDegree(kovasznayCubatureEnrichment);
problem.solutionIncrement()->setCubatureEnrichmentDegree(kovasznayCubatureEnrichment);
problem.backgroundFlow()->setZeroMeanConstraintRho(zmcRho);
problem.solutionIncrement()->setZeroMeanConstraintRho(zmcRho);
FunctionPtr dt_inv;
if (artificialTimeStepping)
{
// // LHS gets u_inc / dt:
BFPtr bf = problem.bf();
dt_inv = ParameterFunction::parameterFunction(1.0 / dt); //Teuchos::rcp( new ConstantScalarFunction(1.0 / dt, "\\frac{1}{dt}") );
bf->addTerm(-dt_inv * u1_vgp, v1_vgp);
bf->addTerm(-dt_inv * u2_vgp, v2_vgp);
problem.setIP( bf->graphNorm() ); // graph norm has changed...
}
else
{
dt_inv = Function::zero();
}
problems.push_back(problem);
if ( useCompliantNorm )
{
problem.setIP(problem.vgpNavierStokesFormulation()->scaleCompliantGraphNorm(dt_inv));
}
else if (useStokesCompliantNorm)
{
VGPStokesFormulation stokesForm(1.0); // pretend Re = 1 in the graph norm
problem.setIP(stokesForm.scaleCompliantGraphNorm());
}
else if (useStokesGraphNorm)
{
VGPStokesFormulation stokesForm(1.0); // pretend Re = 1 in the graph norm
problem.setIP(stokesForm.graphNorm());
}
else if (! useGraphNorm )
{
// then use the naive:
problem.setIP(problem.bf()->naiveNorm(spaceDim));
}
if (rank==0)
{
cout << numCells1D << " x " << numCells1D << ": " << problem.mesh()->numGlobalDofs() << " dofs " << endl;
}
numCells1D *= 2;
}
while (pow(2.0,maxLogElements) >= numCells1D);
// note that rhs and bilinearForm aren't really going to be right here, since they
// involve a background flow which varies over the various problems...
HConvergenceStudy study(problems[0].exactSolution(),
problems[0].mesh()->bilinearForm(),
problems[0].exactSolution()->rhs(),
problems[0].backgroundFlow()->bc(),
problems[0].bf()->graphNorm(),
minLogElements, maxLogElements,
H1Order, pToAdd, false, useTriangles, false);
study.setReportRelativeErrors(computeRelativeErrors);
study.setCubatureDegreeForExact(kovasznayCubatureEnrichment);
vector< SolutionPtr > solutions;
numCells1D = pow(2.0,minLogElements);
for (vector< VGPNavierStokesProblem >::iterator problem = problems.begin();
problem != problems.end(); problem++)
{
SolutionPtr solnIncrement = problem->solutionIncrement();
FunctionPtr u1_incr = Function::solution(u1_vgp, solnIncrement);
FunctionPtr u2_incr = Function::solution(u2_vgp, solnIncrement);
FunctionPtr sigma11_incr = Function::solution(sigma11_vgp, solnIncrement);
FunctionPtr sigma12_incr = Function::solution(sigma12_vgp, solnIncrement);
FunctionPtr sigma21_incr = Function::solution(sigma21_vgp, solnIncrement);
FunctionPtr sigma22_incr = Function::solution(sigma22_vgp, solnIncrement);
FunctionPtr p_incr = Function::solution(p_vgp, solnIncrement);
// LinearTermPtr rhsLT = problem->backgroundFlow()->rhs()->linearTerm();
// if (rank==0) cout << "bilinearForm: " << problems[0].mesh()->bilinearForm()->displayString() << endl;
// if (rank==0) cout << "RHS: " << rhsLT->displayString() << endl;
FunctionPtr l2_incr = u1_incr * u1_incr + u2_incr * u2_incr + p_incr * p_incr
+ sigma11_incr * sigma11_incr + sigma12_incr * sigma12_incr
+ sigma21_incr * sigma21_incr + sigma22_incr * sigma22_incr;
double weight = 1.0;
do
{
weight = problem->iterate(useLineSearch, useCondensedSolve);
LinearTermPtr rhsLT = problem->backgroundFlow()->rhs()->linearTerm();
RieszRep rieszRep(problem->backgroundFlow()->mesh(), problem->backgroundFlow()->ip(), rhsLT);
rieszRep.computeRieszRep();
double costFunction = rieszRep.getNorm();
double incr_norm = sqrt(l2_incr->integrate(problem->mesh()));
if (rank==0)
{
cout << setprecision(6) << scientific;
cout << "\x1B[2K"; // Erase the entire current line.
cout << "\x1B[0E"; // Move to the beginning of the current line.
cout << "Iteration: " << problem->iterationCount() << "; L^2(incr) = " << incr_norm;
flush(cout);
// cout << setprecision(6) << scientific;
// cout << "Took " << weight << "-weighted step for " << numCells1D;
// cout << " x " << numCells1D << " mesh: " << problem->iterationCount();
// cout << setprecision(6) << fixed;
// cout << " iterations; cost function " << costFunction << endl;
}
}
while ((sqrt(l2_incr->integrate(problem->mesh())) > minL2Increment ) && (problem->iterationCount() < maxIters) && (weight != 0));
if (rank==0) cout << endl;
solutions.push_back( problem->backgroundFlow() );
// set the IP to the naive norm for clearer comparison with the best approximation energy error
// problem->backgroundFlow()->setIP(problem->bf()->naiveNorm());
// double energyError = problem->backgroundFlow()->energyErrorTotal();
// if (rank==0) {
// cout << setprecision(6) << fixed;
// cout << numCells1D << " x " << numCells1D << ": " << problem->iterationCount();
// cout << " iterations; actual energy error " << energyError << endl;
// }
numCells1D *= 2;
}
study.setSolutions(solutions);
for (int i=0; i<=maxLogElements-minLogElements; i++)
{
SolutionPtr bestApproximation = study.bestApproximations()[i];
VGPNavierStokesFormulation nsFormBest = VGPNavierStokesFormulation(Re, bestApproximation);
SpatialFilterPtr entireBoundary = Teuchos::rcp( new SpatialFilterUnfiltered ); // SpatialFilterUnfiltered returns true everywhere
Teuchos::RCP<ExactSolution<double>> exact = nsFormBest.exactSolution(u1_exact, u2_exact, p_exact, entireBoundary);
// bestApproximation->setIP( nsFormBest.bf()->naiveNorm() );
// bestApproximation->setRHS( exact->rhs() );
// use backgroundFlow's IP so that they're comparable
IPPtr ip = problems[i].backgroundFlow()->ip();
LinearTermPtr rhsLT = exact->rhs()->linearTerm();
RieszRep rieszRep(bestApproximation->mesh(), ip, rhsLT);
rieszRep.computeRieszRep();
double bestCostFunction = rieszRep.getNorm();
if (rank==0)
cout << "best energy error (measured according to the actual solution's test space IP): " << bestCostFunction << endl;
}
map< int, double > energyNormWeights;
if (useCompliantNorm)
{
energyNormWeights[u1_vgp->ID()] = 1.0; // should be 1/h
energyNormWeights[u2_vgp->ID()] = 1.0; // should be 1/h
energyNormWeights[sigma11_vgp->ID()] = Re; // 1/mu
energyNormWeights[sigma12_vgp->ID()] = Re; // 1/mu
energyNormWeights[sigma21_vgp->ID()] = Re; // 1/mu
energyNormWeights[sigma22_vgp->ID()] = Re; // 1/mu
if (Re < 1) // assuming we're using the experimental small Re thing
{
energyNormWeights[p_vgp->ID()] = Re;
}
else
{
energyNormWeights[p_vgp->ID()] = 1.0;
}
}
else
{
energyNormWeights[u1_vgp->ID()] = 1.0;
energyNormWeights[u2_vgp->ID()] = 1.0;
energyNormWeights[sigma11_vgp->ID()] = 1.0;
energyNormWeights[sigma12_vgp->ID()] = 1.0;
energyNormWeights[sigma21_vgp->ID()] = 1.0;
energyNormWeights[sigma22_vgp->ID()] = 1.0;
energyNormWeights[p_vgp->ID()] = 1.0;
}
vector<double> bestEnergy = study.weightedL2Error(energyNormWeights,true);
vector<double> solnEnergy = study.weightedL2Error(energyNormWeights,false);
map<int, double> velocityWeights;
velocityWeights[u1_vgp->ID()] = 1.0;
velocityWeights[u2_vgp->ID()] = 1.0;
vector<double> bestVelocityError = study.weightedL2Error(velocityWeights,true);
vector<double> solnVelocityError = study.weightedL2Error(velocityWeights,false);
map<int, double> pressureWeight;
pressureWeight[p_vgp->ID()] = 1.0;
vector<double> bestPressureError = study.weightedL2Error(pressureWeight,true);
vector<double> solnPressureError = study.weightedL2Error(pressureWeight,false);
if (rank==0)
{
cout << setw(25);
cout << "Solution Energy Error:" << setw(25) << "Best Energy Error:" << endl;
cout << scientific << setprecision(1);
for (int i=0; i<bestEnergy.size(); i++)
{
cout << setw(25) << solnEnergy[i] << setw(25) << bestEnergy[i] << endl;
}
cout << setw(25);
cout << "Solution Velocity Error:" << setw(25) << "Best Velocity Error:" << endl;
cout << scientific << setprecision(1);
for (int i=0; i<bestEnergy.size(); i++)
{
cout << setw(25) << solnVelocityError[i] << setw(25) << bestVelocityError[i] << endl;
}
cout << setw(25);
cout << "Solution Pressure Error:" << setw(25) << "Best Pressure Error:" << endl;
cout << scientific << setprecision(1);
for (int i=0; i<bestEnergy.size(); i++)
{
cout << setw(25) << solnPressureError[i] << setw(25) << bestPressureError[i] << endl;
}
vector< string > tableHeaders;
vector< vector<double> > dataTable;
vector< double > meshWidths;
for (int i=minLogElements; i<=maxLogElements; i++)
{
double width = pow(2.0,i);
meshWidths.push_back(width);
}
tableHeaders.push_back("mesh_width");
dataTable.push_back(meshWidths);
tableHeaders.push_back("soln_energy_error");
dataTable.push_back(solnEnergy);
tableHeaders.push_back("best_energy_error");
dataTable.push_back(bestEnergy);
tableHeaders.push_back("soln_velocity_error");
dataTable.push_back(solnVelocityError);
tableHeaders.push_back("best_velocity_error");
dataTable.push_back(bestVelocityError);
tableHeaders.push_back("soln_pressure_error");
dataTable.push_back(solnPressureError);
tableHeaders.push_back("best_pressure_error");
dataTable.push_back(bestPressureError);
ostringstream fileNameStream;
fileNameStream << "nsStudy_Re" << Re << "k" << polyOrder << "_results.dat";
DataIO::outputTableToFile(tableHeaders,dataTable,fileNameStream.str());
}
if (rank == 0)
{
cout << study.TeXErrorRateTable();
vector<int> primaryVariables;
stokesForm.primaryTrialIDs(primaryVariables);
vector<int> fieldIDs,traceIDs;
vector<string> fieldFileNames;
stokesForm.trialIDs(fieldIDs,traceIDs,fieldFileNames);
cout << "******** Best Approximation comparison: ********\n";
cout << study.TeXBestApproximationComparisonTable(primaryVariables);
ostringstream filePathPrefix;
filePathPrefix << "navierStokes/" << formulationTypeStr << "_p" << polyOrder << "_velpressure";
study.TeXBestApproximationComparisonTable(primaryVariables,filePathPrefix.str());
filePathPrefix.str("");
filePathPrefix << "navierStokes/" << formulationTypeStr << "_p" << polyOrder << "_all";
study.TeXBestApproximationComparisonTable(fieldIDs);
for (int i=0; i<fieldIDs.size(); i++)
{
int fieldID = fieldIDs[i];
int traceID = traceIDs[i];
string fieldName = fieldFileNames[i];
ostringstream filePathPrefix;
filePathPrefix << "navierStokes/" << fieldName << "_p" << polyOrder;
bool writeMATLABplotData = false;
study.writeToFiles(filePathPrefix.str(),fieldID,traceID, writeMATLABplotData);
}
for (int i=0; i<primaryVariables.size(); i++)
{
string convData = study.convergenceDataMATLAB(primaryVariables[i], minPolyOrder);
cout << convData;
convergenceDataForMATLAB[fieldFileNames[i]] += convData;
}
filePathPrefix.str("");
filePathPrefix << "navierStokes/" << formulationTypeStr << "_p" << polyOrder << "_numDofs";
cout << study.TeXNumGlobalDofsTable();
}
if (computeMaxConditionNumber)
{
for (int i=minLogElements; i<=maxLogElements; i++)
{
SolutionPtr soln = study.getSolution(i);
ostringstream fileNameStream;
fileNameStream << "nsStudy_maxConditionIPMatrix_" << i << ".dat";
IPPtr ip = Teuchos::rcp( dynamic_cast< IP* >(soln->ip().get()), false );
bool jacobiScalingTrue = true;
double maxConditionNumber = MeshUtilities::computeMaxLocalConditionNumber(ip, soln->mesh(), jacobiScalingTrue, fileNameStream.str());
if (rank==0)
{
cout << "max Gram matrix condition number estimate for logElements " << i << ": " << maxConditionNumber << endl;
cout << "putative worst-conditioned Gram matrix written to: " << fileNameStream.str() << "." << endl;
}
}
}
}
if (rank==0)
{
ostringstream filePathPrefix;
filePathPrefix << "navierStokes/" << formulationTypeStr << "_";
for (map<string,string>::iterator convIt = convergenceDataForMATLAB.begin(); convIt != convergenceDataForMATLAB.end(); convIt++)
{
string fileName = convIt->first + ".m";
string data = convIt->second;
fileName = filePathPrefix.str() + fileName;
ofstream fout(fileName.c_str());
fout << data;
fout.close();
}
}
}
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 commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
double epsilon = args.Input<double>("--epsilon", "diffusion parameter");
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation");
bool graphNorm = args.Input<bool>("--graphNorm", "use the graph norm rather than robust test norm");
// Optional arguments (have defaults)
bool highLiftAirfoil = args.Input("--highLift", "use high lift airfoil rather than NACA0012", false);
args.Process();
//////////////////// 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 beta_n_u_minus_sigma_n = varFactory.fluxVar("fhat");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma = varFactory.fieldVar("sigma", VECTOR_L2);
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.25);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma / epsilon, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( beta * u, - v->grad() );
bf->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
if (graphNorm)
{
ip = bf->graphNorm();
}
else
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
if (!enforceLocalConservation)
ip->addTerm( ip_scaling * v );
ip->addTerm( sqrt(epsilon) * v->grad() );
// Weight these two terms for inflow
ip->addTerm( beta * v->grad() );
ip->addTerm( tau->div() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (enforceLocalConservation)
ip->addZeroMeanTerm( v );
}
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
SpatialFilterPtr lBoundary = Teuchos::rcp( new LeftBoundary );
SpatialFilterPtr tBoundary = Teuchos::rcp( new TopBoundary );
SpatialFilterPtr bBoundary = Teuchos::rcp( new BottomBoundary );
SpatialFilterPtr rBoundary = Teuchos::rcp( new RightBoundary );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
SpatialFilterPtr airfoilInflowBoundary = Teuchos::rcp( new AirfoilInflowBoundary(beta) );
SpatialFilterPtr airfoilOutflowBoundary = Teuchos::rcp( new AirfoilOutflowBoundary(beta) );
FunctionPtr u0 = Teuchos::rcp( new ZeroBC );
FunctionPtr u1 = Teuchos::rcp( new OneBC );
bc->addDirichlet(beta_n_u_minus_sigma_n, lBoundary, u0);
bc->addDirichlet(beta_n_u_minus_sigma_n, bBoundary, u0);
// bc->addDirichlet(uhat, airfoilInflowBoundary, u1);
// bc->addDirichlet(uhat, tBoundary, u0);
bc->addDirichlet(beta_n_u_minus_sigma_n, airfoilInflowBoundary, beta*n*u1);
bc->addDirichlet(uhat, airfoilOutflowBoundary, u1);
// pc->addConstraint(beta*uhat->times_normal() - beta_n_u_minus_sigma_n == u0, rBoundary);
// pc->addConstraint(beta*uhat->times_normal() - beta_n_u_minus_sigma_n == u0, tBoundary);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = 3, pToAdd = 2;
Teuchos::RCP<Mesh> mesh;
if (highLiftAirfoil)
mesh = Mesh::readTriangle(Camellia_MeshDir+"HighLift/HighLift.1", bf, H1Order, pToAdd);
else
mesh = Mesh::readTriangle(Camellia_MeshDir+"NACA0012/NACA0012.1", 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(beta_n_u_minus_sigma_n == zero);
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(solution, mesh, varFactory);
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
solution->solve(false);
if (commRank == 0)
{
stringstream outfile;
if (highLiftAirfoil)
outfile << "highlift_" << refIndex;
else
outfile << "naca0012_" << refIndex;
exporter.exportSolution(outfile.str());
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_minus_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(commRank==0); // print to console on commRank 0
// Try pseudo-hp adaptive
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])) < epsilon)
{
int pOrder = mesh->cellPolyOrder(cellsToRefine[i]);
if (pOrder < 8)
cells_p.push_back(cellsToRefine[i]);
else
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 ENABLE_INTEL_FLOATING_POINT_EXCEPTIONS
cout << "NOTE: enabling floating point exceptions for divide by zero.\n";
_MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() & ~_MM_MASK_INVALID);
#endif
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
int rank = Teuchos::GlobalMPISession::getRank();
Teuchos::CommandLineProcessor cmdp(false,true); // false: don't throw exceptions; true: do return errors for unrecognized options
bool useCondensedSolve = false; // condensed solve not yet compatible with minimum rule meshes
int numGridPoints = 32; // in x,y -- idea is to keep the overall order of approximation constant
int k = 4; // poly order for u
double theta = 0.5;
int numTimeSteps = 2000;
int numCells = -1; // in x, y (-1 so we can set a default if unset from the command line.)
int numFrames = 50;
int delta_k = 2; // test space enrichment: should be 2 for 2D
bool useMumpsIfAvailable = true;
bool convertSolutionsToVTK = false; // when true assumes we've already run with precisely the same options, except without VTK support (so we have a bunch of .soln files)
bool usePeriodicBCs = false;
bool useConstantConvection = false;
cmdp.setOption("polyOrder",&k,"polynomial order for field variable u");
cmdp.setOption("delta_k", &delta_k, "test space polynomial order enrichment");
cmdp.setOption("numCells",&numCells,"number of cells in x and y directions");
cmdp.setOption("theta",&theta,"theta weight for time-stepping");
cmdp.setOption("numTimeSteps",&numTimeSteps,"number of time steps");
cmdp.setOption("numFrames",&numFrames,"number of frames for export");
cmdp.setOption("usePeriodicBCs", "useDirichletBCs", &usePeriodicBCs);
cmdp.setOption("useConstantConvection", "useVariableConvection", &useConstantConvection);
cmdp.setOption("useCondensedSolve", "useUncondensedSolve", &useCondensedSolve, "use static condensation to reduce the size of the global solve");
cmdp.setOption("useMumps", "useKLU", &useMumpsIfAvailable, "use MUMPS (if available)");
cmdp.setOption("convertPreComputedSolutionsToVTK", "computeSolutions", &convertSolutionsToVTK);
if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL)
{
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return -1;
}
bool saveSolutionFiles = true;
if (numCells==-1) numCells = numGridPoints / k;
if (rank==0)
{
cout << "solving on " << numCells << " x " << numCells << " mesh " << "of order " << k << ".\n";
}
set<int> timeStepsToExport;
timeStepsToExport.insert(numTimeSteps);
int timeStepsPerFrame = numTimeSteps / (numFrames - 1);
if (timeStepsPerFrame==0) timeStepsPerFrame = 1;
for (int n=0; n<numTimeSteps; n += timeStepsPerFrame)
{
timeStepsToExport.insert(n);
}
int H1Order = k + 1;
const static double PI = 3.141592653589793238462;
double dt = 2 * PI / numTimeSteps;
VarFactory varFactory;
// traces:
VarPtr qHat = varFactory.fluxVar("\\widehat{q}");
// fields:
VarPtr u = varFactory.fieldVar("u", L2);
// test functions:
VarPtr v = varFactory.testVar("v", HGRAD);
FunctionPtr x = Function::xn(1);
FunctionPtr y = Function::yn(1);
FunctionPtr c;
if (useConstantConvection)
{
c = Function::vectorize(Function::constant(0.5), Function::constant(0.5));
}
else
{
c = Function::vectorize(y-0.5, 0.5-x);
}
// FunctionPtr c = Function::vectorize(y, x);
FunctionPtr n = Function::normal();
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
bf->addTerm(u / dt, v);
bf->addTerm(- theta * u, c * v->grad());
// bf->addTerm(theta * u_hat, (c * n) * v);
bf->addTerm(qHat, v);
double width = 2.0, height = 2.0;
int horizontalCells = numCells, verticalCells = numCells;
double x0 = -0.5;
double y0 = -0.5;
if (usePeriodicBCs)
{
x0 = 0.0;
y0 = 0.0;
width = 1.0;
height = 1.0;
}
BCPtr bc = BC::bc();
SpatialFilterPtr inflowFilter = Teuchos::rcp( new InflowFilterForClockwisePlanarRotation (x0,x0+width,y0,y0+height,0.5,0.5));
vector< PeriodicBCPtr > periodicBCs;
if (! usePeriodicBCs)
{
// bc->addDirichlet(u_hat, SpatialFilter::allSpace(), Function::zero());
bc->addDirichlet(qHat, inflowFilter, Function::zero()); // zero BCs enforced at the inflow boundary.
}
else
{
periodicBCs.push_back(PeriodicBC::xIdentification(x0, x0+width));
periodicBCs.push_back(PeriodicBC::yIdentification(y0, y0+height));
}
MeshPtr mesh = MeshFactory::quadMeshMinRule(bf, H1Order, delta_k, width, height,
horizontalCells, verticalCells, false, x0, y0, periodicBCs);
FunctionPtr u0 = Teuchos::rcp( new Cone_U0(0.0, 0.25, 0.1, 1.0, usePeriodicBCs) );
RHSPtr initialRHS = RHS::rhs();
initialRHS->addTerm(u0 / dt * v);
initialRHS->addTerm((1-theta) * u0 * c * v->grad());
IPPtr ip;
// ip = Teuchos::rcp( new IP );
// ip->addTerm(v);
// ip->addTerm(c * v->grad());
ip = bf->graphNorm();
// create two Solution objects; we'll switch between these for time steps
SolutionPtr soln0 = Solution::solution(mesh, bc, initialRHS, ip);
soln0->setCubatureEnrichmentDegree(5);
FunctionPtr u_soln0 = Function::solution(u, soln0);
FunctionPtr qHat_soln0 = Function::solution(qHat, soln0);
RHSPtr rhs1 = RHS::rhs();
rhs1->addTerm(u_soln0 / dt * v);
rhs1->addTerm((1-theta) * u_soln0 * c * v->grad());
SolutionPtr soln1 = Solution::solution(mesh, bc, rhs1, ip);
soln1->setCubatureEnrichmentDegree(5);
FunctionPtr u_soln1 = Function::solution(u, soln1);
FunctionPtr qHat_soln1 = Function::solution(qHat, soln1);
RHSPtr rhs2 = RHS::rhs(); // after the first solve on soln0, we'll swap out initialRHS for rhs2
rhs2->addTerm(u_soln1 / dt * v);
rhs2->addTerm((1-theta) * u_soln1 * c * v->grad());
Teuchos::RCP<Solver> solver = Teuchos::rcp( new KluSolver );
#ifdef HAVE_AMESOS_MUMPS
if (useMumpsIfAvailable) solver = Teuchos::rcp( new MumpsSolver );
#endif
// double energyErrorSum = 0;
ostringstream filePrefix;
filePrefix << "convectingCone_k" << k << "_t";
int frameNumber = 0;
#ifdef USE_HDF5
ostringstream dir_name;
dir_name << "convectingCone_k" << k;
HDF5Exporter exporter(mesh,dir_name.str());
#endif
#ifdef USE_VTK
VTKExporter soln0Exporter(soln0,mesh,varFactory);
VTKExporter soln1Exporter(soln1,mesh,varFactory);
#endif
if (convertSolutionsToVTK)
{
#ifdef USE_VTK
if (rank==0)
{
cout << "Converting .soln files to VTK.\n";
for (int frameNumber=0; frameNumber<=numFrames; frameNumber++)
{
ostringstream filename;
filename << filePrefix.str() << frameNumber << ".soln";
soln0->readFromFile(filename.str());
filename.str("");
filename << filePrefix.str() << frameNumber;
soln0Exporter.exportFields(filename.str());
}
}
#else
if (rank==0) cout << "Driver was built without USE_VTK defined. This must be defined to convert solution files to VTK files.\n";
#endif
exit(0);
}
if (timeStepsToExport.find(0) != timeStepsToExport.end())
{
map<int,FunctionPtr> solnMap;
solnMap[u->ID()] = u0; // project field variables
if (rank==0) cout << "About to project initial solution onto mesh.\n";
soln0->projectOntoMesh(solnMap);
if (rank==0) cout << "...projected initial solution onto mesh.\n";
ostringstream filename;
filename << filePrefix.str() << frameNumber++;
if (rank==0) cout << "About to export initial solution.\n";
#ifdef USE_VTK
if (rank==0) soln0Exporter.exportFields(filename.str());
#endif
#ifdef USE_HDF5
exporter.exportSolution(soln0, varFactory,0);
#endif
if (saveSolutionFiles)
{
if (rank==0)
{
filename << ".soln";
soln0->writeToFile(filename.str());
cout << endl << "wrote " << filename.str() << endl;
}
}
if (rank==0) cout << "...exported initial solution.\n";
}
if (rank==0) cout << "About to solve initial time step.\n";
// first time step:
soln0->setReportTimingResults(true); // added to gain insight into why MPI blocks in some cases on the server...
if (useCondensedSolve) soln0->condensedSolve(solver);
else soln0->solve(solver);
soln0->setReportTimingResults(false);
// energyErrorSum += soln0->energyErrorTotal();
soln0->setRHS(rhs2);
if (rank==0) cout << "Solved initial time step.\n";
if (timeStepsToExport.find(1) != timeStepsToExport.end())
{
ostringstream filename;
filename << filePrefix.str() << frameNumber++;
#ifdef USE_VTK
if (rank==0) soln0Exporter.exportFields(filename.str());
#endif
#ifdef USE_HDF5
exporter.exportSolution(soln0, varFactory);
#endif
if (saveSolutionFiles)
{
if (rank==0)
{
filename << ".soln";
soln0->writeToFile(filename.str());
cout << endl << "wrote " << filename.str() << endl;
}
}
}
bool reportTimings = false;
for (int n=1; n<numTimeSteps; n++)
{
bool odd = (n%2)==1;
SolutionPtr soln_n = odd ? soln1 : soln0;
if (useCondensedSolve) soln_n->solve(solver);
else soln_n->solve(solver);
if (reportTimings)
{
if (rank==0) cout << "time step " << n << ", timing report:\n";
soln_n->reportTimings();
}
if (rank==0)
{
cout << "\x1B[2K"; // Erase the entire current line.
cout << "\x1B[0E"; // Move to the beginning of the current line.
cout << "Solved time step: " << n;
flush(cout);
}
if (timeStepsToExport.find(n+1)!=timeStepsToExport.end())
{
ostringstream filename;
filename << filePrefix.str() << frameNumber++;
#ifdef USE_VTK
if (rank==0)
{
if (odd)
{
soln1Exporter.exportFields(filename.str());
}
else
{
soln0Exporter.exportFields(filename.str());
}
}
#endif
#ifdef USE_HDF5
double t = n * dt;
if (odd)
{
exporter.exportSolution(soln1, varFactory, t);
}
else
{
exporter.exportSolution(soln0, varFactory, t);
}
#endif
if (saveSolutionFiles)
{
if (rank==0)
{
filename << ".soln";
if (odd)
{
soln1->writeToFile(filename.str());
}
else
{
soln0->writeToFile(filename.str());
}
cout << endl << "wrote " << filename.str() << endl;
}
}
}
// energyErrorSum += soln_n->energyErrorTotal();
}
// if (rank==0) cout << "energy error, sum over all time steps: " << energyErrorSum << endl;
return 0;
}
int main(int argc, char *argv[]) {
// TODO: figure out the right thing to do here...
// may want to modify argc and argv before we make the following call:
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#ifdef HAVE_MPI
choice::MpiArgs args( argc, argv );
#else
choice::Args args(argc, argv );
#endif
int polyOrder, pToAdd;
try {
// read args:
polyOrder = args.Input<int>("--polyOrder", "L^2 (field) polynomial order");
pToAdd = args.Input<int>("--delta_p", "delta p for test enrichment", 2);
args.Process();
} catch ( choice::ArgException& e )
{
exit(0);
}
int H1Order = polyOrder + 1;
bool useCompliantGraphNorm = false; // weights to improve conditioning of the local problems
bool useExtendedPrecisionForOptimalTestInversion = false;
/////////////////////////// "VGP_CONFORMING" VERSION ///////////////////////
// fluxes and traces:
VarPtr u1hat, u2hat, t1n, t2n;
// fields for SGP:
VarPtr phi, p, sigma11, sigma12, sigma21, sigma22;
// fields specific to VGP:
VarPtr u1, u2;
BFPtr stokesBF;
IPPtr qoptIP;
double mu = 1;
FunctionPtr h = Teuchos::rcp( new hFunction() );
VarPtr tau1,tau2,v1,v2,q;
VarFactory varFactory;
tau1 = varFactory.testVar("\\tau_1", HDIV);
tau2 = varFactory.testVar("\\tau_2", HDIV);
v1 = varFactory.testVar("v_1", HGRAD);
v2 = varFactory.testVar("v_2", HGRAD);
q = varFactory.testVar("q", HGRAD);
u1hat = varFactory.traceVar("\\widehat{u}_1");
u2hat = varFactory.traceVar("\\widehat{u}_2");
t1n = varFactory.fluxVar("\\widehat{t_{1n}}");
t2n = varFactory.fluxVar("\\widehat{t_{2n}}");
if (!useCompliantGraphNorm) {
u1 = varFactory.fieldVar("u_1");
u2 = varFactory.fieldVar("u_2");
} else {
u1 = varFactory.fieldVar("u_1", HGRAD);
u2 = varFactory.fieldVar("u_2", HGRAD);
}
sigma11 = varFactory.fieldVar("\\sigma_11");
sigma12 = varFactory.fieldVar("\\sigma_12");
sigma21 = varFactory.fieldVar("\\sigma_21");
sigma22 = varFactory.fieldVar("\\sigma_22");
p = varFactory.fieldVar("p");
stokesBF = Teuchos::rcp( new BF(varFactory) );
// tau1 terms:
stokesBF->addTerm(u1,tau1->div());
stokesBF->addTerm(sigma11,tau1->x()); // (sigma1, tau1)
stokesBF->addTerm(sigma12,tau1->y());
stokesBF->addTerm(-u1hat, tau1->dot_normal());
// tau2 terms:
stokesBF->addTerm(u2, tau2->div());
stokesBF->addTerm(sigma21,tau2->x()); // (sigma2, tau2)
stokesBF->addTerm(sigma22,tau2->y());
stokesBF->addTerm(-u2hat, tau2->dot_normal());
// v1:
stokesBF->addTerm(mu * sigma11,v1->dx()); // (mu sigma1, grad v1)
stokesBF->addTerm(mu * sigma12,v1->dy());
stokesBF->addTerm( - p, v1->dx() );
stokesBF->addTerm( -t1n, v1);
// v2:
stokesBF->addTerm(mu * sigma21,v2->dx()); // (mu sigma2, grad v2)
stokesBF->addTerm(mu * sigma22,v2->dy());
stokesBF->addTerm( -p, v2->dy());
stokesBF->addTerm( -t2n, v2);
// q:
stokesBF->addTerm(-u1,q->dx()); // (-u, grad q)
stokesBF->addTerm(-u2,q->dy());
stokesBF->addTerm(u1hat->times_normal_x() + u2hat->times_normal_y(), q);
if (rank==0)
stokesBF->printTrialTestInteractions();
stokesBF->setUseExtendedPrecisionSolveForOptimalTestFunctions(useExtendedPrecisionForOptimalTestInversion);
mesh = MeshFactory::quadMesh(stokesBF, H1Order, pToAdd);
//////////////////// CREATE BCs ///////////////////////
BCPtr bc = BC::bc();
//////////////////// CREATE RHS ///////////////////////
RHSPtr rhs = RHS::rhs(); // zero for now...
IPPtr ip;
qoptIP = Teuchos::rcp(new IP());
if (useCompliantGraphNorm) {
qoptIP->addTerm( mu * v1->dx() + tau1->x() ); // sigma11
qoptIP->addTerm( mu * v1->dy() + tau1->y() ); // sigma12
qoptIP->addTerm( mu * v2->dx() + tau2->x() ); // sigma21
qoptIP->addTerm( mu * v2->dy() + tau2->y() ); // sigma22
qoptIP->addTerm( mu * v1->dx() + mu * v2->dy() ); // pressure
qoptIP->addTerm( h * tau1->div() - h * q->dx() ); // u1
qoptIP->addTerm( h * tau2->div() - h * q->dy()); // u2
qoptIP->addTerm( (mu / h) * v1 );
qoptIP->addTerm( (mu / h) * v2 );
qoptIP->addTerm( q );
qoptIP->addTerm( tau1 );
qoptIP->addTerm( tau2 );
} else { // standard graph norm, then
qoptIP = stokesBF->graphNorm();
}
ip = qoptIP;
if (rank==0)
ip->printInteractions();
// aim is just to answer one simple question:
// have I figured out a trial-space preimage for optimal test function (q=1, tau=0, v=0)?
SolutionPtr soln = Teuchos::rcp(new Solution(mesh));
FunctionPtr x = Function::xn();
FunctionPtr y = Function::yn();
// u1 = u1_hat = x / 2
FunctionPtr u1_exact = x / 2;
// u2 = u2_hat = y / 2
FunctionPtr u2_exact = y / 2;
// sigma = 0.5 * I
FunctionPtr sigma11_exact = Function::constant(0.5);
FunctionPtr sigma22_exact = Function::constant(0.5);
// tn_hat = 0.5 * n
FunctionPtr n = Function::normal();
FunctionPtr t1n_exact = n->x() / 2;
FunctionPtr t2n_exact = n->y() / 2;
map<int, FunctionPtr > exact_soln;
exact_soln[u1->ID()] = u1_exact;
exact_soln[u1hat->ID()] = u1_exact;
exact_soln[u2->ID()] = u2_exact;
exact_soln[u2hat->ID()] = u2_exact;
exact_soln[sigma11->ID()] = sigma11_exact;
exact_soln[sigma22->ID()] = sigma22_exact;
exact_soln[t1n->ID()] = t1n_exact;
exact_soln[t2n->ID()] = t2n_exact;
exact_soln[p->ID()] = Function::zero();
exact_soln[sigma12->ID()] = Function::zero();
exact_soln[sigma21->ID()] = Function::zero();
soln->projectOntoMesh(exact_soln);
LinearTermPtr soln_functional = stokesBF->testFunctional(soln);
RieszRepPtr rieszRep = Teuchos::rcp( new RieszRep(mesh, ip, soln_functional) );
rieszRep->computeRieszRep();
// get test functions:
FunctionPtr q_fxn = Teuchos::rcp( new RepFunction(q, rieszRep) );
FunctionPtr v1_fxn = Teuchos::rcp( new RepFunction(v1, rieszRep) );
FunctionPtr v2_fxn = Teuchos::rcp( new RepFunction(v2, rieszRep) );
FunctionPtr tau1_fxn = Teuchos::rcp( new RepFunction(tau1, rieszRep) );
FunctionPtr tau2_fxn = Teuchos::rcp( new RepFunction(tau2, rieszRep) );
cout << "L2 norm of (q-1) : " << (q_fxn - 1)->l2norm(mesh) << endl;
cout << "L2 norm of (v1) : " << (v1_fxn)->l2norm(mesh) << endl;
cout << "L2 norm of (v2) : " << (v2_fxn)->l2norm(mesh) << endl;
cout << "L2 norm of (tau1) : " << (tau1_fxn)->l2norm(mesh) << endl;
cout << "L2 norm of (tau2) : " << (tau2_fxn)->l2norm(mesh) << endl;
VTKExporter exporter(soln, mesh, varFactory);
exporter.exportSolution("conservationPreimage", H1Order*2);
cout << "Checking that the soln_functional is what I expect:\n";
FunctionPtr xyVector = Function::vectorize(x, y);
cout << "With v1 = x, integral: " << integralOverMesh(soln_functional, v1, x) << endl;
cout << "With v2 = y, integral: " << integralOverMesh(soln_functional, v2, y) << endl;
cout << "With tau1=(x,y), integral: " << integralOverMesh(soln_functional, tau1, xyVector) << endl;
cout << "With tau2=(x,y), integral: " << integralOverMesh(soln_functional, tau2, xyVector) << endl;
cout << "With q =x, integral: " << integralOverMesh(soln_functional, q, x) << endl;
cout << "(Expect 0s all around, except for q, where we expect (1,x) == 0.5.)\n";
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[])
{
// Process command line arguments
#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 v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr beta_n_u_hat = varFactory.fluxVar("\\widehat{\\beta \\cdot n }");
VarPtr u = varFactory.fieldVar("u");
FunctionPtr beta = Teuchos::rcp(new Beta());
//////////////////// BUILD MESH ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// define nodes for mesh
FieldContainer<double> meshBoundary(4,2);
meshBoundary(0,0) = -1.0; // x1
meshBoundary(0,1) = -1.0; // y1
meshBoundary(1,0) = 1.0;
meshBoundary(1,1) = -1.0;
meshBoundary(2,0) = 1.0;
meshBoundary(2,1) = 1.0;
meshBoundary(3,0) = -1.0;
meshBoundary(3,1) = 1.0;
int horizontalCells = 32, verticalCells = 32;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
confusionBF, H1Order, H1Order+pToAdd);
////////////////////////////////////////////////////////////////////
// INITIALIZE 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) );
//////////////////// DEFINE BILINEAR FORM ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr invDt = Teuchos::rcp(new ScalarParamFunction(1.0/dt));
// v terms:
confusionBF->addTerm( beta * u, - v->grad() );
confusionBF->addTerm( beta_n_u_hat, v);
confusionBF->addTerm( u, invDt*v );
rhs->addTerm( u_prev_time * invDt * v );
//////////////////// SPECIFY RHS ///////////////////////
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// robust test norm
IPPtr ip = confusionBF->graphNorm();
// IPPtr ip = Teuchos::rcp(new IP);
// ip->addTerm(v);
// ip->addTerm(invDt*v - beta*v->grad());
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary(beta) );
FunctionPtr u0 = Teuchos::rcp( new ConstantScalarFunction(0) );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
bc->addDirichlet(beta_n_u_hat, inflowBoundary, beta*n*u0);
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
// ==================== Register Solutions ==========================
mesh->registerSolution(solution);
mesh->registerSolution(prevTimeFlow);
mesh->registerSolution(flowResidual);
// ==================== SET INITIAL GUESS ==========================
FunctionPtr u_init = Teuchos::rcp(new InitialCondition());
map<int, Teuchos::RCP<Function> > functionMap;
functionMap[u->ID()] = u_init;
prevTimeFlow->projectOntoMesh(functionMap);
//////////////////// SOLVE & REFINE ///////////////////////
// if (enforceLocalConservation) {
// // FunctionPtr parity = Teuchos::rcp<Function>( new SideParityFunction );
// // LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(parity, beta_n_u_minus_sigma_n) );
// LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(1.0, beta_n_u_minus_sigma_n) );
// LinearTermPtr sourcePart = Teuchos::rcp<LinearTerm>( new LinearTerm(invDt, u) );
// conservedQuantity->addTerm(sourcePart, true);
// solution->lagrangeConstraints()->addConstraint(conservedQuantity == u_prev_time * invDt);
// }
int timestepCount = 0;
double time_tol = 1e-8;
double L2_time_residual = 1e9;
while((L2_time_residual > time_tol) && (timestepCount < numTimeSteps))
{
solution->solve(false);
// Subtract solutions to get residual
flowResidual->setSolution(solution);
flowResidual->addSolution(prevTimeFlow, -1.0);
L2_time_residual = flowResidual->L2NormOfSolutionGlobal(u->ID());
if (rank == 0)
{
cout << endl << "Timestep: " << timestepCount << ", dt = " << dt << ", Time residual = " << L2_time_residual << endl;
stringstream outfile;
outfile << "rotatingCylinder_" << timestepCount;
solution->writeToVTK(outfile.str(), 5);
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_hat) );
FunctionPtr source = Teuchos::rcp( new PreviousSolutionFunction(flowResidual, u) );
source = invDt * source;
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, source, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
}
prevTimeFlow->setSolution(solution); // reset previous time solution to current time sol
timestepCount++;
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
Epetra_SerialComm Comm;
#endif
int commRank = Teuchos::GlobalMPISession::getRank();
Comm.Barrier(); // set breakpoint here to allow debugger attachment to other MPI processes than the one you automatically attached to.
Teuchos::CommandLineProcessor cmdp(false,true); // false: don't throw exceptions; true: do return errors for unrecognized options
// problem parameters:
double mu = 0.1;
double permCoef = 1e4;
int numRefs = 0;
int k = 2, delta_k = 2;
string norm = "Graph";
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("norm", &norm, "norm");
cmdp.setOption("mu", &mu, "mu");
cmdp.setOption("permCoef", &permCoef, "Permeability coefficient");
if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL)
{
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return -1;
}
FunctionPtr zero = TFunction<double>::zero();
FunctionPtr one = TFunction<double>::constant(1);
FunctionPtr sin2pix = Teuchos::rcp( new Sin_ax(2*pi) );
FunctionPtr cos2pix = Teuchos::rcp( new Cos_ax(2*pi) );
FunctionPtr sin2piy = Teuchos::rcp( new Sin_ay(2*pi) );
FunctionPtr cos2piy = Teuchos::rcp( new Cos_ay(2*pi) );
FunctionPtr u1_exact = sin2pix*cos2piy;
FunctionPtr u2_exact = -cos2pix*sin2piy;
FunctionPtr x2 = TFunction<double>::xn(2);
FunctionPtr y2 = TFunction<double>::yn(2);
FunctionPtr p_exact = x2*y2 - 1./9;
FunctionPtr permInv = permCoef*(sin2pix + 1.1);
VarFactoryPtr vf = VarFactory::varFactory();
//fields:
VarPtr sigma1 = vf->fieldVar("sigma1", VECTOR_L2);
VarPtr sigma2 = vf->fieldVar("sigma2", VECTOR_L2);
VarPtr u1 = vf->fieldVar("u1", L2);
VarPtr u2 = vf->fieldVar("u2", L2);
VarPtr p = vf->fieldVar("p", L2);
// traces:
VarPtr u1hat = vf->traceVar("u1hat");
VarPtr u2hat = vf->traceVar("u2hat");
VarPtr t1c = vf->fluxVar("t1c");
VarPtr t2c = vf->fluxVar("t2c");
// test:
VarPtr v1 = vf->testVar("v1", HGRAD);
VarPtr v2 = vf->testVar("v2", HGRAD);
VarPtr tau1 = vf->testVar("tau1", HDIV);
VarPtr tau2 = vf->testVar("tau2", HDIV);
VarPtr q = vf->testVar("q", HGRAD);
BFPtr bf = Teuchos::rcp( new BF(vf) );
bf->addTerm(1./mu*sigma1, tau1);
bf->addTerm(1./mu*sigma2, tau2);
bf->addTerm(u1, tau1->div());
bf->addTerm(u2, tau2->div());
bf->addTerm(-u1hat, tau1->dot_normal());
bf->addTerm(-u2hat, tau2->dot_normal());
bf->addTerm(sigma1, v1->grad());
bf->addTerm(sigma2, v2->grad());
bf->addTerm(-p, v1->dx());
bf->addTerm(-p, v2->dy());
bf->addTerm(t1c, v1);
bf->addTerm(t2c, v2);
bf->addTerm(mu*permInv*u1, v1);
bf->addTerm(mu*permInv*u2, v2);
bf->addTerm(-u1, q->dx());
bf->addTerm(-u2, q->dy());
bf->addTerm(u1hat, q->times_normal_x());
bf->addTerm(u2hat, q->times_normal_y());
RHSPtr rhs = RHS::rhs();
BCPtr bc = BC::bc();
SpatialFilterPtr y_equals_one = SpatialFilter::matchingY(1.0);
SpatialFilterPtr y_equals_zero = SpatialFilter::matchingY(0);
SpatialFilterPtr x_equals_one = SpatialFilter::matchingX(1.0);
SpatialFilterPtr x_equals_zero = SpatialFilter::matchingX(0.0);
bc->addDirichlet(u1hat, y_equals_zero, u1_exact);
bc->addDirichlet(u2hat, y_equals_zero, u2_exact);
bc->addDirichlet(u1hat, x_equals_zero, u1_exact);
bc->addDirichlet(u2hat, x_equals_zero, u2_exact);
bc->addDirichlet(u1hat, y_equals_one, u1_exact);
bc->addDirichlet(u2hat, y_equals_one, u2_exact);
bc->addDirichlet(u1hat, x_equals_one, u1_exact);
bc->addDirichlet(u2hat, x_equals_one, u2_exact);
bc->addZeroMeanConstraint(p);
MeshPtr mesh = MeshFactory::quadMesh(bf, k+1, delta_k, 1, 1, 4, 4);
map<string, IPPtr> brinkmanIPs;
brinkmanIPs["Graph"] = bf->graphNorm();
brinkmanIPs["Decoupled"] = Teuchos::rcp(new IP);
brinkmanIPs["Decoupled"]->addTerm(tau1);
brinkmanIPs["Decoupled"]->addTerm(tau2);
brinkmanIPs["Decoupled"]->addTerm(tau1->div());
brinkmanIPs["Decoupled"]->addTerm(tau2->div());
brinkmanIPs["Decoupled"]->addTerm(permInv*v1);
brinkmanIPs["Decoupled"]->addTerm(permInv*v2);
brinkmanIPs["Decoupled"]->addTerm(v1->grad());
brinkmanIPs["Decoupled"]->addTerm(v2->grad());
brinkmanIPs["Decoupled"]->addTerm(q);
brinkmanIPs["Decoupled"]->addTerm(q->grad());
// brinkmanIPs["CoupledRobust"] = Teuchos::rcp(new IP);
// brinkmanIPs["CoupledRobust"]->addTerm(tau->div()-beta*v->grad());
// brinkmanIPs["CoupledRobust"]->addTerm(Function<double>::min(one/Function<double>::h(),Function<double>::constant(1./sqrt(epsilon)))*tau);
// brinkmanIPs["CoupledRobust"]->addTerm(sqrt(epsilon)*v->grad());
// brinkmanIPs["CoupledRobust"]->addTerm(beta*v->grad());
// brinkmanIPs["CoupledRobust"]->addTerm(Function<double>::min(sqrt(epsilon)*one/Function<double>::h(),one)*v);
IPPtr ip = brinkmanIPs[norm];
SolutionPtr soln = TSolution<double>::solution(mesh, bc, rhs, ip);
double threshold = 0.20;
RefinementStrategy refStrategy(soln, threshold);
ostringstream refName;
refName << "brinkman";
HDF5Exporter exporter(mesh,refName.str());
for (int refIndex=0; refIndex <= numRefs; refIndex++)
{
soln->solve(false);
double energyError = soln->energyErrorTotal();
if (commRank == 0)
{
// if (refIndex > 0)
// refStrategy.printRefinementStatistics(refIndex-1);
cout << "Refinement:\t " << refIndex << " \tElements:\t " << mesh->numActiveElements()
<< " \tDOFs:\t " << mesh->numGlobalDofs() << " \tEnergy Error:\t " << energyError << endl;
}
exporter.exportSolution(soln, refIndex);
if (refIndex != numRefs)
refStrategy.refine();
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef ENABLE_INTEL_FLOATING_POINT_EXCEPTIONS
cout << "NOTE: enabling floating point exceptions for divide by zero.\n";
_MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() & ~_MM_MASK_INVALID);
#endif
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
int rank = Teuchos::GlobalMPISession::getRank();
#ifdef HAVE_MPI
Epetra_MpiComm Comm(MPI_COMM_WORLD);
//cout << "rank: " << rank << " of " << numProcs << endl;
#else
Epetra_SerialComm Comm;
#endif
Comm.Barrier(); // set breakpoint here to allow debugger attachment to other MPI processes than the one you automatically attached to.
Teuchos::CommandLineProcessor cmdp(false,true); // false: don't throw exceptions; true: do return errors for unrecognized options
double minTol = 1e-8;
bool use3D = false;
int refCount = 10;
int k = 4; // poly order for field variables
int delta_k = use3D ? 3 : 2; // test space enrichment
int k_coarse = 0;
bool useMumps = true;
bool useGMGSolver = true;
bool enforceOneIrregularity = true;
bool useStaticCondensation = false;
bool conformingTraces = false;
bool useDiagonalScaling = false; // of the global stiffness matrix in GMGSolver
bool printRefinementDetails = false;
bool useWeightedGraphNorm = true; // graph norm scaled according to units, more or less
int numCells = 2;
int AztecOutputLevel = 1;
int gmgMaxIterations = 10000;
int smootherOverlap = 0;
double relativeTol = 1e-6;
double D = 1.0; // characteristic length scale
cmdp.setOption("polyOrder",&k,"polynomial order for field variable u");
cmdp.setOption("delta_k", &delta_k, "test space polynomial order enrichment");
cmdp.setOption("k_coarse", &k_coarse, "polynomial order for field variables on coarse mesh");
cmdp.setOption("numRefs",&refCount,"number of refinements");
cmdp.setOption("D", &D, "domain dimension");
cmdp.setOption("useConformingTraces", "useNonConformingTraces", &conformingTraces);
cmdp.setOption("enforceOneIrregularity", "dontEnforceOneIrregularity", &enforceOneIrregularity);
cmdp.setOption("smootherOverlap", &smootherOverlap, "overlap for smoother");
cmdp.setOption("printRefinementDetails", "dontPrintRefinementDetails", &printRefinementDetails);
cmdp.setOption("azOutput", &AztecOutputLevel, "Aztec output level");
cmdp.setOption("numCells", &numCells, "number of cells in the initial mesh");
cmdp.setOption("useScaledGraphNorm", "dontUseScaledGraphNorm", &useWeightedGraphNorm);
// cmdp.setOption("gmgTol", &gmgTolerance, "tolerance for GMG convergence");
cmdp.setOption("relativeTol", &relativeTol, "Energy error-relative tolerance for iterative solver.");
cmdp.setOption("gmgMaxIterations", &gmgMaxIterations, "tolerance for GMG convergence");
bool enhanceUField = false;
cmdp.setOption("enhanceUField", "dontEnhanceUField", &enhanceUField);
cmdp.setOption("useStaticCondensation", "dontUseStaticCondensation", &useStaticCondensation);
if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL)
{
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return -1;
}
double width = D, height = D, depth = D;
VarFactory varFactory;
// fields:
VarPtr u = varFactory.fieldVar("u", L2);
VarPtr sigma = varFactory.fieldVar("\\sigma", VECTOR_L2);
FunctionPtr n = Function::normal();
// traces:
VarPtr u_hat;
if (conformingTraces)
{
u_hat = varFactory.traceVar("\\widehat{u}", u);
}
else
{
cout << "Note: using non-conforming traces.\n";
u_hat = varFactory.traceVar("\\widehat{u}", u, L2);
}
VarPtr sigma_n_hat = varFactory.fluxVar("\\widehat{\\sigma}_{n}", sigma * n);
// test functions:
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
BFPtr poissonBF = Teuchos::rcp( new BF(varFactory) );
FunctionPtr alpha = Function::constant(1); // viscosity
// tau terms:
poissonBF->addTerm(sigma / alpha, tau);
poissonBF->addTerm(-u, tau->div()); // (sigma1, tau1)
poissonBF->addTerm(u_hat, tau * n);
// v terms:
poissonBF->addTerm(- sigma, v->grad()); // (mu sigma1, grad v1)
poissonBF->addTerm( sigma_n_hat, v);
int horizontalCells = numCells, verticalCells = numCells, depthCells = numCells;
vector<double> domainDimensions;
domainDimensions.push_back(width);
domainDimensions.push_back(height);
vector<int> elementCounts;
elementCounts.push_back(horizontalCells);
elementCounts.push_back(verticalCells);
if (use3D)
{
domainDimensions.push_back(depth);
elementCounts.push_back(depthCells);
}
MeshPtr mesh, k0Mesh;
int H1Order = k + 1;
int H1Order_coarse = k_coarse + 1;
if (!use3D)
{
Teuchos::ParameterList pl;
map<int,int> trialOrderEnhancements;
if (enhanceUField)
{
trialOrderEnhancements[u->ID()] = 1;
}
BFPtr poissonBilinearForm = poissonBF;
pl.set("useMinRule", true);
pl.set("bf",poissonBilinearForm);
pl.set("H1Order", H1Order);
pl.set("delta_k", delta_k);
pl.set("horizontalElements", horizontalCells);
pl.set("verticalElements", verticalCells);
pl.set("divideIntoTriangles", false);
pl.set("useConformingTraces", conformingTraces);
pl.set("trialOrderEnhancements", &trialOrderEnhancements);
pl.set("x0",(double)0);
pl.set("y0",(double)0);
pl.set("width", width);
pl.set("height",height);
mesh = MeshFactory::quadMesh(pl);
pl.set("H1Order", H1Order_coarse);
k0Mesh = MeshFactory::quadMesh(pl);
}
else
{
mesh = MeshFactory::rectilinearMesh(poissonBF, domainDimensions, elementCounts, H1Order, delta_k);
k0Mesh = MeshFactory::rectilinearMesh(poissonBF, domainDimensions, elementCounts, H1Order_coarse, delta_k);
}
mesh->registerObserver(k0Mesh); // ensure that the k0 mesh refinements track those of the solution mesh
RHSPtr rhs = RHS::rhs(); // zero
FunctionPtr sin_pi_x = Teuchos::rcp( new Sin_ax(PI/D) );
FunctionPtr sin_pi_y = Teuchos::rcp( new Sin_ay(PI/D) );
FunctionPtr u_exact = sin_pi_x * sin_pi_y;
FunctionPtr f = -(2.0 * PI * PI / (D * D)) * sin_pi_x * sin_pi_y;
rhs->addTerm( f * v );
BCPtr bc = BC::bc();
SpatialFilterPtr boundary = SpatialFilter::allSpace();
bc->addDirichlet(u_hat, boundary, u_exact);
IPPtr graphNorm;
FunctionPtr h = Teuchos::rcp( new hFunction() );
if (useWeightedGraphNorm)
{
graphNorm = IP::ip();
graphNorm->addTerm( tau->div() ); // u
graphNorm->addTerm( (h / alpha) * tau - h * v->grad() ); // sigma
graphNorm->addTerm( v ); // boundary term (adjoint to u)
graphNorm->addTerm( h * tau );
// // new effort, with the idea that the test norm should be considered in reference space, basically
// graphNorm = IP::ip();
// graphNorm->addTerm( tau->div() ); // u
// graphNorm->addTerm( tau / h - v->grad() ); // sigma
// graphNorm->addTerm( v / h ); // boundary term (adjoint to u)
// graphNorm->addTerm( tau / h );
}
else
{
map<int, double> trialWeights; // on the squared terms in the trial space norm
trialWeights[u->ID()] = 1.0 / (D * D);
trialWeights[sigma->ID()] = 1.0;
graphNorm = poissonBF->graphNorm(trialWeights, 1.0); // 1.0: weight on the L^2 terms
}
SolutionPtr solution = Solution::solution(mesh, bc, rhs, graphNorm);
solution->setUseCondensedSolve(useStaticCondensation);
mesh->registerSolution(solution); // sign up for projection of old solution onto refined cells.
double energyThreshold = 0.2;
RefinementStrategy refinementStrategy( solution, energyThreshold );
refinementStrategy.setReportPerCellErrors(true);
refinementStrategy.setEnforceOneIrregularity(enforceOneIrregularity);
Teuchos::RCP<Solver> coarseSolver, fineSolver;
if (useMumps)
{
#ifdef HAVE_AMESOS_MUMPS
coarseSolver = Teuchos::rcp( new MumpsSolver(512, true) );
#else
cout << "useMumps=true, but MUMPS is not available!\n";
exit(0);
#endif
}
else
{
coarseSolver = Teuchos::rcp( new KluSolver );
}
GMGSolver* gmgSolver;
if (useGMGSolver)
{
double tol = relativeTol;
int maxIters = gmgMaxIterations;
BCPtr zeroBCs = bc->copyImposingZero();
gmgSolver = new GMGSolver(zeroBCs, k0Mesh, graphNorm, mesh, solution->getDofInterpreter(),
solution->getPartitionMap(), maxIters, tol, coarseSolver,
useStaticCondensation);
gmgSolver->setAztecOutput(AztecOutputLevel);
gmgSolver->setUseConjugateGradient(true);
gmgSolver->gmgOperator()->setSmootherType(GMGOperator::IFPACK_ADDITIVE_SCHWARZ);
gmgSolver->gmgOperator()->setSmootherOverlap(smootherOverlap);
fineSolver = Teuchos::rcp( gmgSolver );
}
else
{
fineSolver = coarseSolver;
}
// if (rank==0) cout << "experimentally starting by solving with MUMPS on the fine mesh.\n";
// solution->solve( Teuchos::rcp( new MumpsSolver) );
solution->solve(fineSolver);
#ifdef HAVE_EPETRAEXT_HDF5
ostringstream dir_name;
dir_name << "poissonCavityFlow_k" << k;
HDF5Exporter exporter(mesh,dir_name.str());
exporter.exportSolution(solution,varFactory,0);
#endif
#ifdef HAVE_AMESOS_MUMPS
if (useMumps) coarseSolver = Teuchos::rcp( new MumpsSolver(512, true) );
#endif
solution->reportTimings();
if (useGMGSolver) gmgSolver->gmgOperator()->reportTimings();
for (int refIndex=0; refIndex < refCount; refIndex++)
{
double energyError = solution->energyErrorTotal();
GlobalIndexType numFluxDofs = mesh->numFluxDofs();
if (rank==0)
{
cout << "Before refinement " << refIndex << ", energy error = " << energyError;
cout << " (using " << numFluxDofs << " trace degrees of freedom)." << endl;
}
bool printToConsole = printRefinementDetails && (rank==0);
refinementStrategy.refine(printToConsole);
if (useStaticCondensation)
{
CondensedDofInterpreter* condensedDofInterpreter = dynamic_cast<CondensedDofInterpreter*>(solution->getDofInterpreter().get());
if (condensedDofInterpreter != NULL)
{
condensedDofInterpreter->reinitialize();
}
}
GlobalIndexType fineDofs = mesh->globalDofCount();
GlobalIndexType coarseDofs = k0Mesh->globalDofCount();
if (rank==0)
{
cout << "After refinement, coarse mesh has " << k0Mesh->numActiveElements() << " elements and " << coarseDofs << " dofs.\n";
cout << " Fine mesh has " << mesh->numActiveElements() << " elements and " << fineDofs << " dofs.\n";
}
if (!use3D)
{
ostringstream fineMeshLocation, coarseMeshLocation;
fineMeshLocation << "poissonFineMesh_k" << k << "_ref" << refIndex;
GnuPlotUtil::writeComputationalMeshSkeleton(fineMeshLocation.str(), mesh, true); // true: label cells
coarseMeshLocation << "poissonCoarseMesh_k" << k << "_ref" << refIndex;
GnuPlotUtil::writeComputationalMeshSkeleton(coarseMeshLocation.str(), k0Mesh, true); // true: label cells
}
if (useGMGSolver) // create fresh fineSolver now that the meshes have changed:
{
#ifdef HAVE_AMESOS_MUMPS
if (useMumps) coarseSolver = Teuchos::rcp( new MumpsSolver(512, true) );
#endif
double tol = max(relativeTol * energyError, minTol);
int maxIters = gmgMaxIterations;
BCPtr zeroBCs = bc->copyImposingZero();
gmgSolver = new GMGSolver(zeroBCs, k0Mesh, graphNorm, mesh, solution->getDofInterpreter(),
solution->getPartitionMap(), maxIters, tol, coarseSolver, useStaticCondensation);
gmgSolver->setAztecOutput(AztecOutputLevel);
gmgSolver->setUseDiagonalScaling(useDiagonalScaling);
fineSolver = Teuchos::rcp( gmgSolver );
}
solution->solve(fineSolver);
solution->reportTimings();
if (useGMGSolver) gmgSolver->gmgOperator()->reportTimings();
#ifdef HAVE_EPETRAEXT_HDF5
exporter.exportSolution(solution,varFactory,refIndex+1);
#endif
}
double energyErrorTotal = solution->energyErrorTotal();
GlobalIndexType numFluxDofs = mesh->numFluxDofs();
GlobalIndexType numGlobalDofs = mesh->numGlobalDofs();
if (rank==0)
{
cout << "Final mesh has " << mesh->numActiveElements() << " elements and " << numFluxDofs << " trace dofs (";
cout << numGlobalDofs << " total dofs, including fields).\n";
cout << "Final energy error: " << energyErrorTotal << endl;
}
#ifdef HAVE_EPETRAEXT_HDF5
exporter.exportSolution(solution,varFactory,0);
#endif
if (!use3D)
{
GnuPlotUtil::writeComputationalMeshSkeleton("poissonRefinedMesh", mesh, true);
}
coarseSolver = Teuchos::rcp((Solver*) NULL); // without this when useMumps = true and running on one rank, we see a crash on exit, which may have to do with MPI being finalized before coarseSolver is deleted.
return 0;
}
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 commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
double epsilon = args.Input<double>("--epsilon", "diffusion parameter");
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation");
int norm = args.Input<int>("--norm", "0 = graph\n 1 = robust\n 2 = modified robust");
// Optional arguments (have defaults)
bool zeroL2 = args.Input("--zeroL2", "take L2 term on v in robust norm to zero", true);
args.Process();
//////////////////// 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 fhat = varFactory.fluxVar("fhat");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma = varFactory.fieldVar("sigma", VECTOR_L2);
//////////////////// BUILD MESH ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
int H1Order = 3, pToAdd = 2;
// define nodes for mesh
FieldContainer<double> meshBoundary(4,2);
meshBoundary(0,0) = 0.0; // x1
meshBoundary(0,1) = 0.0; // y1
meshBoundary(1,0) = 1.0;
meshBoundary(1,1) = 0.0;
meshBoundary(2,0) = 1.0;
meshBoundary(2,1) = 1.0;
meshBoundary(3,0) = 0.0;
meshBoundary(3,1) = 1.0;
int horizontalCells = 4, verticalCells = 4;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
bf, H1Order, H1Order+pToAdd, false);
vector<double> beta;
beta.push_back(2.0);
beta.push_back(1.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
// tau terms:
bf->addTerm(sigma / epsilon, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( beta * u, - v->grad() );
bf->addTerm( fhat, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
if (norm == 0)
{
ip = bf->graphNorm();
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
ip->addZeroMeanTerm( h2_scaling*v );
}
// Robust norm
else if (norm == 1)
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
if (!zeroL2)
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
// Weight these two terms for inflow
ip->addTerm( beta * v->grad() );
ip->addTerm( tau->div() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (zeroL2)
ip->addZeroMeanTerm( h2_scaling*v );
}
// Modified robust norm
else if (norm == 2)
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
// FunctionPtr ip_weight = Teuchos::rcp( new IPWeight() );
if (!zeroL2)
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
ip->addTerm( beta * v->grad() );
ip->addTerm( tau->div() - beta*v->grad() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (zeroL2)
ip->addZeroMeanTerm( h2_scaling*v );
}
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
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 InflowBoundary );
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowBoundary );
FunctionPtr u0 = Teuchos::rcp( new U0 );
bc->addDirichlet(uhat, outflowBoundary, u0);
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
bc->addDirichlet(fhat, inflowBoundary, beta*n*u0);
// Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp(new PenaltyConstraints);
// pc->addConstraint(uhat==u0,inflowBoundary);
//////////////////// 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(fhat == zero);
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(solution, mesh, varFactory);
ofstream errOut;
if (commRank == 0)
errOut.open("confusion_err.txt");
for (int refIndex=0; refIndex<=numRefs; refIndex++){
solution->solve(false);
double energy_error = solution->energyErrorTotal();
if (commRank==0){
stringstream outfile;
outfile << "confusion_" << refIndex;
exporter.exportSolution(outfile.str());
// solution->writeToVTK(outfile.str());
// Check local conservation
FunctionPtr flux = Function::solution(fhat, solution);
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;
errOut << mesh->numGlobalDofs() << " " << energy_error << " "
<< fluxImbalances[0] << " " << fluxImbalances[1] << " " << fluxImbalances[2] << endl;
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
if (commRank == 0)
errOut.close();
return 0;
}
