int main(int argc, char *argv[]) { #ifdef HAVE_MPI Teuchos::GlobalMPISession mpiSession(&argc, &argv,0); int rank=mpiSession.getRank(); int numProcs=mpiSession.getNProc(); #else int rank = 0; int numProcs = 1; #endif int polyOrder = 2; // define our manufactured solution or problem bilinear form: double epsilon = 1e-3; bool useTriangles = false; int pToAdd = 2; int nCells = 2; if ( argc > 1) { nCells = atoi(argv[1]); if (rank==0) { cout << "numCells = " << nCells << endl; } } int numSteps = 20; if ( argc > 2) { numSteps = atoi(argv[2]); if (rank==0) { cout << "num NR steps = " << numSteps << endl; } } int useHessian = 0; // defaults to "not use" if ( argc > 3) { useHessian = atoi(argv[3]); if (rank==0) { cout << "useHessian = " << useHessian << endl; } } int thresh = numSteps; // threshhold for when to apply linesearch/hessian if ( argc > 4) { thresh = atoi(argv[4]); if (rank==0) { cout << "thresh = " << thresh << endl; } } int H1Order = polyOrder + 1; double energyThreshold = 0.2; // for mesh refinements double nonlinearStepSize = 0.5; double nonlinearRelativeEnergyTolerance = 1e-8; // used to determine convergence of the nonlinear solution //////////////////////////////////////////////////////////////////// // DEFINE VARIABLES //////////////////////////////////////////////////////////////////// // new-style bilinear form definition VarFactory varFactory; VarPtr uhat = varFactory.traceVar("\\widehat{u}"); VarPtr beta_n_u_minus_sigma_hat = varFactory.fluxVar("\\widehat{\\beta_n u - \\sigma_n}"); VarPtr u = varFactory.fieldVar("u"); VarPtr sigma1 = varFactory.fieldVar("\\sigma_1"); VarPtr sigma2 = varFactory.fieldVar("\\sigma_2"); VarPtr tau = varFactory.testVar("\\tau",HDIV); VarPtr v = varFactory.testVar("v",HGRAD); BFPtr bf = Teuchos::rcp( new BF(varFactory) ); // initialize bilinear form //////////////////////////////////////////////////////////////////// // CREATE MESH //////////////////////////////////////////////////////////////////// // create a pointer to a new mesh: Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells, bf, H1Order, H1Order+pToAdd); mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC"))); //////////////////////////////////////////////////////////////////// // INITIALIZE BACKGROUND FLOW FUNCTIONS //////////////////////////////////////////////////////////////////// BCPtr nullBC = Teuchos::rcp((BC*)NULL); RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL); IPPtr nullIP = Teuchos::rcp((IP*)NULL); SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) ); vector<double> e1(2); // (1,0) e1[0] = 1; vector<double> e2(2); // (0,1) e2[1] = 1; FunctionPtr u_prev = Teuchos::rcp( new PreviousSolutionFunction(backgroundFlow, u) ); FunctionPtr beta = e1 * u_prev + Teuchos::rcp( new ConstantVectorFunction( e2 ) ); //////////////////////////////////////////////////////////////////// // DEFINE BILINEAR FORM //////////////////////////////////////////////////////////////////// // tau parts: // 1/eps (sigma, tau)_K + (u, div tau)_K - (u_hat, tau_n)_dK bf->addTerm(sigma1 / epsilon, tau->x()); bf->addTerm(sigma2 / epsilon, tau->y()); bf->addTerm(u, tau->div()); bf->addTerm( - uhat, tau->dot_normal() ); // v: // (sigma, grad v)_K - (sigma_hat_n, v)_dK - (u, beta dot grad v) + (u_hat * n dot beta, v)_dK bf->addTerm( sigma1, v->dx() ); bf->addTerm( sigma2, v->dy() ); bf->addTerm( -u, beta * v->grad()); bf->addTerm( beta_n_u_minus_sigma_hat, v); // ==================== SET INITIAL GUESS ========================== mesh->registerSolution(backgroundFlow); FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) ); FunctionPtr u0 = Teuchos::rcp( new U0 ); map<int, Teuchos::RCP<Function> > functionMap; functionMap[u->ID()] = u0; functionMap[sigma1->ID()] = zero; functionMap[sigma2->ID()] = zero; backgroundFlow->projectOntoMesh(functionMap); // ==================== END SET INITIAL GUESS ========================== //////////////////////////////////////////////////////////////////// // DEFINE INNER PRODUCT //////////////////////////////////////////////////////////////////// // function to scale the squared guy by epsilon/h FunctionPtr epsilonOverHScaling = Teuchos::rcp( new EpsilonScaling(epsilon) ); IPPtr ip = Teuchos::rcp( new IP ); ip->addTerm( epsilonOverHScaling * (1.0/sqrt(epsilon))* tau); ip->addTerm( tau->div()); // ip->addTerm( epsilonOverHScaling * v ); ip->addTerm( v ); ip->addTerm( sqrt(epsilon) * v->grad() ); ip->addTerm(v->grad()); // ip->addTerm( beta * v->grad() ); //////////////////////////////////////////////////////////////////// // DEFINE RHS //////////////////////////////////////////////////////////////////// RHSPtr rhs = RHS::rhs(); FunctionPtr u_prev_squared_div2 = 0.5 * u_prev * u_prev; rhs->addTerm((e1 * u_prev_squared_div2 + e2 * u_prev) * v->grad() - u_prev * tau->div()); //////////////////////////////////////////////////////////////////// // DEFINE DIRICHLET BC //////////////////////////////////////////////////////////////////// FunctionPtr n = Teuchos::rcp( new UnitNormalFunction ); SpatialFilterPtr outflowBoundary = Teuchos::rcp( new TopBoundary); SpatialFilterPtr inflowBoundary = Teuchos::rcp( new NegatedSpatialFilter(outflowBoundary) ); BCPtr inflowBC = BC::bc(); FunctionPtr u0_squared_div_2 = 0.5 * u0 * u0; inflowBC->addDirichlet(beta_n_u_minus_sigma_hat,inflowBoundary, ( e1 * u0_squared_div_2 + e2 * u0) * n ); //////////////////////////////////////////////////////////////////// // CREATE SOLUTION OBJECT //////////////////////////////////////////////////////////////////// Teuchos::RCP<Solution> solution = Teuchos::rcp(new Solution(mesh, inflowBC, rhs, ip)); mesh->registerSolution(solution); //////////////////////////////////////////////////////////////////// // WARNING: UNFINISHED HESSIAN BIT //////////////////////////////////////////////////////////////////// VarFactory hessianVars = varFactory.getBubnovFactory(VarFactory::BUBNOV_TRIAL); VarPtr du = hessianVars.test(u->ID()); BFPtr hessianBF = Teuchos::rcp( new BF(hessianVars) ); // initialize bilinear form // FunctionPtr e_v = Function::constant(1.0); // dummy error rep function for now - should do nothing FunctionPtr u_current = Teuchos::rcp( new PreviousSolutionFunction(solution, u) ); FunctionPtr sig1_prev = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma1) ); FunctionPtr sig2_prev = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma2) ); FunctionPtr sig_prev = (e1*sig1_prev + e2*sig2_prev); FunctionPtr fnhat = Teuchos::rcp(new PreviousSolutionFunction(solution,beta_n_u_minus_sigma_hat)); FunctionPtr uhat_prev = Teuchos::rcp(new PreviousSolutionFunction(solution,uhat)); LinearTermPtr residual = Teuchos::rcp(new LinearTerm);// residual residual->addTerm(fnhat*v - (e1 * (u_prev_squared_div2 - sig1_prev) + e2 * (u_prev - sig2_prev)) * v->grad()); residual->addTerm((1/epsilon)*sig_prev * tau + u_prev * tau->div() - uhat_prev*tau->dot_normal()); LinearTermPtr Bdu = Teuchos::rcp(new LinearTerm);// residual Bdu->addTerm( u_current*tau->div() - u_current*(beta*v->grad())); Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ip, residual)); Teuchos::RCP<RieszRep> duRiesz = Teuchos::rcp(new RieszRep(mesh, ip, Bdu)); riesz->computeRieszRep(); FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,riesz)); e_v->writeValuesToMATLABFile(mesh, "e_v.m"); FunctionPtr posErrPart = Teuchos::rcp(new PositivePart(e_v->dx())); hessianBF->addTerm(e_v->dx()*u,du); // hessianBF->addTerm(posErrPart*u,du); Teuchos::RCP<HessianFilter> hessianFilter = Teuchos::rcp(new HessianFilter(hessianBF)); if (useHessian) { solution->setWriteMatrixToFile(true,"hessianStiffness.dat"); } else { solution->setWriteMatrixToFile(true,"stiffness.dat"); } Teuchos::RCP< LineSearchStep > LS_Step = Teuchos::rcp(new LineSearchStep(riesz)); ofstream out; out.open("Burgers.txt"); double NL_residual = 9e99; for (int i = 0; i<numSteps; i++) { solution->solve(false); // do one solve to initialize things... double stepLength = 1.0; stepLength = LS_Step->stepSize(backgroundFlow,solution, NL_residual); if (useHessian) { solution->setFilter(hessianFilter); } backgroundFlow->addSolution(solution,stepLength); NL_residual = LS_Step->getNLResidual(); if (rank==0) { cout << "NL residual after adding = " << NL_residual << " with step size " << stepLength << endl; out << NL_residual << endl; // saves initial NL error } } out.close(); //////////////////////////////////////////////////////////////////// // DEFINE REFINEMENT STRATEGY //////////////////////////////////////////////////////////////////// Teuchos::RCP<RefinementStrategy> refinementStrategy; refinementStrategy = Teuchos::rcp(new RefinementStrategy(solution,energyThreshold)); int numRefs = 0; Teuchos::RCP<NonlinearStepSize> stepSize = Teuchos::rcp(new NonlinearStepSize(nonlinearStepSize)); Teuchos::RCP<NonlinearSolveStrategy> solveStrategy; solveStrategy = Teuchos::rcp( new NonlinearSolveStrategy(backgroundFlow, solution, stepSize, nonlinearRelativeEnergyTolerance)); //////////////////////////////////////////////////////////////////// // SOLVE //////////////////////////////////////////////////////////////////// for (int refIndex=0; refIndex<numRefs; refIndex++) { solveStrategy->solve(rank==0); // print to console on rank 0 refinementStrategy->refine(rank==0); // print to console on rank 0 } // solveStrategy->solve(rank==0); if (rank==0) { backgroundFlow->writeToVTK("Burgers.vtu",min(H1Order+1,4)); solution->writeFluxesToFile(uhat->ID(), "burgers.dat"); cout << "wrote solution files" << endl; } return 0; }
int main(int argc, char *argv[]) { #ifdef HAVE_MPI Teuchos::GlobalMPISession mpiSession(&argc, &argv,0); int rank=mpiSession.getRank(); int numProcs=mpiSession.getNProc(); #else int rank = 0; int numProcs = 1; #endif //////////////////// DECLARE VARIABLES /////////////////////// // define test variables VarFactory varFactory; VarPtr tau = varFactory.testVar("\\tau", HDIV); VarPtr v = varFactory.testVar("v", HGRAD); // define trial variables VarPtr uhat = varFactory.traceVar("\\widehat{u}"); VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}"); VarPtr u = varFactory.fieldVar("u"); VarPtr sigma1 = varFactory.fieldVar("\\sigma_1"); VarPtr sigma2 = varFactory.fieldVar("\\sigma_2"); vector<double> beta_const; double c = sqrt(1.25); beta_const.push_back(1.0/c); beta_const.push_back(.5/c); // FunctionPtr beta = Teuchos::rcp(new Beta()); double eps = 1e-3; //////////////////// DEFINE BILINEAR FORM /////////////////////// BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) ); // tau terms: confusionBF->addTerm(sigma1 / eps, tau->x()); confusionBF->addTerm(sigma2 / eps, tau->y()); confusionBF->addTerm(u, tau->div()); confusionBF->addTerm(-uhat, tau->dot_normal()); // v terms: confusionBF->addTerm( sigma1, v->dx() ); confusionBF->addTerm( sigma2, v->dy() ); confusionBF->addTerm( beta_const * u, - v->grad() ); confusionBF->addTerm( beta_n_u_minus_sigma_n, v); //////////////////// DEFINE INNER PRODUCT(S) /////////////////////// // quasi-optimal norm IPPtr qoptIP = Teuchos::rcp(new IP); qoptIP->addTerm( v ); qoptIP->addTerm( tau / eps + v->grad() ); qoptIP->addTerm( beta_const * v->grad() - tau->div() ); // robust test norm IPPtr robIP = Teuchos::rcp(new IP); FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(eps) ); if (enforceLocalConservation) { robIP->addZeroMeanTerm( v ); } else { robIP->addTerm( ip_scaling * v ); } robIP->addTerm( sqrt(eps) * v->grad() ); bool useNewBC = false; FunctionPtr weight = Teuchos::rcp( new SqrtWeight(eps) ); if (useNewBC) { robIP->addTerm( beta_const * v->grad() ); robIP->addTerm( tau->div() ); robIP->addTerm( ip_scaling/sqrt(eps) * tau ); } else { robIP->addTerm( weight * beta_const * v->grad() ); robIP->addTerm( weight * tau->div() ); robIP->addTerm( weight * ip_scaling/sqrt(eps) * tau ); } //////////////////// SPECIFY RHS /////////////////////// FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) ); Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy ); FunctionPtr f = zero; rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary! //////////////////// CREATE BCs /////////////////////// Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy ); SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary ); SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary ); FunctionPtr u0 = Teuchos::rcp( new U0 ); FunctionPtr n = Teuchos::rcp( new UnitNormalFunction ); bc->addDirichlet(uhat, outflowBoundary, zero); if (useNewBC) { bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, beta_const*n*u0); } else { SpatialFilterPtr inflowBot = Teuchos::rcp( new InflowSquareBot ); SpatialFilterPtr inflowLeft = Teuchos::rcp( new InflowSquareLeft ); bc->addDirichlet(beta_n_u_minus_sigma_n, inflowLeft, beta_const*n*u0); bc->addDirichlet(uhat, inflowBot, u0); } // Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp(new PenaltyConstraints); // pc->addConstraint(uhat==u0,inflowBoundary); //////////////////// BUILD MESH /////////////////////// // define nodes for mesh int H1Order = 2, pToAdd = 2; FieldContainer<double> quadPoints(4,2); quadPoints(0,0) = 0.0; // x1 quadPoints(0,1) = 0.0; // y1 quadPoints(1,0) = 1.0; quadPoints(1,1) = 0.0; quadPoints(2,0) = 1.0; quadPoints(2,1) = 1.0; quadPoints(3,0) = 0.0; quadPoints(3,1) = 1.0; int nCells = 2; int horizontalCells = nCells, verticalCells = nCells; // create a pointer to a new mesh: Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(quadPoints, horizontalCells, verticalCells, confusionBF, H1Order, H1Order+pToAdd); //////////////////// SOLVE & REFINE /////////////////////// Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) ); // solution->setFilter(pc); if (enforceLocalConservation) { FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) ); solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero); } double energyThreshold = 0.2; // for mesh refinements RefinementStrategy refinementStrategy( solution, energyThreshold ); int numRefs = 9; for (int refIndex=0; refIndex<numRefs; refIndex++) { solution->solve(false); refinementStrategy.refine(rank==0); // print to console on rank 0 } // one more solve on the final refined mesh: solution->solve(false); if (rank==0) { solution->writeToVTK("Hughes.vtu",min(H1Order+1,4)); solution->writeFluxesToFile(uhat->ID(), "uhat.dat"); cout << "wrote files: u.m, uhat.dat\n"; } return 0; }
int main(int argc, char *argv[]) { #ifdef HAVE_MPI Teuchos::GlobalMPISession mpiSession(&argc, &argv,0); choice::MpiArgs args( argc, argv ); int rank=mpiSession.getRank(); int numProcs=mpiSession.getNProc(); #else choice::Args args( argc, argv ); int rank = 0; int numProcs = 1; #endif int nCells = args.Input<int>("--nCells", "num cells",2); int numRefs = args.Input<int>("--numRefs","num adaptive refinements",0); double eps = args.Input<double>("--epsilon","diffusion parameter",1e-2); double energyThreshold = args.Input<double>("--energyThreshold","adaptivity thresh",.5); if (rank==0){ cout << "nCells = " << nCells << ", numRefs = " << numRefs << ", eps = " << eps << endl; } //////////////////// DECLARE VARIABLES /////////////////////// // define test variables VarFactory varFactory; VarPtr tau = varFactory.testVar("\\tau", HDIV); VarPtr v = varFactory.testVar("v", HGRAD); // define trial variables VarPtr uhat = varFactory.traceVar("\\widehat{u}"); VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}"); VarPtr u = varFactory.fieldVar("u"); VarPtr sigma1 = varFactory.fieldVar("\\sigma_1"); VarPtr sigma2 = varFactory.fieldVar("\\sigma_2"); vector<double> beta; beta.push_back(1.0); beta.push_back(0.0); //////////////////// DEFINE BILINEAR FORM /////////////////////// BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) ); // tau terms: confusionBF->addTerm(sigma1 / eps, tau->x()); confusionBF->addTerm(sigma2 / eps, tau->y()); confusionBF->addTerm(u, tau->div()); confusionBF->addTerm(uhat, -tau->dot_normal()); // v terms: confusionBF->addTerm( sigma1, v->dx() ); confusionBF->addTerm( sigma2, v->dy() ); confusionBF->addTerm( -u, beta * v->grad() ); confusionBF->addTerm( beta_n_u_minus_sigma_n, v); //////////////////// DEFINE INNER PRODUCT(S) /////////////////////// // quasi-optimal norm IPPtr qoptIP = Teuchos::rcp(new IP); qoptIP->addTerm( v ); qoptIP->addTerm( tau / eps + v->grad() ); qoptIP->addTerm( beta * v->grad() - tau->div() ); // robust test norm IPPtr robIP = Teuchos::rcp(new IP); FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(eps) ); FunctionPtr invSqrtH = Teuchos::rcp(new InvSqrtHScaling); robIP->addTerm( ip_scaling * v); robIP->addTerm( ip_scaling/sqrt(eps) * tau ); robIP->addTerm( sqrt(eps) * v->grad() ); robIP->addTerm( beta * v->grad() ); robIP->addTerm( tau->div() ); /* robIP->addTerm(v); robIP->addTerm(v->grad()); robIP->addTerm(tau->div()); robIP->addTerm(invSqrtH*tau); */ FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling ); // see what effect this has // robIP->addZeroMeanTerm( h2_scaling*v ); //////////////////// SPECIFY RHS /////////////////////// FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) ); Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy ); // FunctionPtr f = zero; // rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary! //////////////////// CREATE BCs /////////////////////// Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy ); // SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary(beta) ); SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary ); SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary); FunctionPtr u_exact = Teuchos::rcp( new Uex(eps,0) ); FunctionPtr sig1_exact = Teuchos::rcp( new Uex(eps,1) ); FunctionPtr sig2_exact = Teuchos::rcp( new Uex(eps,2) ); FunctionPtr n = Teuchos::rcp( new UnitNormalFunction ); vector<double> e1(2); // (1,0) vector<double> e2(2); // (0,1) e1[0] = 1; e2[1] = 1; FunctionPtr sigma = sig1_exact*e1 + sig2_exact*e2; bc->addDirichlet(uhat, outflowBoundary, zero); bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, beta*n*u_exact-sigma*n); // bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, beta*n*u_exact); // ignoring sigma FunctionPtr u_disc = Teuchos::rcp( new Udisc ); // bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, beta*n*u_disc); // bc->addDirichlet(uhat, inflowBoundary, u_exact); //////////////////// BUILD MESH /////////////////////// // define nodes for mesh int H1Order = 2, pToAdd = 3; int horizontalCells = nCells, verticalCells = nCells; // create a pointer to a new mesh: Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd); //////////////////// SOLVE & REFINE /////////////////////// Teuchos::RCP<Solution> solution; solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) ); // solution = Teuchos::rcp( new Solution(mesh, bc, rhs, qoptIP) ); if (enforceLocalConservation) { FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) ); solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero); } RefinementStrategy refinementStrategy( solution, energyThreshold ); ofstream convOut; stringstream convOutFile; convOutFile << "erickson_conv_" << round(-log(eps)/log(10.0)) <<".txt"; convOut.open(convOutFile.str().c_str()); for (int refIndex=0; refIndex < numRefs; refIndex++){ solution->condensedSolve(false); // solution->solve(false); double quadTol = 1e-7; int cubEnrich = 25; FunctionPtr u_soln = Teuchos::rcp( new PreviousSolutionFunction(solution, u) ); FunctionPtr sigma1_soln = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma1) ); FunctionPtr sigma2_soln = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma2) ); FunctionPtr u_diff = (u_soln - u_exact)*(u_soln - u_exact); FunctionPtr sig1_diff = (sigma1_soln - sig1_exact)*(sigma1_soln - sig1_exact); FunctionPtr sig2_diff = (sigma2_soln - sig2_exact)*(sigma2_soln - sig2_exact); double u_L2_error = u_diff->integrate(mesh,cubEnrich); double sigma_L2_error = sig1_diff->integrate(mesh,cubEnrich) + sig2_diff->integrate(mesh,cubEnrich); double L2_error = sqrt(u_L2_error + sigma_L2_error); double energy_error = solution->energyErrorTotal(); u_soln->writeValuesToMATLABFile(mesh, "u_soln.m"); u_diff->writeValuesToMATLABFile(mesh, "u_diff.m"); u_exact->writeValuesToMATLABFile(mesh, "u_exact.m"); sig1_exact->writeValuesToMATLABFile(mesh, "s1_exact.m"); sig2_exact->writeValuesToMATLABFile(mesh, "s2_exact.m"); convOut << mesh->numGlobalDofs() << " " << L2_error << " " << energy_error << endl; if (rank==0){ cout << "L2 error = " << L2_error << ", energy error = " << energy_error << ", ratio = " << L2_error/energy_error << endl; cout << "u squared L2 error = " << u_L2_error << ", sigma squared l2 error = " << sigma_L2_error << ", num dofs = " << mesh->numGlobalDofs() << endl; } refinementStrategy.refine(rank==0); // print to console on rank 0 } convOut.close(); // one more solve on the final refined mesh: solution->condensedSolve(false); VTKExporter exporter(solution, mesh, varFactory); if (rank==0){ exporter.exportSolution("robustIP"); cout << endl; } return 0; /* // determine trialIDs vector< int > trialIDs = mesh->bilinearForm()->trialIDs(); vector< int > fieldIDs; vector< int > fluxIDs; vector< int >::iterator idIt; for (idIt = trialIDs.begin();idIt!=trialIDs.end();idIt++){ int trialID = *(idIt); if (!mesh->bilinearForm()->isFluxOrTrace(trialID)){ // if field fieldIDs.push_back(trialID); } else { fluxIDs.push_back(trialID); } } int numFieldInds = 0; map<int,vector<int> > globalFluxInds; // from cellID to localDofInd vector map<int,vector<int> > globalFieldInds; // from cellID to localDofInd vector map<int,vector<int> > localFieldInds; // from cellID to localDofInd vector map<int,vector<int> > localFluxInds; // from cellID to localDofInd vector set<int> allFluxInds; // unique set of all flux inds mesh->getDofIndices(allFluxInds,globalFluxInds,globalFieldInds,localFluxInds,localFieldInds); if (rank==0){ vector< ElementPtr > activeElems = mesh->activeElements(); vector< ElementPtr >::iterator elemIt; cout << "num flux dofs = " << allFluxInds.size() << endl; cout << "num field dofs = " << mesh->numFieldDofs() << endl; cout << "num flux dofs = " << mesh->numFluxDofs() << endl; elemIt = activeElems.begin(); int cellID = (*elemIt)->cellID(); cout << "num LOCAL field dofs = " << localFieldInds[cellID].size() << endl; ofstream fieldInds; fieldInds.open("fieldInds.dat"); for (elemIt = activeElems.begin();elemIt!=activeElems.end();elemIt++){ int cellID = (*elemIt)->cellID(); vector<int> inds = globalFieldInds[cellID]; vector<int> locFieldInds = localFieldInds[cellID]; cout << "local field inds for cell ID " << cellID << endl; for (int i = 0;i<inds.size();++i){ fieldInds << inds[i]+1 << endl; cout << locFieldInds[i] << endl; } vector<int> finds = globalFluxInds[cellID]; vector<int> locFluxInds = localFluxInds[cellID]; cout << "local flux inds for cell ID " << cellID << endl; for (int i = 0;i<finds.size();++i){ cout << locFluxInds[i] << endl; } cout << "global flux inds for cell ID " << cellID << endl; for (int i = 0;i<finds.size();++i){ cout << globalFluxInds[cellID][i] << endl; } } fieldInds.close(); ofstream fluxInds; fluxInds.open("fluxInds.dat"); set<int>::iterator fluxIt; for (fluxIt = allFluxInds.begin();fluxIt!=allFluxInds.end();fluxIt++){ fluxInds << (*fluxIt)+1 << endl; // offset by 1 for matlab } fluxInds.close(); } return 0; */ }
int main(int argc, char *argv[]) { // Process command line arguments if (argc > 1) numRefs = atof(argv[1]); #ifdef HAVE_MPI Teuchos::GlobalMPISession mpiSession(&argc, &argv,0); int rank=mpiSession.getRank(); int numProcs=mpiSession.getNProc(); #else int rank = 0; int numProcs = 1; #endif FunctionPtr beta = Teuchos::rcp(new Beta()); //////////////////////////////////////////////////////////////////// // DEFINE VARIABLES //////////////////////////////////////////////////////////////////// // test variables VarFactory varFactory; VarPtr tau = varFactory.testVar("\\tau", HDIV); VarPtr v = varFactory.testVar("v", HGRAD); // trial variables VarPtr uhat = varFactory.traceVar("\\widehat{u}"); VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}"); VarPtr u = varFactory.fieldVar("u"); VarPtr sigma1 = varFactory.fieldVar("\\sigma_1"); VarPtr sigma2 = varFactory.fieldVar("\\sigma_2"); //////////////////////////////////////////////////////////////////// // CREATE MESH //////////////////////////////////////////////////////////////////// BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) ); FieldContainer<double> meshBoundary(4,2); meshBoundary(0,0) = 0.0; // x1 meshBoundary(0,1) = -2.0; // y1 meshBoundary(1,0) = 4.0; meshBoundary(1,1) = -2.0; meshBoundary(2,0) = 4.0; meshBoundary(2,1) = 2.0; meshBoundary(3,0) = 0.0; meshBoundary(3,1) = 2.0; int horizontalCells = 4, verticalCells = 4; // create a pointer to a new mesh: Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells, confusionBF, H1Order, H1Order+pToAdd, false); //////////////////////////////////////////////////////////////////// // INITIALIZE BACKGROUND FLOW FUNCTIONS //////////////////////////////////////////////////////////////////// BCPtr nullBC = Teuchos::rcp((BC*)NULL); RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL); IPPtr nullIP = Teuchos::rcp((IP*)NULL); SolutionPtr prevTimeFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) ); SolutionPtr flowResidual = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) ); FunctionPtr u_prev_time = Teuchos::rcp( new PreviousSolutionFunction(prevTimeFlow, u) ); // ==================== SET INITIAL GUESS ========================== double u_free = 0.0; double sigma1_free = 0.0; double sigma2_free = 0.0; map<int, Teuchos::RCP<Function> > functionMap; functionMap[u->ID()] = Teuchos::rcp( new ConstantScalarFunction(u_free) ); functionMap[sigma1->ID()] = Teuchos::rcp( new ConstantScalarFunction(sigma1_free) ); functionMap[sigma2->ID()] = Teuchos::rcp( new ConstantScalarFunction(sigma2_free) ); prevTimeFlow->projectOntoMesh(functionMap); // ==================== END SET INITIAL GUESS ========================== //////////////////////////////////////////////////////////////////// // DEFINE BILINEAR FORM //////////////////////////////////////////////////////////////////// // tau terms: confusionBF->addTerm(sigma1 / epsilon, tau->x()); confusionBF->addTerm(sigma2 / epsilon, tau->y()); confusionBF->addTerm(u, tau->div()); confusionBF->addTerm(-uhat, tau->dot_normal()); // v terms: confusionBF->addTerm( sigma1, v->dx() ); confusionBF->addTerm( sigma2, v->dy() ); confusionBF->addTerm( beta * u, - v->grad() ); confusionBF->addTerm( beta_n_u_minus_sigma_n, v); //////////////////////////////////////////////////////////////////// // TIMESTEPPING TERMS //////////////////////////////////////////////////////////////////// Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy ); double dt = 0.25; FunctionPtr invDt = Teuchos::rcp(new ScalarParamFunction(1.0/dt)); if (rank==0) { cout << "Timestep dt = " << dt << endl; } if (transient) { confusionBF->addTerm( u, invDt*v ); rhs->addTerm( u_prev_time * invDt * v ); } //////////////////////////////////////////////////////////////////// // DEFINE INNER PRODUCT //////////////////////////////////////////////////////////////////// // mathematician's norm IPPtr mathIP = Teuchos::rcp(new IP()); mathIP->addTerm(tau); mathIP->addTerm(tau->div()); mathIP->addTerm(v); mathIP->addTerm(v->grad()); // quasi-optimal norm IPPtr qoptIP = Teuchos::rcp(new IP); qoptIP->addTerm( v ); qoptIP->addTerm( tau / epsilon + v->grad() ); qoptIP->addTerm( beta * v->grad() - tau->div() ); // robust test norm IPPtr robIP = Teuchos::rcp(new IP); FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) ); if (!enforceLocalConservation) { robIP->addTerm( ip_scaling * v ); if (transient) robIP->addTerm( invDt * v ); } robIP->addTerm( sqrt(epsilon) * v->grad() ); // Weight these two terms for inflow FunctionPtr ip_weight = Teuchos::rcp( new IPWeight() ); robIP->addTerm( ip_weight * beta * v->grad() ); robIP->addTerm( ip_weight * tau->div() ); robIP->addTerm( ip_scaling/sqrt(epsilon) * tau ); if (enforceLocalConservation) robIP->addZeroMeanTerm( v ); //////////////////////////////////////////////////////////////////// // DEFINE RHS //////////////////////////////////////////////////////////////////// FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) ); rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary! //////////////////////////////////////////////////////////////////// // DEFINE BC //////////////////////////////////////////////////////////////////// Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy ); // Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints ); SpatialFilterPtr lBoundary = Teuchos::rcp( new LeftBoundary ); SpatialFilterPtr tbBoundary = Teuchos::rcp( new TopBottomBoundary ); SpatialFilterPtr rBoundary = Teuchos::rcp( new RightBoundary ); FunctionPtr u0 = Teuchos::rcp( new ZeroBC ); FunctionPtr u_inlet = Teuchos::rcp( new InletBC ); // FunctionPtr n = Teuchos::rcp( new UnitNormalFunction ); bc->addDirichlet(beta_n_u_minus_sigma_n, lBoundary, u_inlet); bc->addDirichlet(beta_n_u_minus_sigma_n, tbBoundary, u0); bc->addDirichlet(uhat, rBoundary, u0); // pc->addConstraint(beta_n_u_minus_sigma_n - uhat == u0, rBoundary); //////////////////////////////////////////////////////////////////// // CREATE SOLUTION OBJECT //////////////////////////////////////////////////////////////////// Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) ); // solution->setFilter(pc); // ==================== Enforce Local Conservation ================== if (enforceLocalConservation) { if (transient) { FunctionPtr conserved_rhs = u_prev_time * invDt; LinearTermPtr conserved_quantity = invDt * u; LinearTermPtr flux_part = Teuchos::rcp(new LinearTerm(-1.0, beta_n_u_minus_sigma_n)); conserved_quantity->addTerm(flux_part, true); // conserved_quantity = conserved_quantity - beta_n_u_minus_sigma_n; solution->lagrangeConstraints()->addConstraint(conserved_quantity == conserved_rhs); } else { FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) ); solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero); } } // ==================== Register Solutions ========================== mesh->registerSolution(solution); mesh->registerSolution(prevTimeFlow); // u_t(i-1) mesh->registerSolution(flowResidual); // u_t(i-1) double energyThreshold = 0.25; // for mesh refinements Teuchos::RCP<RefinementStrategy> refinementStrategy; refinementStrategy = Teuchos::rcp(new RefinementStrategy(solution,energyThreshold)); //////////////////////////////////////////////////////////////////// // PSEUDO-TIME SOLVE STRATEGY //////////////////////////////////////////////////////////////////// double time_tol = 1e-8; for (int refIndex=0; refIndex<=numRefs; refIndex++) { double L2_time_residual = 1e7; int timestepCount = 0; if (!transient) numTimeSteps = 1; while((L2_time_residual > time_tol) && (timestepCount < numTimeSteps)) { solution->solve(false); // subtract solutions to get residual flowResidual->setSolution(solution); // reset previous time solution to current time sol flowResidual->addSolution(prevTimeFlow, -1.0); double L2u = flowResidual->L2NormOfSolutionGlobal(u->ID()); double L2sigma1 = flowResidual->L2NormOfSolutionGlobal(sigma1->ID()); double L2sigma2 = flowResidual->L2NormOfSolutionGlobal(sigma2->ID()); L2_time_residual = sqrt(L2u*L2u + L2sigma1*L2sigma1 + L2sigma2*L2sigma2); cout << endl << "Timestep: " << timestepCount << ", dt = " << dt << ", Time residual = " << L2_time_residual << endl; if (rank == 0) { stringstream outfile; if (transient) outfile << "TransientConfusion_" << refIndex << "_" << timestepCount; else outfile << "TransientConfusion_" << refIndex; solution->writeToVTK(outfile.str(), 5); } ////////////////////////////////////////////////////////////////////////// // Check conservation by testing against one ////////////////////////////////////////////////////////////////////////// VarPtr testOne = varFactory.testVar("1", CONSTANT_SCALAR); // Create a fake bilinear form for the testing BFPtr fakeBF = Teuchos::rcp( new BF(varFactory) ); // Define our mass flux FunctionPtr flux_current_time = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_minus_sigma_n) ); FunctionPtr delta_u = Teuchos::rcp( new PreviousSolutionFunction(flowResidual, u) ); LinearTermPtr surfaceFlux = -1.0 * flux_current_time * testOne; LinearTermPtr volumeChange = invDt * delta_u * testOne; LinearTermPtr massFluxTerm; if (transient) { massFluxTerm = volumeChange; // massFluxTerm->addTerm(surfaceFlux); } else { massFluxTerm = surfaceFlux; } // cout << "surface case = " << surfaceFlux->summands()[0].first->boundaryValueOnly() << " volume case = " << volumeChange->summands()[0].first->boundaryValueOnly() << endl; // FunctionPtr massFlux= Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_minus_sigma_n) ); // LinearTermPtr massFluxTerm = massFlux * testOne; Teuchos::RCP<shards::CellTopology> quadTopoPtr = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() )); DofOrderingFactory dofOrderingFactory(fakeBF); int fakeTestOrder = H1Order; DofOrderingPtr testOrdering = dofOrderingFactory.testOrdering(fakeTestOrder, *quadTopoPtr); int testOneIndex = testOrdering->getDofIndex(testOne->ID(),0); vector< ElementTypePtr > elemTypes = mesh->elementTypes(); // global element types map<int, double> massFluxIntegral; // cellID -> integral double maxMassFluxIntegral = 0.0; double totalMassFlux = 0.0; double totalAbsMassFlux = 0.0; for (vector< ElementTypePtr >::iterator elemTypeIt = elemTypes.begin(); elemTypeIt != elemTypes.end(); elemTypeIt++) { ElementTypePtr elemType = *elemTypeIt; vector< ElementPtr > elems = mesh->elementsOfTypeGlobal(elemType); vector<int> cellIDs; for (int i=0; i<elems.size(); i++) { cellIDs.push_back(elems[i]->cellID()); } FieldContainer<double> physicalCellNodes = mesh->physicalCellNodesGlobal(elemType); BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(elemType,mesh) ); basisCache->setPhysicalCellNodes(physicalCellNodes,cellIDs,true); // true: create side caches FieldContainer<double> cellMeasures = basisCache->getCellMeasures(); FieldContainer<double> fakeRHSIntegrals(elems.size(),testOrdering->totalDofs()); massFluxTerm->integrate(fakeRHSIntegrals,testOrdering,basisCache,true); // true: force side evaluation for (int i=0; i<elems.size(); i++) { int cellID = cellIDs[i]; // pick out the ones for testOne: massFluxIntegral[cellID] = fakeRHSIntegrals(i,testOneIndex); } // find the largest: for (int i=0; i<elems.size(); i++) { int cellID = cellIDs[i]; maxMassFluxIntegral = max(abs(massFluxIntegral[cellID]), maxMassFluxIntegral); } for (int i=0; i<elems.size(); i++) { int cellID = cellIDs[i]; maxMassFluxIntegral = max(abs(massFluxIntegral[cellID]), maxMassFluxIntegral); totalMassFlux += massFluxIntegral[cellID]; totalAbsMassFlux += abs( massFluxIntegral[cellID] ); } } // Print results from processor with rank 0 if (rank == 0) { cout << "largest mass flux: " << maxMassFluxIntegral << endl; cout << "total mass flux: " << totalMassFlux << endl; cout << "sum of mass flux absolute value: " << totalAbsMassFlux << endl; } prevTimeFlow->setSolution(solution); // reset previous time solution to current time sol timestepCount++; } if (refIndex < numRefs) { if (rank==0) { cout << "Performing refinement number " << refIndex << endl; } refinementStrategy->refine(rank==0); // RESET solution every refinement - make sure discretization error doesn't creep in // prevTimeFlow->projectOntoMesh(functionMap); } } return 0; }
int main(int argc, char *argv[]) { #ifdef HAVE_MPI Teuchos::GlobalMPISession mpiSession(&argc, &argv,0); int rank=mpiSession.getRank(); int numProcs=mpiSession.getNProc(); #else int rank = 0; int numProcs = 1; #endif int polyOrder = 3; int pToAdd = 2; // for tests // define our manufactured solution or problem bilinear form: bool useTriangles = false; FieldContainer<double> meshPoints(4,2); meshPoints(0,0) = 0.0; // x1 meshPoints(0,1) = 0.0; // y1 meshPoints(1,0) = 1.0; meshPoints(1,1) = 0.0; meshPoints(2,0) = 1.0; meshPoints(2,1) = 1.0; meshPoints(3,0) = 0.0; meshPoints(3,1) = 1.0; int H1Order = polyOrder + 1; int horizontalCells = 4, verticalCells = 4; double energyThreshold = 0.2; // for mesh refinements double nonlinearStepSize = 0.5; double nonlinearRelativeEnergyTolerance = 1e-8; // used to determine convergence of the nonlinear solution //////////////////////////////////////////////////////////////////// // DEFINE VARIABLES //////////////////////////////////////////////////////////////////// // new-style bilinear form definition VarFactory varFactory; VarPtr fhat = varFactory.fluxVar("\\widehat{f}"); VarPtr u = varFactory.fieldVar("u"); VarPtr v = varFactory.testVar("v",HGRAD); BFPtr bf = Teuchos::rcp( new BF(varFactory) ); // initialize bilinear form //////////////////////////////////////////////////////////////////// // CREATE MESH //////////////////////////////////////////////////////////////////// // create a pointer to a new mesh: Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshPoints, horizontalCells, verticalCells, bf, H1Order, H1Order+pToAdd, useTriangles); mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC"))); //////////////////////////////////////////////////////////////////// // INITIALIZE BACKGROUND FLOW FUNCTIONS //////////////////////////////////////////////////////////////////// BCPtr nullBC = Teuchos::rcp((BC*)NULL); RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL); IPPtr nullIP = Teuchos::rcp((IP*)NULL); SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) ); vector<double> e1(2); // (1,0) e1[0] = 1; vector<double> e2(2); // (0,1) e2[1] = 1; FunctionPtr u_prev = Teuchos::rcp( new PreviousSolutionFunction(backgroundFlow, u) ); FunctionPtr beta = e1 * u_prev + Teuchos::rcp( new ConstantVectorFunction( e2 ) ); //////////////////////////////////////////////////////////////////// // DEFINE BILINEAR FORM //////////////////////////////////////////////////////////////////// // v: // (sigma, grad v)_K - (sigma_hat_n, v)_dK - (u, beta dot grad v) + (u_hat * n dot beta, v)_dK bf->addTerm( -u, beta * v->grad()); bf->addTerm( fhat, v); // ==================== SET INITIAL GUESS ========================== mesh->registerSolution(backgroundFlow); FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) ); FunctionPtr u0 = Teuchos::rcp( new U0 ); map<int, Teuchos::RCP<Function> > functionMap; functionMap[u->ID()] = u0; backgroundFlow->projectOntoMesh(functionMap); // ==================== END SET INITIAL GUESS ========================== //////////////////////////////////////////////////////////////////// // DEFINE INNER PRODUCT //////////////////////////////////////////////////////////////////// IPPtr ip = Teuchos::rcp( new IP ); ip->addTerm( v ); ip->addTerm( beta * v->grad() ); //////////////////////////////////////////////////////////////////// // DEFINE RHS //////////////////////////////////////////////////////////////////// Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy ); FunctionPtr u_prev_squared_div2 = 0.5 * u_prev * u_prev; rhs->addTerm( (e1 * u_prev_squared_div2 + e2 * u_prev) * v->grad()); //////////////////////////////////////////////////////////////////// // DEFINE DIRICHLET BC //////////////////////////////////////////////////////////////////// Teuchos::RCP<BCEasy> inflowBC = Teuchos::rcp( new BCEasy ); // Create spatial filters SpatialFilterPtr bottomBoundary = Teuchos::rcp( new BottomBoundary ); SpatialFilterPtr leftBoundary = Teuchos::rcp( new LeftBoundary ); SpatialFilterPtr rightBoundary = Teuchos::rcp( new LeftBoundary ); // Create BCs FunctionPtr n = Teuchos::rcp( new UnitNormalFunction ); FunctionPtr u0_squared_div_2 = 0.5 * u0 * u0; SimpleFunction* u0Ptr = static_cast<SimpleFunction *>(u0.get()); double u0Left = u0Ptr->value(0,0); double u0Right = u0Ptr->value(1.0,0); FunctionPtr leftVal = Teuchos::rcp( new ConstantScalarFunction( -0.5*u0Left*u0Left ) ); FunctionPtr rightVal = Teuchos::rcp( new ConstantScalarFunction( 0.5*u0Right*u0Right ) ); inflowBC->addDirichlet(fhat, bottomBoundary, -u0 ); inflowBC->addDirichlet(fhat, leftBoundary, leftVal ); inflowBC->addDirichlet(fhat, rightBoundary, rightVal ); //////////////////////////////////////////////////////////////////// // CREATE SOLUTION OBJECT //////////////////////////////////////////////////////////////////// Teuchos::RCP<Solution> solution = Teuchos::rcp(new Solution(mesh, inflowBC, rhs, ip)); mesh->registerSolution(solution); if (enforceLocalConservation) { FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) ); solution->lagrangeConstraints()->addConstraint(fhat == zero); } //////////////////////////////////////////////////////////////////// // DEFINE REFINEMENT STRATEGY //////////////////////////////////////////////////////////////////// Teuchos::RCP<RefinementStrategy> refinementStrategy; refinementStrategy = Teuchos::rcp(new RefinementStrategy(solution,energyThreshold)); //////////////////////////////////////////////////////////////////// // SOLVE //////////////////////////////////////////////////////////////////// for (int refIndex=0; refIndex<=numRefs; refIndex++) { double L2Update = 1e7; int iterCount = 0; while (L2Update > nonlinearRelativeEnergyTolerance && iterCount < maxNewtonIterations) { solution->solve(); L2Update = solution->L2NormOfSolutionGlobal(u->ID()); cout << "L2 Norm of Update = " << L2Update << endl; // backgroundFlow->clear(); backgroundFlow->addSolution(solution, newtonStepSize); iterCount++; } cout << endl; // check conservation VarPtr testOne = varFactory.testVar("1", CONSTANT_SCALAR); // Create a fake bilinear form for the testing BFPtr fakeBF = Teuchos::rcp( new BF(varFactory) ); // Define our mass flux FunctionPtr massFlux = Teuchos::rcp( new PreviousSolutionFunction(solution, fhat) ); LinearTermPtr massFluxTerm = massFlux * testOne; Teuchos::RCP<shards::CellTopology> quadTopoPtr = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() )); DofOrderingFactory dofOrderingFactory(fakeBF); int fakeTestOrder = H1Order; DofOrderingPtr testOrdering = dofOrderingFactory.testOrdering(fakeTestOrder, *quadTopoPtr); int testOneIndex = testOrdering->getDofIndex(testOne->ID(),0); vector< ElementTypePtr > elemTypes = mesh->elementTypes(); // global element types map<int, double> massFluxIntegral; // cellID -> integral double maxMassFluxIntegral = 0.0; double totalMassFlux = 0.0; double totalAbsMassFlux = 0.0; for (vector< ElementTypePtr >::iterator elemTypeIt = elemTypes.begin(); elemTypeIt != elemTypes.end(); elemTypeIt++) { ElementTypePtr elemType = *elemTypeIt; vector< ElementPtr > elems = mesh->elementsOfTypeGlobal(elemType); vector<int> cellIDs; for (int i=0; i<elems.size(); i++) { cellIDs.push_back(elems[i]->cellID()); } FieldContainer<double> physicalCellNodes = mesh->physicalCellNodesGlobal(elemType); BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(elemType,mesh) ); basisCache->setPhysicalCellNodes(physicalCellNodes,cellIDs,true); // true: create side caches FieldContainer<double> cellMeasures = basisCache->getCellMeasures(); FieldContainer<double> fakeRHSIntegrals(elems.size(),testOrdering->totalDofs()); massFluxTerm->integrate(fakeRHSIntegrals,testOrdering,basisCache,true); // true: force side evaluation for (int i=0; i<elems.size(); i++) { int cellID = cellIDs[i]; // pick out the ones for testOne: massFluxIntegral[cellID] = fakeRHSIntegrals(i,testOneIndex); } // find the largest: for (int i=0; i<elems.size(); i++) { int cellID = cellIDs[i]; maxMassFluxIntegral = max(abs(massFluxIntegral[cellID]), maxMassFluxIntegral); } for (int i=0; i<elems.size(); i++) { int cellID = cellIDs[i]; maxMassFluxIntegral = max(abs(massFluxIntegral[cellID]), maxMassFluxIntegral); totalMassFlux += massFluxIntegral[cellID]; totalAbsMassFlux += abs( massFluxIntegral[cellID] ); } } if (rank==0) { cout << endl; cout << "largest mass flux: " << maxMassFluxIntegral << endl; cout << "total mass flux: " << totalMassFlux << endl; cout << "sum of mass flux absolute value: " << totalAbsMassFlux << endl; cout << endl; stringstream outfile; outfile << "burgers_" << refIndex; backgroundFlow->writeToVTK(outfile.str(), 5); } if (refIndex < numRefs) refinementStrategy->refine(rank==0); // print to console on rank 0 } return 0; }
int main(int argc, char *argv[]) { int rank = 0; #ifdef HAVE_MPI // 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); rank=mpiSession.getRank(); #else #endif bool useLineSearch = false; int pToAdd = 2; // for optimal test function approximation int pToAddForStreamFunction = 2; double nonlinearStepSize = 1.0; double dt = 0.5; double nonlinearRelativeEnergyTolerance = 0.015; // used to determine convergence of the nonlinear solution // double nonlinearRelativeEnergyTolerance = 0.15; // used to determine convergence of the nonlinear solution double eps = 1.0/64.0; // width of ramp up to 1.0 for top BC; eps == 0 ==> soln not in H1 // epsilon above is chosen to match our initial 16x16 mesh, to avoid quadrature errors. // double eps = 0.0; // John Evans's problem: not in H^1 bool enforceLocalConservation = false; bool enforceOneIrregularity = true; bool reportPerCellErrors = true; bool useMumps = true; int horizontalCells, verticalCells; int maxIters = 50; // for nonlinear steps vector<double> ReValues; // usage: polyOrder [numRefinements] // parse args: if (argc < 6) { cout << "Usage: NavierStokesCavityFlowContinuationFixedMesh fieldPolyOrder hCells vCells energyErrorGoal Re0 [Re1 ...]\n"; return -1; } int polyOrder = atoi(argv[1]); horizontalCells = atoi(argv[2]); verticalCells = atoi(argv[3]); double energyErrorGoal = atof(argv[4]); for (int i=5; i<argc; i++) { ReValues.push_back(atof(argv[i])); } if (rank == 0) { cout << "L^2 order: " << polyOrder << endl; cout << "initial mesh size: " << horizontalCells << " x " << verticalCells << endl; cout << "energy error goal: " << energyErrorGoal << endl; cout << "Reynolds number values for continuation:\n"; for (int i=0; i<ReValues.size(); i++) { cout << ReValues[i] << ", "; } cout << endl; } FieldContainer<double> quadPoints(4,2); quadPoints(0,0) = 0.0; // x1 quadPoints(0,1) = 0.0; // y1 quadPoints(1,0) = 1.0; quadPoints(1,1) = 0.0; quadPoints(2,0) = 1.0; quadPoints(2,1) = 1.0; quadPoints(3,0) = 0.0; quadPoints(3,1) = 1.0; // define meshes: int H1Order = polyOrder + 1; bool useTriangles = false; bool meshHasTriangles = useTriangles; double minL2Increment = 1e-8; // get variable definitions: VarFactory varFactory = VGPStokesFormulation::vgpVarFactory(); u1 = varFactory.fieldVar(VGP_U1_S); u2 = varFactory.fieldVar(VGP_U2_S); sigma11 = varFactory.fieldVar(VGP_SIGMA11_S); sigma12 = varFactory.fieldVar(VGP_SIGMA12_S); sigma21 = varFactory.fieldVar(VGP_SIGMA21_S); sigma22 = varFactory.fieldVar(VGP_SIGMA22_S); p = varFactory.fieldVar(VGP_P_S); u1hat = varFactory.traceVar(VGP_U1HAT_S); u2hat = varFactory.traceVar(VGP_U2HAT_S); t1n = varFactory.fluxVar(VGP_T1HAT_S); t2n = varFactory.fluxVar(VGP_T2HAT_S); v1 = varFactory.testVar(VGP_V1_S, HGRAD); v2 = varFactory.testVar(VGP_V2_S, HGRAD); tau1 = varFactory.testVar(VGP_TAU1_S, HDIV); tau2 = varFactory.testVar(VGP_TAU2_S, HDIV); q = varFactory.testVar(VGP_Q_S, HGRAD); FunctionPtr u1_0 = Teuchos::rcp( new U1_0(eps) ); FunctionPtr u2_0 = Teuchos::rcp( new U2_0 ); FunctionPtr zero = Function::zero(); ParameterFunctionPtr Re_param = ParameterFunction::parameterFunction(1); VGPNavierStokesProblem problem = VGPNavierStokesProblem(Re_param,quadPoints, horizontalCells,verticalCells, H1Order, pToAdd, u1_0, u2_0, // BC for u zero, zero); // zero forcing function SolutionPtr solution = problem.backgroundFlow(); SolutionPtr solnIncrement = problem.solutionIncrement(); Teuchos::RCP<Mesh> mesh = problem.mesh(); mesh->registerSolution(solution); mesh->registerSolution(solnIncrement); /////////////////////////////////////////////////////////////////////////// // define bilinear form for stream function: VarFactory streamVarFactory; VarPtr phi_hat = streamVarFactory.traceVar("\\widehat{\\phi}"); VarPtr psin_hat = streamVarFactory.fluxVar("\\widehat{\\psi}_n"); VarPtr psi_1 = streamVarFactory.fieldVar("\\psi_1"); VarPtr psi_2 = streamVarFactory.fieldVar("\\psi_2"); VarPtr phi = streamVarFactory.fieldVar("\\phi"); VarPtr q_s = streamVarFactory.testVar("q_s", HGRAD); VarPtr v_s = streamVarFactory.testVar("v_s", HDIV); BFPtr streamBF = Teuchos::rcp( new BF(streamVarFactory) ); streamBF->addTerm(psi_1, q_s->dx()); streamBF->addTerm(psi_2, q_s->dy()); streamBF->addTerm(-psin_hat, q_s); streamBF->addTerm(psi_1, v_s->x()); streamBF->addTerm(psi_2, v_s->y()); streamBF->addTerm(phi, v_s->div()); streamBF->addTerm(-phi_hat, v_s->dot_normal()); Teuchos::RCP<Mesh> streamMesh, overkillMesh; streamMesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells, streamBF, H1Order+pToAddForStreamFunction, H1Order+pToAdd+pToAddForStreamFunction, useTriangles); mesh->registerObserver(streamMesh); // will refine streamMesh in the same way as mesh. map<int, double> dofsToL2error; // key: numGlobalDofs, value: total L2error compared with overkill vector< VarPtr > fields; fields.push_back(u1); fields.push_back(u2); fields.push_back(sigma11); fields.push_back(sigma12); fields.push_back(sigma21); fields.push_back(sigma22); fields.push_back(p); if (rank == 0) { cout << "Starting mesh has " << horizontalCells << " x " << verticalCells << " elements and "; cout << mesh->numGlobalDofs() << " total dofs.\n"; cout << "polyOrder = " << polyOrder << endl; cout << "pToAdd = " << pToAdd << endl; cout << "eps for top BC = " << eps << endl; if (useTriangles) { cout << "Using triangles.\n"; } if (enforceLocalConservation) { cout << "Enforcing local conservation.\n"; } else { cout << "NOT enforcing local conservation.\n"; } if (enforceOneIrregularity) { cout << "Enforcing 1-irregularity.\n"; } else { cout << "NOT enforcing 1-irregularity.\n"; } } //////////////////// CREATE BCs /////////////////////// SpatialFilterPtr entireBoundary = Teuchos::rcp( new SpatialFilterUnfiltered ); FunctionPtr u1_prev = Function::solution(u1,solution); FunctionPtr u2_prev = Function::solution(u2,solution); FunctionPtr u1hat_prev = Function::solution(u1hat,solution); FunctionPtr u2hat_prev = Function::solution(u2hat,solution); //////////////////// SOLVE & REFINE /////////////////////// FunctionPtr vorticity = Teuchos::rcp( new PreviousSolutionFunction(solution, - u1->dy() + u2->dx() ) ); // FunctionPtr vorticity = Teuchos::rcp( new PreviousSolutionFunction(solution,sigma12 - sigma21) ); RHSPtr streamRHS = RHS::rhs(); streamRHS->addTerm(vorticity * q_s); ((PreviousSolutionFunction*) vorticity.get())->setOverrideMeshCheck(true); ((PreviousSolutionFunction*) u1_prev.get())->setOverrideMeshCheck(true); ((PreviousSolutionFunction*) u2_prev.get())->setOverrideMeshCheck(true); BCPtr streamBC = BC::bc(); // streamBC->addDirichlet(psin_hat, entireBoundary, u0_cross_n); streamBC->addDirichlet(phi_hat, entireBoundary, zero); // streamBC->addZeroMeanConstraint(phi); IPPtr streamIP = Teuchos::rcp( new IP ); streamIP->addTerm(q_s); streamIP->addTerm(q_s->grad()); streamIP->addTerm(v_s); streamIP->addTerm(v_s->div()); SolutionPtr streamSolution = Teuchos::rcp( new Solution( streamMesh, streamBC, streamRHS, streamIP ) ); if (enforceLocalConservation) { FunctionPtr zero = Function::zero(); solution->lagrangeConstraints()->addConstraint(u1hat->times_normal_x() + u2hat->times_normal_y()==zero); solnIncrement->lagrangeConstraints()->addConstraint(u1hat->times_normal_x() + u2hat->times_normal_y()==zero); } if (true) { FunctionPtr u1_incr = Function::solution(u1, solnIncrement); FunctionPtr u2_incr = Function::solution(u2, solnIncrement); FunctionPtr sigma11_incr = Function::solution(sigma11, solnIncrement); FunctionPtr sigma12_incr = Function::solution(sigma12, solnIncrement); FunctionPtr sigma21_incr = Function::solution(sigma21, solnIncrement); FunctionPtr sigma22_incr = Function::solution(sigma22, solnIncrement); FunctionPtr p_incr = Function::solution(p, solnIncrement); 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 energyThreshold = 0.20; Teuchos::RCP< RefinementStrategy > refinementStrategy = Teuchos::rcp( new RefinementStrategy( solnIncrement, energyThreshold )); for (int i=0; i<ReValues.size(); i++) { double Re = ReValues[i]; Re_param->setValue(Re); if (rank==0) cout << "Solving with Re = " << Re << ":\n"; double energyErrorTotal; do { double incr_norm; do { problem.iterate(useLineSearch); incr_norm = sqrt(l2_incr->integrate(problem.mesh())); if (rank==0) { 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); } } while ((incr_norm > minL2Increment ) && (problem.iterationCount() < maxIters)); if (rank==0) cout << endl; problem.setIterationCount(1); // 1 means reuse background flow (which we must, given that we want continuation in Re...) energyErrorTotal = solnIncrement->energyErrorTotal(); //solution->energyErrorTotal(); if (energyErrorTotal > energyErrorGoal) { refinementStrategy->refine(false); } if (rank==0) { cout << "Energy error: " << energyErrorTotal << endl; } } while (energyErrorTotal > energyErrorGoal); } } double energyErrorTotal = solution->energyErrorTotal(); double incrementalEnergyErrorTotal = solnIncrement->energyErrorTotal(); if (rank == 0) { cout << "final mesh has " << mesh->numActiveElements() << " elements and " << mesh->numGlobalDofs() << " dofs.\n"; cout << "energy error: " << energyErrorTotal << endl; cout << " (Incremental solution's energy error is " << incrementalEnergyErrorTotal << ".)\n"; } FunctionPtr u1_sq = u1_prev * u1_prev; FunctionPtr u_dot_u = u1_sq + (u2_prev * u2_prev); FunctionPtr u_mag = Teuchos::rcp( new SqrtFunction( u_dot_u ) ); FunctionPtr u_div = Teuchos::rcp( new PreviousSolutionFunction(solution, u1->dx() + u2->dy() ) ); FunctionPtr massFlux = Teuchos::rcp( new PreviousSolutionFunction(solution, u1hat->times_normal_x() + u2hat->times_normal_y()) ); // check that the zero mean pressure is being correctly imposed: FunctionPtr p_prev = Teuchos::rcp( new PreviousSolutionFunction(solution,p) ); double p_avg = p_prev->integrate(mesh); if (rank==0) cout << "Integral of pressure: " << p_avg << endl; // integrate massFlux over each element (a test): // fake a new bilinear form so we can integrate against 1 VarPtr testOne = varFactory.testVar("1",CONSTANT_SCALAR); BFPtr fakeBF = Teuchos::rcp( new BF(varFactory) ); LinearTermPtr massFluxTerm = massFlux * testOne; CellTopoPtrLegacy quadTopoPtr = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() )); DofOrderingFactory dofOrderingFactory(fakeBF); int fakeTestOrder = H1Order; DofOrderingPtr testOrdering = dofOrderingFactory.testOrdering(fakeTestOrder, *quadTopoPtr); int testOneIndex = testOrdering->getDofIndex(testOne->ID(),0); vector< ElementTypePtr > elemTypes = mesh->elementTypes(); // global element types map<int, double> massFluxIntegral; // cellID -> integral double maxMassFluxIntegral = 0.0; double totalMassFlux = 0.0; double totalAbsMassFlux = 0.0; double maxCellMeasure = 0; double minCellMeasure = 1; for (vector< ElementTypePtr >::iterator elemTypeIt = elemTypes.begin(); elemTypeIt != elemTypes.end(); elemTypeIt++) { ElementTypePtr elemType = *elemTypeIt; vector< ElementPtr > elems = mesh->elementsOfTypeGlobal(elemType); vector<GlobalIndexType> cellIDs; for (int i=0; i<elems.size(); i++) { cellIDs.push_back(elems[i]->cellID()); } FieldContainer<double> physicalCellNodes = mesh->physicalCellNodesGlobal(elemType); BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(elemType,mesh,polyOrder) ); // enrich by trial space order basisCache->setPhysicalCellNodes(physicalCellNodes,cellIDs,true); // true: create side caches FieldContainer<double> cellMeasures = basisCache->getCellMeasures(); FieldContainer<double> fakeRHSIntegrals(elems.size(),testOrdering->totalDofs()); massFluxTerm->integrate(fakeRHSIntegrals,testOrdering,basisCache,true); // true: force side evaluation // cout << "fakeRHSIntegrals:\n" << fakeRHSIntegrals; for (int i=0; i<elems.size(); i++) { int cellID = cellIDs[i]; // pick out the ones for testOne: massFluxIntegral[cellID] = fakeRHSIntegrals(i,testOneIndex); } // find the largest: for (int i=0; i<elems.size(); i++) { int cellID = cellIDs[i]; maxMassFluxIntegral = max(abs(massFluxIntegral[cellID]), maxMassFluxIntegral); } for (int i=0; i<elems.size(); i++) { int cellID = cellIDs[i]; maxCellMeasure = max(maxCellMeasure,cellMeasures(i)); minCellMeasure = min(minCellMeasure,cellMeasures(i)); maxMassFluxIntegral = max(abs(massFluxIntegral[cellID]), maxMassFluxIntegral); totalMassFlux += massFluxIntegral[cellID]; totalAbsMassFlux += abs( massFluxIntegral[cellID] ); } } if (rank==0) { cout << "largest mass flux: " << maxMassFluxIntegral << endl; cout << "total mass flux: " << totalMassFlux << endl; cout << "sum of mass flux absolute value: " << totalAbsMassFlux << endl; cout << "largest h: " << sqrt(maxCellMeasure) << endl; cout << "smallest h: " << sqrt(minCellMeasure) << endl; cout << "ratio of largest / smallest h: " << sqrt(maxCellMeasure) / sqrt(minCellMeasure) << endl; } if (rank == 0) { cout << "phi ID: " << phi->ID() << endl; cout << "psi1 ID: " << psi_1->ID() << endl; cout << "psi2 ID: " << psi_2->ID() << endl; cout << "streamMesh has " << streamMesh->numActiveElements() << " elements.\n"; cout << "solving for approximate stream function...\n"; } streamSolution->solve(useMumps); energyErrorTotal = streamSolution->energyErrorTotal(); if (rank == 0) { cout << "...solved.\n"; cout << "Stream mesh has energy error: " << energyErrorTotal << endl; } if (rank==0){ solution->writeToVTK("nsCavitySoln.vtk"); if (! meshHasTriangles ) { massFlux->writeBoundaryValuesToMATLABFile(solution->mesh(), "massFlux.dat"); u_mag->writeValuesToMATLABFile(solution->mesh(), "u_mag.m"); u_div->writeValuesToMATLABFile(solution->mesh(), "u_div.m"); solution->writeFieldsToFile(u1->ID(), "u1.m"); solution->writeFluxesToFile(u1hat->ID(), "u1_hat.dat"); solution->writeFieldsToFile(u2->ID(), "u2.m"); solution->writeFluxesToFile(u2hat->ID(), "u2_hat.dat"); solution->writeFieldsToFile(p->ID(), "p.m"); streamSolution->writeFieldsToFile(phi->ID(), "phi.m"); streamSolution->writeFluxesToFile(phi_hat->ID(), "phi_hat.dat"); streamSolution->writeFieldsToFile(psi_1->ID(), "psi1.m"); streamSolution->writeFieldsToFile(psi_2->ID(), "psi2.m"); vorticity->writeValuesToMATLABFile(streamMesh, "vorticity.m"); FunctionPtr ten = Teuchos::rcp( new ConstantScalarFunction(10) ); ten->writeBoundaryValuesToMATLABFile(solution->mesh(), "skeleton.dat"); cout << "wrote files: u_mag.m, u_div.m, u1.m, u1_hat.dat, u2.m, u2_hat.dat, p.m, phi.m, vorticity.m.\n"; } else { solution->writeToFile(u1->ID(), "u1.dat"); solution->writeToFile(u2->ID(), "u2.dat"); solution->writeToFile(u2->ID(), "p.dat"); cout << "wrote files: u1.dat, u2.dat, p.dat\n"; } FieldContainer<double> points = pointGrid(0, 1, 0, 1, 100); FieldContainer<double> pointData = solutionData(points, streamSolution, phi); GnuPlotUtil::writeXYPoints("phi_patch_navierStokes_cavity.dat", pointData); set<double> patchContourLevels = diagonalContourLevels(pointData,1); vector<string> patchDataPath; patchDataPath.push_back("phi_patch_navierStokes_cavity.dat"); GnuPlotUtil::writeContourPlotScript(patchContourLevels, patchDataPath, "lidCavityNavierStokes.p"); GnuPlotUtil::writeExactMeshSkeleton("lid_navierStokes_continuation_adaptive", mesh, 2); writePatchValues(0, 1, 0, 1, streamSolution, phi, "phi_patch.m"); writePatchValues(0, .1, 0, .1, streamSolution, phi, "phi_patch_detail.m"); writePatchValues(0, .01, 0, .01, streamSolution, phi, "phi_patch_minute_detail.m"); writePatchValues(0, .001, 0, .001, streamSolution, phi, "phi_patch_minute_minute_detail.m"); } 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; }
bool ScratchPadTests::testResidualMemoryError() { int rank = Teuchos::GlobalMPISession::getRank(); double tol = 1e-11; bool success = true; int nCells = 2; double eps = 1e-2; //////////////////// DECLARE VARIABLES /////////////////////// // define test variables VarFactoryPtr varFactory = VarFactory::varFactory(); VarPtr tau = varFactory->testVar("\\tau", HDIV); VarPtr v = varFactory->testVar("v", HGRAD); // define trial variables VarPtr uhat = varFactory->traceVar("\\widehat{u}"); VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}"); VarPtr u = varFactory->fieldVar("u"); VarPtr sigma1 = varFactory->fieldVar("\\sigma_1"); VarPtr sigma2 = varFactory->fieldVar("\\sigma_2"); vector<double> beta; beta.push_back(1.0); beta.push_back(0.0); //////////////////// DEFINE BILINEAR FORM /////////////////////// BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) ); // tau terms: confusionBF->addTerm(sigma1 / eps, tau->x()); confusionBF->addTerm(sigma2 / eps, tau->y()); confusionBF->addTerm(u, tau->div()); confusionBF->addTerm(uhat, -tau->dot_normal()); // v terms: confusionBF->addTerm( sigma1, v->dx() ); confusionBF->addTerm( sigma2, v->dy() ); confusionBF->addTerm( -u, beta * v->grad() ); confusionBF->addTerm( beta_n_u_minus_sigma_n, v); //////////////////// DEFINE INNER PRODUCT(S) /////////////////////// // robust test norm IPPtr robIP = Teuchos::rcp(new IP); robIP->addTerm(tau); robIP->addTerm(tau->div()); robIP->addTerm(v->grad()); robIP->addTerm(v); //////////////////// SPECIFY RHS /////////////////////// FunctionPtr zero = Function::constant(0.0); FunctionPtr one = Function::constant(1.0); RHSPtr rhs = RHS::rhs(); FunctionPtr f = zero; // FunctionPtr f = one; rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary! //////////////////// CREATE BCs /////////////////////// BCPtr bc = BC::bc(); SpatialFilterPtr inflowBoundary = Teuchos::rcp( new LRInflowSquareBoundary ); SpatialFilterPtr outflowBoundary = Teuchos::rcp( new LROutflowSquareBoundary); FunctionPtr n = Function::normal(); vector<double> e1,e2; e1.push_back(1.0); e1.push_back(0.0); e2.push_back(0.0); e2.push_back(1.0); bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, beta*n*one); bc->addDirichlet(uhat, outflowBoundary, zero); //////////////////// BUILD MESH /////////////////////// // define nodes for mesh int order = 2; int H1Order = order+1; int pToAdd = 2; // create a pointer to a new mesh: Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd); // mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC"))); //////////////////// SOLVE & REFINE /////////////////////// Teuchos::RCP<Solution> solution; solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) ); solution->solve(false); mesh->registerSolution(solution); double energyErr1 = solution->energyErrorTotal(); LinearTermPtr residual = rhs->linearTermCopy(); residual->addTerm(-confusionBF->testFunctional(solution)); RieszRepPtr rieszResidual = Teuchos::rcp(new RieszRep(mesh, robIP, residual)); rieszResidual->computeRieszRep(); FunctionPtr e_v = RieszRep::repFunction(v,rieszResidual); FunctionPtr e_tau = RieszRep::repFunction(tau,rieszResidual); double energyThreshold = 0.2; // for mesh refinements RefinementStrategy refinementStrategy( solution, energyThreshold ); refinementStrategy.refine(); solution->solve(false); double energyErr2 = solution->energyErrorTotal(); // if energy error rises if (energyErr1 < energyErr2) { if (rank==0) cout << "energy error increased from " << energyErr1 << " to " << energyErr2 << " after refinement.\n"; success = false; } return success; }
// tests whether a mixed type LT bool ScratchPadTests::testLinearTermEvaluationConsistency() { bool success = true; //////////////////// DECLARE VARIABLES /////////////////////// // define test variables VarFactoryPtr varFactory = VarFactory::varFactory(); VarPtr v = varFactory->testVar("v", HGRAD); vector<double> beta; beta.push_back(1.0); beta.push_back(1.0); //////////////////// DEFINE INNER PRODUCT(S) /////////////////////// // robust test norm IPPtr ip = Teuchos::rcp(new IP); ip->addTerm(v); ip->addTerm(beta*v->grad()); // define trial variables VarPtr beta_n_u = varFactory->fluxVar("\\widehat{\\beta \\cdot n }"); VarPtr u = varFactory->fieldVar("u"); //////////////////// BUILD MESH /////////////////////// BFPtr convectionBF = Teuchos::rcp( new BF(varFactory) ); // v terms: convectionBF->addTerm( -u, beta * v->grad() ); convectionBF->addTerm( beta_n_u, v); // define nodes for mesh int order = 1; int H1Order = order+1; int pToAdd = 1; // create a pointer to a new mesh: Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(1, convectionBF, H1Order, H1Order+pToAdd); //////////////////// get fake residual /////////////////////// LinearTermPtr lt = Teuchos::rcp(new LinearTerm); FunctionPtr edgeFxn = Teuchos::rcp(new EdgeFunction); FunctionPtr Xsq = Function::xn(2); FunctionPtr Ysq = Function::yn(2); FunctionPtr XYsq = Xsq*Ysq; lt->addTerm(edgeFxn*v + (beta*XYsq)*v->grad()); Teuchos::RCP<RieszRep> ltRiesz = Teuchos::rcp(new RieszRep(mesh, ip, lt)); ltRiesz->computeRieszRep(); FunctionPtr repFxn = RieszRep::repFunction(v,ltRiesz); map<int,FunctionPtr> rep_map; rep_map[v->ID()] = repFxn; FunctionPtr edgeLt = lt->evaluate(rep_map, true) ; FunctionPtr elemLt = lt->evaluate(rep_map, false); double edgeVal = edgeLt->integrate(mesh,10); double elemVal = elemLt->integrate(mesh,10); LinearTermPtr edgeOnlyLt = Teuchos::rcp(new LinearTerm);// residual edgeOnlyLt->addTerm(edgeFxn*v); FunctionPtr edgeOnly = edgeOnlyLt->evaluate(rep_map,true); double edgeOnlyVal = edgeOnly->integrate(mesh,10); double diff = edgeOnlyVal-edgeVal; if (abs(diff)>1e-11) { success = false; cout << "Failed testLinearTermEvaluationConsistency() with diff = " << diff << endl; } return success; }
// tests residual computation on simple convection bool ScratchPadTests::testLTResidualSimple() { double tol = 1e-11; int rank = Teuchos::GlobalMPISession::getRank(); bool success = true; int nCells = 2; //////////////////// DECLARE VARIABLES /////////////////////// // define test variables VarFactoryPtr varFactory = VarFactory::varFactory(); VarPtr v = varFactory->testVar("v", HGRAD); // define trial variables VarPtr beta_n_u = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}"); VarPtr u = varFactory->fieldVar("u"); vector<double> beta; beta.push_back(1.0); beta.push_back(1.0); //////////////////// DEFINE BILINEAR FORM /////////////////////// BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) ); // v terms: confusionBF->addTerm( -u, beta * v->grad() ); confusionBF->addTerm( beta_n_u, v); //////////////////// DEFINE INNER PRODUCT(S) /////////////////////// // robust test norm IPPtr ip = Teuchos::rcp(new IP); // choose the mesh-independent norm even though it may have BLs ip->addTerm(v->grad()); ip->addTerm(v); //////////////////// SPECIFY RHS AND HELPFUL FUNCTIONS /////////////////////// FunctionPtr n = Function::normal(); vector<double> e1,e2; e1.push_back(1.0); e1.push_back(0.0); e2.push_back(0.0); e2.push_back(1.0); FunctionPtr one = Function::constant(1.0); FunctionPtr zero = Function::constant(0.0); RHSPtr rhs = RHS::rhs(); FunctionPtr f = one; rhs->addTerm( f * v ); //////////////////// CREATE BCs /////////////////////// BCPtr bc = BC::bc(); SpatialFilterPtr boundary = Teuchos::rcp( new InflowSquareBoundary ); FunctionPtr u_in = Teuchos::rcp(new Uinflow); bc->addDirichlet(beta_n_u, boundary, beta*n*u_in); //////////////////// BUILD MESH /////////////////////// // define nodes for mesh int order = 2; int H1Order = order+1; int pToAdd = 2; // create a pointer to a new mesh: Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd); //////////////////// SOLVE & REFINE /////////////////////// int cubEnrich = 0; Teuchos::RCP<Solution> solution; solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) ); solution->solve(false); double energyError = solution->energyErrorTotal(); LinearTermPtr residual = rhs->linearTermCopy(); residual->addTerm(-confusionBF->testFunctional(solution),true); Teuchos::RCP<RieszRep> rieszResidual = Teuchos::rcp(new RieszRep(mesh, ip, residual)); rieszResidual->computeRieszRep(cubEnrich); double energyErrorLT = rieszResidual->getNorm(); bool testVsTest = true; FunctionPtr e_v = RieszRep::repFunction(v,rieszResidual); map<int,FunctionPtr> errFxns; errFxns[v->ID()] = e_v; FunctionPtr err = (ip->evaluate(errFxns,false))->evaluate(errFxns,false); // don't need boundary terms unless they're in IP double energyErrorIntegrated = sqrt(err->integrate(mesh,cubEnrich,testVsTest)); // check that energy error computed thru Solution and through rieszRep are the same success = abs(energyError-energyErrorLT) < tol; if (success==false) { if (rank==0) cout << "Failed testLTResidualSimple; energy error = " << energyError << ", while linearTerm error is computed to be " << energyErrorLT << endl; return success; } // checks that matrix-computed and integrated errors are the same success = abs(energyErrorLT-energyErrorIntegrated)<tol; if (success==false) { if (rank==0) cout << "Failed testLTResidualSimple; energy error = " << energyError << ", while error computed via integration is " << energyErrorIntegrated << endl; return success; } return success; }
// tests to make sure the energy error calculated thru direct integration works for vector valued test functions too bool ScratchPadTests::testLTResidual() { double tol = 1e-11; int rank = Teuchos::GlobalMPISession::getRank(); bool success = true; int nCells = 2; double eps = .1; //////////////////// DECLARE VARIABLES /////////////////////// // define test variables VarFactoryPtr varFactory = VarFactory::varFactory(); VarPtr tau = varFactory->testVar("\\tau", HDIV); VarPtr v = varFactory->testVar("v", HGRAD); // define trial variables VarPtr uhat = varFactory->traceVar("\\widehat{u}"); VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}"); VarPtr u = varFactory->fieldVar("u"); VarPtr sigma1 = varFactory->fieldVar("\\sigma_1"); VarPtr sigma2 = varFactory->fieldVar("\\sigma_2"); vector<double> beta; beta.push_back(1.0); beta.push_back(0.0); //////////////////// DEFINE BILINEAR FORM /////////////////////// BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) ); // tau terms: confusionBF->addTerm(sigma1 / eps, tau->x()); confusionBF->addTerm(sigma2 / eps, tau->y()); confusionBF->addTerm(u, tau->div()); confusionBF->addTerm(uhat, -tau->dot_normal()); // v terms: confusionBF->addTerm( sigma1, v->dx() ); confusionBF->addTerm( sigma2, v->dy() ); confusionBF->addTerm( -u, beta * v->grad() ); confusionBF->addTerm( beta_n_u_minus_sigma_n, v); //////////////////// DEFINE INNER PRODUCT(S) /////////////////////// // robust test norm IPPtr ip = Teuchos::rcp(new IP); // choose the mesh-independent norm even though it may have boundary layers ip->addTerm(v->grad()); ip->addTerm(v); ip->addTerm(tau); ip->addTerm(tau->div()); //////////////////// SPECIFY RHS AND HELPFUL FUNCTIONS /////////////////////// FunctionPtr n = Function::normal(); vector<double> e1,e2; e1.push_back(1.0); e1.push_back(0.0); e2.push_back(0.0); e2.push_back(1.0); FunctionPtr one = Function::constant(1.0); FunctionPtr zero = Function::constant(0.0); RHSPtr rhs = RHS::rhs(); FunctionPtr f = one; // if this is set to zero instead, we pass the test (a clue?) rhs->addTerm( f * v ); //////////////////// CREATE BCs /////////////////////// BCPtr bc = BC::bc(); SpatialFilterPtr squareBoundary = Teuchos::rcp( new SquareBoundary ); bc->addDirichlet(uhat, squareBoundary, one); //////////////////// BUILD MESH /////////////////////// // define nodes for mesh int order = 2; int H1Order = order+1; int pToAdd = 2; // create a pointer to a new mesh: Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd); //////////////////// SOLVE & REFINE /////////////////////// Teuchos::RCP<Solution> solution; solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) ); solution->solve(false); double energyError = solution->energyErrorTotal(); LinearTermPtr residual = rhs->linearTermCopy(); residual->addTerm(-confusionBF->testFunctional(solution),true); // FunctionPtr uh = Function::solution(uhat,solution); // FunctionPtr fn = Function::solution(beta_n_u_minus_sigma_n,solution); // FunctionPtr uF = Function::solution(u,solution); // FunctionPtr sigma = e1*Function::solution(sigma1,solution)+e2*Function::solution(sigma2,solution); // residual->addTerm(- (fn*v - uh*tau->dot_normal())); // residual->addTerm(- (uF*(tau->div() - beta*v->grad()) + sigma*((1/eps)*tau + v->grad()))); // residual->addTerm(-(fn*v - uF*beta*v->grad() + sigma*v->grad())); // just v portion // residual->addTerm(uh*tau->dot_normal() - uF*tau->div() - sigma*((1/eps)*tau)); // just tau portion Teuchos::RCP<RieszRep> rieszResidual = Teuchos::rcp(new RieszRep(mesh, ip, residual)); rieszResidual->computeRieszRep(); double energyErrorLT = rieszResidual->getNorm(); int cubEnrich = 0; bool testVsTest = true; FunctionPtr e_v = RieszRep::repFunction(v,rieszResidual); FunctionPtr e_tau = RieszRep::repFunction(tau,rieszResidual); // experiment by Nate: manually specify the error (this appears to produce identical results, as it should) // FunctionPtr err = e_v * e_v + e_tau * e_tau + e_v->grad() * e_v->grad() + e_tau->div() * e_tau->div(); map<int,FunctionPtr> errFxns; errFxns[v->ID()] = e_v; errFxns[tau->ID()] = e_tau; LinearTermPtr ipAtErrFxns = ip->evaluate(errFxns); FunctionPtr err = ip->evaluate(errFxns)->evaluate(errFxns); double energyErrorIntegrated = sqrt(err->integrate(mesh,cubEnrich,testVsTest)); // check that energy error computed thru Solution and through rieszRep are the same bool success1 = abs(energyError-energyErrorLT)<tol; // checks that matrix-computed and integrated errors are the same bool success2 = abs(energyErrorLT-energyErrorIntegrated)<tol; success = success1==true && success2==true; if (!success) { if (rank==0) cout << "Failed testLTResidual; energy error = " << energyError << ", while linearTerm error is computed to be " << energyErrorLT << ", and when computing through integration of the Riesz rep function, error = " << energyErrorIntegrated << endl; } // VTKExporter exporter(solution, mesh, varFactory); // exporter.exportSolution("testLTRes"); // cout << endl; return success; }
int main(int argc, char *argv[]) { #ifdef HAVE_MPI Teuchos::GlobalMPISession mpiSession(&argc, &argv,0); int rank=mpiSession.getRank(); int numProcs=mpiSession.getNProc(); #else int rank = 0; int numProcs = 1; #endif int polyOrder = 0; // define our manufactured solution or problem bilinear form: bool useTriangles = false; int pToAdd = 1; int nCells = 2; if ( argc > 1) { nCells = atoi(argv[1]); if (rank==0) { cout << "numCells = " << nCells << endl; } } int numSteps = 20; if ( argc > 2) { numSteps = atoi(argv[2]); if (rank==0) { cout << "num NR steps = " << numSteps << endl; } } int useHessian = 0; // defaults to "not use" if ( argc > 3) { useHessian = atoi(argv[3]); if (rank==0) { cout << "useHessian = " << useHessian << endl; } } int H1Order = polyOrder + 1; double energyThreshold = 0.2; // for mesh refinements double nonlinearStepSize = 0.5; double nonlinearRelativeEnergyTolerance = 1e-8; // used to determine convergence of the nonlinear solution //////////////////////////////////////////////////////////////////// // DEFINE VARIABLES //////////////////////////////////////////////////////////////////// // new-style bilinear form definition VarFactory varFactory; VarPtr fn = varFactory.fluxVar("\\widehat{\\beta_n_u}"); VarPtr u = varFactory.fieldVar("u"); VarPtr v = varFactory.testVar("v",HGRAD); BFPtr bf = Teuchos::rcp( new BF(varFactory) ); // initialize bilinear form //////////////////////////////////////////////////////////////////// // CREATE MESH //////////////////////////////////////////////////////////////////// // create a pointer to a new mesh: Teuchos::RCP<Mesh> mesh = Mesh::buildUnitQuadMesh(2,1 , bf, H1Order, H1Order+pToAdd); //////////////////////////////////////////////////////////////////// // 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) ); SolutionPtr solnPerturbation = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) ); vector<double> e1(2); // (1,0) e1[0] = 1; vector<double> e2(2); // (0,1) e2[1] = 1; FunctionPtr u_prev = Teuchos::rcp( new PreviousSolutionFunction(backgroundFlow, u) ); FunctionPtr beta = e1 * u_prev + Teuchos::rcp( new ConstantVectorFunction( e2 ) ); //////////////////////////////////////////////////////////////////// // DEFINE BILINEAR FORM //////////////////////////////////////////////////////////////////// // v: bf->addTerm( -u, beta * v->grad()); bf->addTerm( fn, v); //////////////////////////////////////////////////////////////////// // DEFINE RHS //////////////////////////////////////////////////////////////////// Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy ); FunctionPtr u_prev_squared_div2 = 0.5 * u_prev * u_prev; rhs->addTerm((e1 * u_prev_squared_div2 + e2 * u_prev) * v->grad()); // ==================== SET INITIAL GUESS ========================== mesh->registerSolution(backgroundFlow); FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) ); FunctionPtr u0 = Teuchos::rcp( new U0 ); FunctionPtr n = Teuchos::rcp( new UnitNormalFunction ); FunctionPtr parity = Teuchos::rcp(new SideParityFunction); FunctionPtr u0_squared_div_2 = 0.5 * u0 * u0; map<int, Teuchos::RCP<Function> > functionMap; functionMap[u->ID()] = u0; // functionMap[fn->ID()] = -(e1 * u0_squared_div_2 + e2 * u0) * n * parity; backgroundFlow->projectOntoMesh(functionMap); // ==================== END SET INITIAL GUESS ========================== //////////////////////////////////////////////////////////////////// // DEFINE INNER PRODUCT //////////////////////////////////////////////////////////////////// IPPtr ip = Teuchos::rcp( new IP ); ip->addTerm( v ); ip->addTerm(v->grad()); // ip->addTerm( beta * v->grad() ); //////////////////////////////////////////////////////////////////// // DEFINE DIRICHLET BC //////////////////////////////////////////////////////////////////// SpatialFilterPtr outflowBoundary = Teuchos::rcp( new TopBoundary); SpatialFilterPtr inflowBoundary = Teuchos::rcp( new NegatedSpatialFilter(outflowBoundary) ); Teuchos::RCP<BCEasy> inflowBC = Teuchos::rcp( new BCEasy ); inflowBC->addDirichlet(fn,inflowBoundary, ( e1 * u0_squared_div_2 + e2 * u0) * n ); // inflowBC->addDirichlet(fn,inflowBoundary,zero); //////////////////////////////////////////////////////////////////// // CREATE SOLUTION OBJECT //////////////////////////////////////////////////////////////////// Teuchos::RCP<Solution> solution = Teuchos::rcp(new Solution(mesh, inflowBC, rhs, ip)); mesh->registerSolution(solution); solution->setCubatureEnrichmentDegree(10); //////////////////////////////////////////////////////////////////// // HESSIAN BIT + CHECKS ON GRADIENT + HESSIAN //////////////////////////////////////////////////////////////////// VarFactory hessianVars = varFactory.getBubnovFactory(VarFactory::BUBNOV_TRIAL); VarPtr du = hessianVars.test(u->ID()); BFPtr hessianBF = Teuchos::rcp( new BF(hessianVars) ); // initialize bilinear form FunctionPtr du_current = Teuchos::rcp( new PreviousSolutionFunction(solution, u) ); FunctionPtr fnhat = Teuchos::rcp(new PreviousSolutionFunction(solution,fn)); LinearTermPtr residual = Teuchos::rcp(new LinearTerm);// residual residual->addTerm(fnhat*v,true); residual->addTerm( - (e1 * (u_prev_squared_div2) + e2 * (u_prev)) * v->grad(),true); LinearTermPtr Bdu = Teuchos::rcp(new LinearTerm);// residual Bdu->addTerm( - du_current*(beta*v->grad())); Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ip, residual)); Teuchos::RCP<RieszRep> duRiesz = Teuchos::rcp(new RieszRep(mesh, ip, Bdu)); riesz->computeRieszRep(); FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,riesz)); e_v->writeValuesToMATLABFile(mesh, "e_v.m"); FunctionPtr posErrPart = Teuchos::rcp(new PositivePart(e_v->dx())); hessianBF->addTerm(e_v->dx()*u,du); // hessianBF->addTerm(posErrPart*u,du); Teuchos::RCP<HessianFilter> hessianFilter = Teuchos::rcp(new HessianFilter(hessianBF)); if (useHessian) { solution->setWriteMatrixToFile(true,"hessianStiffness.dat"); } else { solution->setWriteMatrixToFile(true,"stiffness.dat"); } Teuchos::RCP< LineSearchStep > LS_Step = Teuchos::rcp(new LineSearchStep(riesz)); double NL_residual = 9e99; for (int i = 0; i<numSteps; i++) { solution->solve(false); // do one solve to initialize things... double stepLength = 1.0; stepLength = LS_Step->stepSize(backgroundFlow,solution, NL_residual); if (useHessian) { solution->setFilter(hessianFilter); } backgroundFlow->addSolution(solution,stepLength); NL_residual = LS_Step->getNLResidual(); if (rank==0) { cout << "NL residual after adding = " << NL_residual << " with step size " << stepLength << endl; } int numGlobalDofs = mesh->numGlobalDofs(); double fd_gradient; for (int dofIndex = 0; dofIndex<numGlobalDofs; dofIndex++) { TestingUtilities::initializeSolnCoeffs(solnPerturbation); TestingUtilities::setSolnCoeffForGlobalDofIndex(solnPerturbation,1.0,dofIndex); fd_gradient = FiniteDifferenceUtilities::finiteDifferenceGradient(mesh, riesz, backgroundFlow, dofIndex); // CHECK GRADIENT LinearTermPtr b_u = bf->testFunctional(solnPerturbation); map<int,FunctionPtr> NL_err_rep_map; NL_err_rep_map[v->ID()] = Teuchos::rcp(new RepFunction(v,riesz)); FunctionPtr gradient = b_u->evaluate(NL_err_rep_map, TestingUtilities::isFluxOrTraceDof(mesh,dofIndex)); // use boundary part only if flux or trace double grad; if (TestingUtilities::isFluxOrTraceDof(mesh,dofIndex)) { grad = gradient->integralOfJump(mesh,10); } else { grad = gradient->integrate(mesh,10); } double fdgrad = fd_gradient; double diff = grad-fdgrad; if (abs(diff)>1e-6 && i>0) { cout << "Found difference of " << diff << ", " << " with fd val = " << fdgrad << " and gradient = " << grad << " in dof " << dofIndex << ", isTraceDof = " << TestingUtilities::isFluxOrTraceDof(mesh,dofIndex) << endl; } } } if (rank==0) { backgroundFlow->writeToVTK("BurgersTest.vtu",min(H1Order+1,4)); solution->writeFluxesToFile(fn->ID(),"fn.dat"); cout << "wrote solution files" << endl; } return 0; }
int main(int argc, char *argv[]) { Teuchos::GlobalMPISession mpiSession(&argc, &argv, NULL); // initialize MPI Teuchos::CommandLineProcessor cmdp(false,true); // false: don't throw exceptions; true: do return errors for unrecognized options int numElements = 3; vector<vector<double>> domainDim(3,vector<double>{0.0,1.0}); // first index: spaceDim; second: 0/1 for x0, x1, etc. int polyOrder = 2, delta_k = 1; int spaceDim = 2; cmdp.setOption("numElements", &numElements ); cmdp.setOption("polyOrder", &polyOrder ); cmdp.setOption("delta_k", &delta_k ); cmdp.setOption("x0", &domainDim[0][0] ); cmdp.setOption("x1", &domainDim[0][1] ); cmdp.setOption("y0", &domainDim[1][0] ); cmdp.setOption("y1", &domainDim[1][1] ); cmdp.setOption("z0", &domainDim[2][0] ); cmdp.setOption("z1", &domainDim[2][1] ); cmdp.setOption("spaceDim", &spaceDim); if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL) { #ifdef HAVE_MPI MPI_Finalize(); #endif return -1; } vector<double> x0(spaceDim); vector<double> domainSize(spaceDim); vector<int> elementCounts(spaceDim); for (int d=0; d<spaceDim; d++) { x0[d] = domainDim[d][0]; domainSize[d] = domainDim[d][1] - x0[d]; elementCounts[d] = numElements; } bool conformingTraces = true; // no difference for primal/continuous formulations PoissonFormulation formCG(spaceDim, conformingTraces, PoissonFormulation::CONTINUOUS_GALERKIN); VarPtr q = formCG.q(); VarPtr phi = formCG.phi(); BFPtr bf = formCG.bf(); MeshPtr bubnovMesh = MeshFactory::rectilinearMesh(bf, domainSize, elementCounts, polyOrder, 0, x0); // Right now, hanging nodes don't work with continuous field variables // there is a GDAMinimumRule test demonstrating the failure, SolvePoisson2DContinuousGalerkinHangingNode. // make a mesh with hanging nodes (when spaceDim > 1) // { // set<GlobalIndexType> cellsToRefine = {0}; // bubnovMesh->hRefine(cellsToRefine); // } RHSPtr rhs = RHS::rhs(); rhs->addTerm(1.0 * q); // unit forcing IPPtr ip = Teuchos::null; // will give Bubnov-Galerkin BCPtr bc = BC::bc(); bc->addDirichlet(phi, SpatialFilter::allSpace(), Function::zero()); SolutionPtr solution = Solution::solution(bf, bubnovMesh, bc, rhs, ip); solution->solve(); HDF5Exporter exporter(bubnovMesh, "PoissonContinuousGalerkin"); exporter.exportSolution(solution); /**** Sort-of-primal experiment ****/ // an experiment: try doing "primal" DPG with IBP to the boundary // ip = IP::ip(); // ip->addTerm(q->grad()); // ip->addTerm(q); // // solution = Solution::solution(bf, bubnovMesh, bc, rhs, ip); // solution->solve(); // // HDF5Exporter primalNoFluxExporter(bubnovMesh, "PoissonPrimalNoFlux"); // primalNoFluxExporter.exportSolution(solution); //*** Primal Formulation ***// PoissonFormulation form(spaceDim, conformingTraces, PoissonFormulation::PRIMAL); q = form.q(); phi = form.phi(); bf = form.bf(); bc = BC::bc(); bc->addDirichlet(phi, SpatialFilter::allSpace(), Function::zero()); rhs = RHS::rhs(); rhs->addTerm(1.0 * q); // unit forcing MeshPtr primalMesh = MeshFactory::rectilinearMesh(bf, domainSize, elementCounts, polyOrder, delta_k, x0); ip = IP::ip(); ip->addTerm(q->grad()); ip->addTerm(q); // Right now, hanging nodes don't work with continuous field variables // there is a GDAMinimumRule test demonstrating the failure, SolvePoisson2DContinuousGalerkinHangingNode. // make a mesh with hanging nodes (when spaceDim > 1) // { // set<GlobalIndexType> cellsToRefine = {0}; // primalMesh->hRefine(cellsToRefine); // } solution = Solution::solution(bf, primalMesh, bc, rhs, ip); solution->solve(); HDF5Exporter primalExporter(primalMesh, "PoissonPrimal"); primalExporter.exportSolution(solution); 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 v1 = varFactory.testVar("v1", HGRAD); VarPtr v2 = varFactory.testVar("v2", 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 u1hat = varFactory.traceVar("u1hat"); VarPtr u2hat = varFactory.traceVar("u2hat"); VarPtr t1hat = varFactory.fluxVar("t1hat"); VarPtr t2hat = varFactory.fluxVar("t2hat"); //////////////////// 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 = MeshFactory::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 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) ); // ==================== SET INITIAL GUESS ========================== map<int, Teuchos::RCP<Function> > functionMap; // functionMap[u1->ID()] = u1Exact; // functionMap[u2->ID()] = u2Exact; functionMap[u1->ID()] = zero; functionMap[u2->ID()] = zero; backgroundFlow->projectOntoMesh(functionMap); //////////////////// DEFINE BILINEAR FORM /////////////////////// // stress equation bf->addTerm( 1./nu*sigma11, tau11 ); bf->addTerm( 1./nu*sigma12, tau12 ); bf->addTerm( 1./nu*sigma12, tau12 ); bf->addTerm( 1./nu*sigma22, tau22 ); bf->addTerm( -0.5/nu*sigma11, tau11 ); bf->addTerm( -0.5/nu*sigma22, tau11 ); bf->addTerm( -0.5/nu*sigma11, tau22 ); bf->addTerm( -0.5/nu*sigma22, tau22 ); bf->addTerm( 2*u1, tau11->dx() ); bf->addTerm( 2*u1, tau12->dy() ); bf->addTerm( 2*u2, tau12->dx() ); bf->addTerm( 2*u2, tau22->dy() ); bf->addTerm( -2*u1hat, tau11->times_normal_x() ); bf->addTerm( -2*u1hat, tau12->times_normal_y() ); bf->addTerm( -2*u2hat, tau12->times_normal_x() ); bf->addTerm( -2*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, v2->dx() ); bf->addTerm( -2.*u2_prev*u2, v2->dy() ); bf->addTerm( sigma11, v1->dx() ); bf->addTerm( sigma12, v1->dy() ); bf->addTerm( sigma12, v2->dx() ); bf->addTerm( sigma22, v2->dy() ); bf->addTerm( t1hat, v1); bf->addTerm( t2hat, v2); //////////////////// SPECIFY RHS /////////////////////// RHSPtr rhs = RHS::rhs(); // stress equation rhs->addTerm( -2*u1_prev * tau11->dx() ); rhs->addTerm( -2*u1_prev * tau12->dy() ); rhs->addTerm( -2*u2_prev * tau12->dx() ); rhs->addTerm( -2*u2_prev * tau22->dy() ); // momentum equation rhs->addTerm( u1_prev*u1_prev * v1->dx() ); rhs->addTerm( u2_prev*u1_prev * v1->dy() ); rhs->addTerm( u2_prev*u1_prev * v2->dx() ); rhs->addTerm( u2_prev*u2_prev * v2->dy() ); //////////////////// DEFINE INNER PRODUCT(S) /////////////////////// IPPtr ip = Teuchos::rcp(new IP); if (norm == 0) { ip = bf->graphNorm(); } else if (norm == 1) { ip->addTerm( 0.5/nu*tau11-0.5/nu*tau22 + v1->dx() ); ip->addTerm( 1./nu*tau12 + v1->dy() ); ip->addTerm( 1./nu*tau12 + v2->dx() ); ip->addTerm( 0.5/nu*tau22-0.5/nu*tau11 + v2->dy() ); ip->addTerm( 2*tau11->dx() + 2*tau12->dy() - 2*u1_prev*v1->dx() - u2_prev*v1->dy() - u2_prev*v2->dx() ); ip->addTerm( 2*tau12->dx() + 2*tau22->dy() - 2*u2_prev*v2->dy() - u1_prev*v1->dy() - u1_prev*v2->dx() ); ip->addTerm( v1 ); ip->addTerm( v2 ); ip->addTerm( tau11 ); ip->addTerm( tau12 ); ip->addTerm( tau12 ); ip->addTerm( tau22 ); } else if (norm == 2) { // ip->addTerm( 0.5/sqrt(nu)*tau11-0.5/nu*tau22 ); // ip->addTerm( 1./sqrt(nu)*tau12 ); // ip->addTerm( 1./sqrt(nu)*tau12 ); // ip->addTerm( 0.5/sqrt(nu)*tau22-0.5/nu*tau11 ); ip->addTerm( tau11 ); ip->addTerm( tau12 ); ip->addTerm( tau12 ); ip->addTerm( tau22 ); ip->addTerm( 2*tau11->dx() + 2*tau12->dy() - 2*u1_prev*v1->dx() - u2_prev*v1->dy() - u2_prev*v2->dx() ); ip->addTerm( 2*tau12->dx() + 2*tau22->dy() - 2*u2_prev*v2->dy() - u1_prev*v1->dy() - u1_prev*v2->dx() ); ip->addTerm( 2*u1_prev*v1->dx() + u2_prev*v1->dy() + u2_prev*v2->dx() ); ip->addTerm( 2*u2_prev*v2->dy() + u1_prev*v1->dy() + u1_prev*v2->dx() ); ip->addTerm( sqrt(nu)*v1->grad() ); ip->addTerm( sqrt(nu)*v2->grad() ); ip->addTerm( v1 ); ip->addTerm( v2 ); } //////////////////// CREATE BCs /////////////////////// BCPtr bc = BC::bc(); // 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); // bc->addDirichlet(u1hat, left, zero); // bc->addDirichlet(u2hat, left, zero); // bc->addDirichlet(u1hat, right, zero); // 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); // 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 ); HDF5Exporter exporter(mesh, "Kovasznay_np"); ofstream convOut; stringstream convOutFile; convOutFile << "Kovasznay_conv_" << Re <<".txt"; if (commRank == 0) convOut.open(convOutFile.str().c_str()); set<int> nonlinearVars; nonlinearVars.insert(u1->ID()); nonlinearVars.insert(u2->ID()); 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, nonlinearVars); iterCount++; } exporter.exportSolution(backgroundFlow, varFactory, refIndex, 2, cellIDToSubdivision(mesh, 4)); FunctionPtr u1Soln = Function::solution(u1, backgroundFlow); FunctionPtr u2Soln = Function::solution(u2, backgroundFlow); FunctionPtr u1Sqr = (u1Soln-u1Exact)*(u1Soln-u1Exact); FunctionPtr u2Sqr = (u2Soln-u2Exact)*(u2Soln-u2Exact); double u1L2Error = u1Sqr->integrate(mesh, 1e-5); double u2L2Error = u2Sqr->integrate(mesh, 1e-5); double l2Error = sqrt(u1L2Error+u2L2Error); double energyError = solution->energyErrorTotal(); cout << "L2 Error: " << l2Error << " Energy Error: " << energyError << endl; 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); int rank=mpiSession.getRank(); int numProcs=mpiSession.getNProc(); #else int rank = 0; int numProcs = 1; #endif //////////////////// DECLARE VARIABLES /////////////////////// // define test variables VarFactory varFactory; VarPtr tau = varFactory.testVar("\\tau", HDIV); VarPtr v = varFactory.testVar("v", HGRAD); // define trial variables VarPtr uhat = varFactory.traceVar("\\widehat{u}"); VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}"); VarPtr u = varFactory.fieldVar("u"); VarPtr sigma1 = varFactory.fieldVar("\\sigma_1"); VarPtr sigma2 = varFactory.fieldVar("\\sigma_2"); vector<double> beta_const; beta_const.push_back(1.0); beta_const.push_back(0.0); // FunctionPtr beta = Teuchos::rcp(new Beta()); double eps = 1e-2; //////////////////// DEFINE BILINEAR FORM /////////////////////// BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) ); // tau terms: confusionBF->addTerm(sigma1 / eps, tau->x()); confusionBF->addTerm(sigma2 / eps, tau->y()); confusionBF->addTerm(u, tau->div()); confusionBF->addTerm(-uhat, tau->dot_normal()); // v terms: confusionBF->addTerm( sigma1, v->dx() ); confusionBF->addTerm( sigma2, v->dy() ); confusionBF->addTerm( beta_const * u, - v->grad() ); confusionBF->addTerm( beta_n_u_minus_sigma_n, v); //////////////////// DEFINE INNER PRODUCT(S) /////////////////////// // mathematician's norm IPPtr mathIP = Teuchos::rcp(new IP()); mathIP->addTerm(tau); mathIP->addTerm(tau->div()); mathIP->addTerm(v); mathIP->addTerm(v->grad()); // quasi-optimal norm IPPtr qoptIP = Teuchos::rcp(new IP); qoptIP->addTerm( v ); qoptIP->addTerm( tau / eps + v->grad() ); qoptIP->addTerm( beta_const * v->grad() - tau->div() ); // robust test norm IPPtr robIP = Teuchos::rcp(new IP); FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(eps) ); if (enforceLocalConservation) { robIP->addZeroMeanTerm( v ); } else { robIP->addTerm( ip_scaling * v ); } robIP->addTerm( sqrt(eps) * v->grad() ); robIP->addTerm( beta_const * v->grad() ); robIP->addTerm( tau->div() ); robIP->addTerm( ip_scaling/sqrt(eps) * tau ); //////////////////// SPECIFY RHS /////////////////////// FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) ); Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy ); FunctionPtr f = zero; rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary! //////////////////// CREATE BCs /////////////////////// Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy ); // SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary ); // SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary ); SpatialFilterPtr inflowTop = Teuchos::rcp(new InflowLshapeTop); SpatialFilterPtr inflowBot = Teuchos::rcp(new InflowLshapeBottom); SpatialFilterPtr LshapeBot1 = Teuchos::rcp(new LshapeBottom1); SpatialFilterPtr LshapeBot2 = Teuchos::rcp(new LshapeBottom2); SpatialFilterPtr Top = Teuchos::rcp(new LshapeTop); SpatialFilterPtr Out = Teuchos::rcp(new LshapeOutflow); FunctionPtr u0 = Teuchos::rcp( new U0 ); bc->addDirichlet(uhat, LshapeBot1, u0); bc->addDirichlet(uhat, LshapeBot2, u0); bc->addDirichlet(uhat, Top, u0); bc->addDirichlet(uhat, Out, u0); FunctionPtr n = Teuchos::rcp( new UnitNormalFunction ); // bc->addDirichlet(uhat, inflowBot, u0); FunctionPtr u0Top = Teuchos::rcp(new ParabolicProfile); FunctionPtr u0Bot = Teuchos::rcp(new LinearProfile); bc->addDirichlet(beta_n_u_minus_sigma_n, inflowTop, beta_const*n*u0Top); // bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBot, beta_const*n*u0Bot); bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBot, beta_const*n*zero); //////////////////// BUILD MESH /////////////////////// // define nodes for mesh int H1Order = 2, pToAdd = 2; /* FieldContainer<double> quadPoints(4,2); quadPoints(0,0) = 0.0; // x1 quadPoints(0,1) = 0.0; // y1 quadPoints(1,0) = 1.0; quadPoints(1,1) = 0.0; quadPoints(2,0) = 1.0; quadPoints(2,1) = 1.0; quadPoints(3,0) = 0.0; quadPoints(3,1) = 1.0; int horizontalCells = 1, verticalCells = 1; // create a pointer to a new mesh: Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(quadPoints, horizontalCells, verticalCells, confusionBF, H1Order, H1Order+pToAdd); */ Teuchos::RCP<Mesh> mesh; // L-shaped domain for double ramp problem FieldContainer<double> A(2), B(2), C(2), D(2), E(2), F(2), G(2), H(2); A(0) = 0.0; A(1) = 0.5; B(0) = 0.0; B(1) = 1.0; C(0) = 0.5; C(1) = 1.0; D(0) = 1.0; D(1) = 1.0; E(0) = 1.0; E(1) = 0.5; F(0) = 1.0; F(1) = 0.0; G(0) = 0.5; G(1) = 0.0; H(0) = 0.5; H(1) = 0.5; vector<FieldContainer<double> > vertices; vertices.push_back(A); int A_index = 0; vertices.push_back(B); int B_index = 1; vertices.push_back(C); int C_index = 2; vertices.push_back(D); int D_index = 3; vertices.push_back(E); int E_index = 4; vertices.push_back(F); int F_index = 5; vertices.push_back(G); int G_index = 6; vertices.push_back(H); int H_index = 7; vector< vector<int> > elementVertices; vector<int> el1, el2, el3, el4, el5; // left patch: el1.push_back(A_index); el1.push_back(H_index); el1.push_back(C_index); el1.push_back(B_index); // top right: el2.push_back(H_index); el2.push_back(E_index); el2.push_back(D_index); el2.push_back(C_index); // bottom right: el3.push_back(G_index); el3.push_back(F_index); el3.push_back(E_index); el3.push_back(H_index); elementVertices.push_back(el1); elementVertices.push_back(el2); elementVertices.push_back(el3); mesh = Teuchos::rcp( new Mesh(vertices, elementVertices, confusionBF, H1Order, pToAdd) ); //////////////////// SOLVE & REFINE /////////////////////// // Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, qoptIP) ); Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) ); // solution->setFilter(pc); if (enforceLocalConservation) { FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) ); solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero); } double energyThreshold = 0.2; // for mesh refinements RefinementStrategy refinementStrategy( solution, energyThreshold ); int numRefs = 8; for (int refIndex=0; refIndex<numRefs; refIndex++) { solution->solve(false); refinementStrategy.refine(rank==0); // print to console on rank 0 } // one more solve on the final refined mesh: solution->solve(false); if (rank==0) { solution->writeToVTK("step.vtu",min(H1Order+1,4)); solution->writeFluxesToFile(uhat->ID(), "uhat.dat"); cout << "wrote files: u.m, uhat.dat\n"; } return 0; }
// tests whether a mixed type LT bool ScratchPadTests::testIntegrateDiscontinuousFunction() { bool success = true; //////////////////// DECLARE VARIABLES /////////////////////// // define test variables VarFactoryPtr varFactory = VarFactory::varFactory(); VarPtr v = varFactory->testVar("v", HGRAD); vector<double> beta; beta.push_back(1.0); beta.push_back(1.0); //////////////////// DEFINE INNER PRODUCT(S) /////////////////////// // robust test norm IPPtr ip = Teuchos::rcp(new IP); ip->addTerm(v); ip->addTerm(beta*v->grad()); // for projections IPPtr ipL2 = Teuchos::rcp(new IP); ipL2->addTerm(v); // define trial variables VarPtr beta_n_u = varFactory->fluxVar("\\widehat{\\beta \\cdot n }"); VarPtr u = varFactory->fieldVar("u"); //////////////////// BUILD MESH /////////////////////// BFPtr convectionBF = Teuchos::rcp( new BF(varFactory) ); // v terms: convectionBF->addTerm( -u, beta * v->grad() ); convectionBF->addTerm( beta_n_u, v); // define nodes for mesh int order = 1; int H1Order = order+1; int pToAdd = 1; // create a pointer to a new mesh: Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(2, 1, convectionBF, H1Order, H1Order+pToAdd); //////////////////// integrate discontinuous function - cellIDFunction /////////////////////// // FunctionPtr cellIDFxn = Teuchos::rcp(new CellIDFunction); // should be 0 on cellID 0, 1 on cellID 1 set<int> cellIDs; cellIDs.insert(1); // 0 on cell 0, 1 on cell 1 FunctionPtr indicator = Teuchos::rcp(new IndicatorFunction(cellIDs)); // should be 0 on cellID 0, 1 on cellID 1 double jumpWeight = 13.3; // some random number FunctionPtr edgeRestrictionFxn = Teuchos::rcp(new EdgeFunction); FunctionPtr X = Function::xn(1); LinearTermPtr integrandLT = Function::constant(1.0)*v + Function::constant(jumpWeight)*X*edgeRestrictionFxn*v; // make riesz representation function to more closely emulate the error rep LinearTermPtr indicatorLT = Teuchos::rcp(new LinearTerm);// residual indicatorLT->addTerm(indicator*v); Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ipL2, indicatorLT)); riesz->computeRieszRep(); map<int,FunctionPtr> vmap; vmap[v->ID()] = RieszRep::repFunction(v,riesz); // SHOULD BE L2 projection = same thing!!! FunctionPtr volumeIntegrand = integrandLT->evaluate(vmap,false); FunctionPtr edgeRestrictedIntegrand = integrandLT->evaluate(vmap,true); double edgeRestrictedValue = volumeIntegrand->integrate(mesh,10) + edgeRestrictedIntegrand->integrate(mesh,10); double expectedValue = .5 + .5*jumpWeight; double diff = abs(expectedValue-edgeRestrictedValue); if (abs(diff)>1e-11) { success = false; cout << "Failed testIntegrateDiscontinuousFunction() with expectedValue = " << expectedValue << " and actual value = " << edgeRestrictedValue << endl; } return success; }
int main(int argc, char *argv[]) { #ifdef HAVE_MPI Teuchos::GlobalMPISession mpiSession(&argc, &argv,0); choice::MpiArgs args( argc, argv ); #else choice::Args args( argc, argv ); #endif int rank = Teuchos::GlobalMPISession::getRank(); int numProcs = Teuchos::GlobalMPISession::getNProc(); int nCells = args.Input<int>("--nCells", "num cells",2); int numRefs = args.Input<int>("--numRefs","num adaptive refinements",0); int numPreRefs = args.Input<int>("--numPreRefs","num preemptive adaptive refinements",0); int order = args.Input<int>("--order","order of approximation",2); double eps = args.Input<double>("--epsilon","diffusion parameter",1e-2); double energyThreshold = args.Input<double>("-energyThreshold","energy thresh for adaptivity", .5); double rampHeight = args.Input<double>("--rampHeight","ramp height at x = 2", 0.0); bool useAnisotropy = args.Input<bool>("--useAnisotropy","aniso flag ", false); FunctionPtr zero = Function::constant(0.0); FunctionPtr one = Function::constant(1.0); FunctionPtr n = Teuchos::rcp( new UnitNormalFunction ); vector<double> e1,e2; e1.push_back(1.0); e1.push_back(0.0); e2.push_back(0.0); e2.push_back(1.0); //////////////////// DECLARE VARIABLES /////////////////////// // define test variables VarFactory varFactory; VarPtr tau = varFactory.testVar("\\tau", HDIV); VarPtr v = varFactory.testVar("v", HGRAD); // define trial variables VarPtr uhat = varFactory.traceVar("\\widehat{u}"); VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}"); VarPtr u = varFactory.fieldVar("u"); VarPtr sigma1 = varFactory.fieldVar("\\sigma_1"); VarPtr sigma2 = varFactory.fieldVar("\\sigma_2"); vector<double> beta; beta.push_back(1.0); beta.push_back(0.0); //////////////////// DEFINE BILINEAR FORM /////////////////////// BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) ); // tau terms: confusionBF->addTerm(sigma1 / eps, tau->x()); confusionBF->addTerm(sigma2 / eps, tau->y()); confusionBF->addTerm(u, tau->div()); confusionBF->addTerm(uhat, -tau->dot_normal()); // v terms: confusionBF->addTerm( sigma1, v->dx() ); confusionBF->addTerm( sigma2, v->dy() ); confusionBF->addTerm( -u, beta * v->grad() ); confusionBF->addTerm( beta_n_u_minus_sigma_n, v); // first order term with magnitude alpha double alpha = 0.0; confusionBF->addTerm(alpha * u, v); //////////////////// DEFINE INNER PRODUCT(S) /////////////////////// // robust test norm IPPtr robIP = Teuchos::rcp(new IP); FunctionPtr C_h = Teuchos::rcp( new EpsilonScaling(eps) ); FunctionPtr invH = Teuchos::rcp(new InvHScaling); FunctionPtr invSqrtH = Teuchos::rcp(new InvSqrtHScaling); FunctionPtr sqrtH = Teuchos::rcp(new SqrtHScaling); robIP->addTerm(v*alpha); robIP->addTerm(invSqrtH*v); // robIP->addTerm(v); robIP->addTerm(sqrt(eps) * v->grad() ); robIP->addTerm(beta * v->grad() ); robIP->addTerm(tau->div() ); robIP->addTerm(C_h/sqrt(eps) * tau ); LinearTermPtr vVecLT = Teuchos::rcp(new LinearTerm); LinearTermPtr tauVecLT = Teuchos::rcp(new LinearTerm); vVecLT->addTerm(sqrt(eps)*v->grad()); tauVecLT->addTerm(C_h/sqrt(eps)*tau); LinearTermPtr restLT = Teuchos::rcp(new LinearTerm); restLT->addTerm(alpha*v); restLT->addTerm(invSqrtH*v); restLT = restLT + beta * v->grad(); restLT = restLT + tau->div(); //////////////////// SPECIFY RHS /////////////////////// Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy ); FunctionPtr f = zero; // f = one; rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary! //////////////////// CREATE BCs /////////////////////// Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy ); // SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary ); // SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary); // bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, zero); // bc->addDirichlet(uhat, outflowBoundary, zero); SpatialFilterPtr rampInflow = Teuchos::rcp(new LeftInflow); SpatialFilterPtr rampBoundary = MeshUtilities::rampBoundary(rampHeight); SpatialFilterPtr freeStream = Teuchos::rcp(new FreeStreamBoundary); SpatialFilterPtr outflowBoundary = Teuchos::rcp(new OutflowBoundary); bc->addDirichlet(uhat, rampBoundary, one); // bc->addDirichlet(uhat, outflowBoundary, one); bc->addDirichlet(beta_n_u_minus_sigma_n, rampInflow, zero); bc->addDirichlet(beta_n_u_minus_sigma_n, freeStream, zero); //////////////////// BUILD MESH /////////////////////// // define nodes for mesh int H1Order = order+1; int pToAdd = 2; // create a pointer to a new mesh: // Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd); Teuchos::RCP<Mesh> mesh = MeshUtilities::buildRampMesh(rampHeight,confusionBF, H1Order, H1Order+pToAdd); mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC"))); //////////////////// SOLVE & REFINE /////////////////////// Teuchos::RCP<Solution> solution; solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) ); // solution->solve(false); solution->condensedSolve(); LinearTermPtr residual = rhs->linearTermCopy(); residual->addTerm(-confusionBF->testFunctional(solution)); RieszRepPtr rieszResidual = Teuchos::rcp(new RieszRep(mesh, robIP, residual)); rieszResidual->computeRieszRep(); FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,rieszResidual)); FunctionPtr e_tau = Teuchos::rcp(new RepFunction(tau,rieszResidual)); map<int,FunctionPtr> errRepMap; errRepMap[v->ID()] = e_v; errRepMap[tau->ID()] = e_tau; FunctionPtr errTau = tauVecLT->evaluate(errRepMap,false); FunctionPtr errV = vVecLT->evaluate(errRepMap,false); FunctionPtr errRest = restLT->evaluate(errRepMap,false); FunctionPtr xErr = (errTau->x())*(errTau->x()) + (errV->dx())*(errV->dx()); FunctionPtr yErr = (errTau->y())*(errTau->y()) + (errV->dy())*(errV->dy()); FunctionPtr restErr = errRest*errRest; RefinementStrategy refinementStrategy( solution, energyThreshold ); //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// // PRE REFINEMENTS //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// if (rank==0) { cout << "Number of pre-refinements = " << numPreRefs << endl; } for (int i =0; i<=numPreRefs; i++) { vector<ElementPtr> elems = mesh->activeElements(); vector<ElementPtr>::iterator elemIt; vector<int> wallCells; for (elemIt=elems.begin(); elemIt != elems.end(); elemIt++) { int cellID = (*elemIt)->cellID(); int numSides = mesh->getElement(cellID)->numSides(); FieldContainer<double> vertices(numSides,2); //for quads mesh->verticesForCell(vertices, cellID); bool cellIDset = false; for (int j = 0; j<numSides; j++) { if ((abs(vertices(j,0)-1.0)<1e-7) && (abs(vertices(j,1))<1e-7) && !cellIDset) // if at singularity, i.e. if a vertex is (1,0) { wallCells.push_back(cellID); cellIDset = true; } } } if (i<numPreRefs) { refinementStrategy.refineCells(wallCells); } } //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// VTKExporter exporter(solution, mesh, varFactory); for (int refIndex=0; refIndex<numRefs; refIndex++) { if (rank==0) { cout << "on ref index " << refIndex << endl; } rieszResidual->computeRieszRep(); // in preparation to get anisotropy vector<int> cellIDs; refinementStrategy.getCellsAboveErrorThreshhold(cellIDs); map<int,double> energyError = solution->energyError(); map<int,double> xErrMap = xErr->cellIntegrals(cellIDs,mesh,5,true); map<int,double> yErrMap = yErr->cellIntegrals(cellIDs,mesh,5,true); map<int,double> restErrMap = restErr->cellIntegrals(cellIDs,mesh,5,true); for (vector<ElementPtr>::iterator elemIt = mesh->activeElements().begin(); elemIt!=mesh->activeElements().end(); elemIt++) { int cellID = (*elemIt)->cellID(); double err = xErrMap[cellID]+ yErrMap[cellID] + restErrMap[cellID]; if (rank==0) cout << "err thru LT = " << sqrt(err) << ", while energy err = " << energyError[cellID] << endl; } map<int,double> ratio,xErr,yErr; vector<ElementPtr> elems = mesh->activeElements(); for (vector<ElementPtr>::iterator elemIt = elems.begin(); elemIt!=elems.end(); elemIt++) { int cellID = (*elemIt)->cellID(); ratio[cellID] = 0.0; xErr[cellID] = 0.0; yErr[cellID] = 0.0; if (std::find(cellIDs.begin(),cellIDs.end(),cellID)!=cellIDs.end()) // if this cell is above energy thresh { ratio[cellID] = yErrMap[cellID]/xErrMap[cellID]; xErr[cellID] = xErrMap[cellID]; yErr[cellID] = yErrMap[cellID]; } } FunctionPtr ratioFxn = Teuchos::rcp(new EnergyErrorFunction(ratio)); FunctionPtr xErrFxn = Teuchos::rcp(new EnergyErrorFunction(xErr)); FunctionPtr yErrFxn = Teuchos::rcp(new EnergyErrorFunction(yErr)); std::ostringstream oss; oss << refIndex; exporter.exportFunction(ratioFxn, string("ratio")+oss.str()); exporter.exportFunction(xErrFxn, string("xErr")+oss.str()); exporter.exportFunction(yErrFxn, string("yErr")+oss.str()); if (useAnisotropy) { refinementStrategy.refine(rank==0,xErrMap,yErrMap); //anisotropic refinements } else { refinementStrategy.refine(rank==0); // no anisotropy } solution->condensedSolve(); } // final solve on final mesh solution->condensedSolve(); //////////////////// print to file /////////////////////// FunctionPtr orderFxn = Teuchos::rcp(new MeshPolyOrderFunction(mesh)); std::ostringstream oss; oss << nCells; if (rank==0) { exporter.exportSolution(string("robustIP")+oss.str()); exporter.exportFunction(orderFxn, "meshOrder"); cout << endl; } return 0; }
bool ScratchPadTests::testGalerkinOrthogonality() { double tol = 1e-11; bool success = true; //////////////////// DECLARE VARIABLES /////////////////////// // define test variables VarFactoryPtr varFactory = VarFactory::varFactory(); VarPtr v = varFactory->testVar("v", HGRAD); vector<double> beta; beta.push_back(1.0); beta.push_back(1.0); //////////////////// DEFINE INNER PRODUCT(S) /////////////////////// // robust test norm IPPtr ip = Teuchos::rcp(new IP); ip->addTerm(v); ip->addTerm(beta*v->grad()); // define trial variables VarPtr beta_n_u = varFactory->fluxVar("\\widehat{\\beta \\cdot n }"); VarPtr u = varFactory->fieldVar("u"); //////////////////// BUILD MESH /////////////////////// BFPtr convectionBF = Teuchos::rcp( new BF(varFactory) ); FunctionPtr n = Function::normal(); // v terms: convectionBF->addTerm( -u, beta * v->grad() ); convectionBF->addTerm( beta_n_u, v); // define nodes for mesh int order = 2; int H1Order = order+1; int pToAdd = 1; // create a pointer to a new mesh: Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(4, convectionBF, H1Order, H1Order+pToAdd); //////////////////// SOLVE /////////////////////// RHSPtr rhs = RHS::rhs(); BCPtr bc = BC::bc(); SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary ); SpatialFilterPtr outflowBoundary = Teuchos::rcp( new NegatedSpatialFilter(inflowBoundary) ); FunctionPtr uIn; uIn = Teuchos::rcp(new Uinflow); // uses a discontinuous piecewise-constant basis function on left and bottom sides of square bc->addDirichlet(beta_n_u, inflowBoundary, beta*n*uIn); Teuchos::RCP<Solution> solution; solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) ); solution->solve(false); FunctionPtr uFxn = Function::solution(u, solution); FunctionPtr fnhatFxn = Function::solution(beta_n_u,solution); // make residual for riesz representation function LinearTermPtr residual = Teuchos::rcp(new LinearTerm);// residual FunctionPtr parity = Function::sideParity(); residual->addTerm(-fnhatFxn*v + (beta*uFxn)*v->grad()); Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ip, residual)); riesz->computeRieszRep(); map<int,FunctionPtr> err_rep_map; err_rep_map[v->ID()] = RieszRep::repFunction(v,riesz); //////////////////// GET BOUNDARY CONDITION DATA /////////////////////// FieldContainer<GlobalIndexType> bcGlobalIndices; FieldContainer<double> bcGlobalValues; mesh->boundary().bcsToImpose(bcGlobalIndices,bcGlobalValues,*(solution->bc()), NULL); set<int> bcInds; for (int i=0; i<bcGlobalIndices.dimension(0); i++) { bcInds.insert(bcGlobalIndices(i)); } //////////////////// CHECK GALERKIN ORTHOGONALITY /////////////////////// BCPtr nullBC; RHSPtr nullRHS; IPPtr nullIP; SolutionPtr solnPerturbation = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) ); map< int, vector<DofInfo> > infoMap = constructGlobalDofToLocalDofInfoMap(mesh); for (map< int, vector<DofInfo> >::iterator mapIt = infoMap.begin(); mapIt != infoMap.end(); mapIt++) { int dofIndex = mapIt->first; vector< DofInfo > dofInfoVector = mapIt->second; // all the local dofs that map to dofIndex // create perturbation in direction du solnPerturbation->clear(); // clear all solns // set each corresponding local dof to 1.0 for (vector< DofInfo >::iterator dofInfoIt = dofInfoVector.begin(); dofInfoIt != dofInfoVector.end(); dofInfoIt++) { DofInfo info = *dofInfoIt; FieldContainer<double> solnCoeffs(info.basisCardinality); solnCoeffs(info.basisOrdinal) = 1.0; solnPerturbation->setSolnCoeffsForCellID(solnCoeffs, info.cellID, info.trialID, info.sideIndex); } // solnPerturbation->setSolnCoeffForGlobalDofIndex(1.0,dofIndex); LinearTermPtr b_du = convectionBF->testFunctional(solnPerturbation); FunctionPtr gradient = b_du->evaluate(err_rep_map, TestingUtilities::isFluxOrTraceDof(mesh,dofIndex)); // use boundary part only if flux double grad = gradient->integrate(mesh,10); if (!TestingUtilities::isFluxOrTraceDof(mesh,dofIndex) && abs(grad)>tol) // if we're not single-precision zero FOR FIELDS { // int cellID = mesh->getGlobalToLocalMap()[dofIndex].first; cout << "Failed testGalerkinOrthogonality() for fields with diff " << abs(grad) << " at dof " << dofIndex << "; info:" << endl; cout << dofInfoString(infoMap[dofIndex]); success = false; } } FieldContainer<double> errorJumps(mesh->numGlobalDofs()); //initialized to zero // just test fluxes ON INTERNAL SKELETON here set<GlobalIndexType> activeCellIDs = mesh->getActiveCellIDsGlobal(); for (GlobalIndexType activeCellID : activeCellIDs) { ElementPtr elem = mesh->getElement(activeCellID); for (int sideIndex = 0; sideIndex < 4; sideIndex++) { ElementTypePtr elemType = elem->elementType(); vector<int> localDofIndices = elemType->trialOrderPtr->getDofIndices(beta_n_u->ID(), sideIndex); for (int i = 0; i<localDofIndices.size(); i++) { int globalDofIndex = mesh->globalDofIndex(elem->cellID(), localDofIndices[i]); vector< DofInfo > dofInfoVector = infoMap[globalDofIndex]; solnPerturbation->clear(); TestingUtilities::setSolnCoeffForGlobalDofIndex(solnPerturbation,1.0,globalDofIndex); // also add in BCs for (int i = 0; i<bcGlobalIndices.dimension(0); i++) { TestingUtilities::setSolnCoeffForGlobalDofIndex(solnPerturbation,bcGlobalValues(i),bcGlobalIndices(i)); } LinearTermPtr b_du = convectionBF->testFunctional(solnPerturbation); FunctionPtr gradient = b_du->evaluate(err_rep_map, TestingUtilities::isFluxOrTraceDof(mesh,globalDofIndex)); // use boundary part only if flux double jump = gradient->integrate(mesh,10); errorJumps(globalDofIndex) += jump; } } } for (int i = 0; i<mesh->numGlobalDofs(); i++) { if (abs(errorJumps(i))>tol) { cout << "Failing Galerkin orthogonality test for fluxes with diff " << errorJumps(i) << " at dof " << i << endl; cout << dofInfoString(infoMap[i]); success = false; } } return success; }
int main(int argc, char *argv[]) { #ifdef HAVE_MPI Teuchos::GlobalMPISession mpiSession(&argc, &argv,0); int rank=mpiSession.getRank(); int numProcs=mpiSession.getNProc(); #else int rank = 0; int numProcs = 1; #endif bool useCompliantGraphNorm = false; bool enforceOneIrregularity = true; bool writeStiffnessMatrices = false; bool writeWorstCaseGramMatrices = false; int numRefs = 10; // problem parameters: double eps = 1e-8; vector<double> beta_const; beta_const.push_back(2.0); beta_const.push_back(1.0); int k = 2, delta_k = 2; Teuchos::CommandLineProcessor cmdp(false,true); // false: don't throw exceptions; true: do return errors for unrecognized options cmdp.setOption("polyOrder",&k,"polynomial order for field variable u"); cmdp.setOption("delta_k", &delta_k, "test space polynomial order enrichment"); cmdp.setOption("numRefs",&numRefs,"number of refinements"); cmdp.setOption("eps", &eps, "epsilon"); if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL) { #ifdef HAVE_MPI MPI_Finalize(); #endif return -1; } int H1Order = k + 1; if (rank==0) { string normChoice = useCompliantGraphNorm ? "unit-compliant graph norm" : "standard graph norm"; cout << "Using " << normChoice << "." << endl; cout << "eps = " << eps << endl; cout << "numRefs = " << numRefs << endl; cout << "p = " << k << endl; } //////////////////// DECLARE VARIABLES /////////////////////// // define test variables VarFactory varFactory; VarPtr tau = varFactory.testVar("\\tau", HDIV); VarPtr v = varFactory.testVar("v", HGRAD); // define trial variables VarPtr uhat = varFactory.traceVar("\\widehat{u}"); VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}"); VarPtr u; if (useCompliantGraphNorm) { u = varFactory.fieldVar("u",HGRAD); } else { u = varFactory.fieldVar("u"); } VarPtr sigma1 = varFactory.fieldVar("\\sigma_1"); VarPtr sigma2 = varFactory.fieldVar("\\sigma_2"); //////////////////// DEFINE BILINEAR FORM /////////////////////// BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) ); // tau terms: confusionBF->addTerm(sigma1 / eps, tau->x()); confusionBF->addTerm(sigma2 / eps, tau->y()); confusionBF->addTerm(u, tau->div()); confusionBF->addTerm(-uhat, tau->dot_normal()); // v terms: confusionBF->addTerm( sigma1, v->dx() ); confusionBF->addTerm( sigma2, v->dy() ); confusionBF->addTerm( beta_const * u, - v->grad() ); confusionBF->addTerm( beta_n_u_minus_sigma_n, v); //////////////////// DEFINE INNER PRODUCT(S) /////////////////////// // mathematician's norm IPPtr mathIP = Teuchos::rcp(new IP()); mathIP->addTerm(tau); mathIP->addTerm(tau->div()); mathIP->addTerm(v); mathIP->addTerm(v->grad()); // quasi-optimal norm IPPtr qoptIP = Teuchos::rcp(new IP); if (!useCompliantGraphNorm) { qoptIP->addTerm( tau / eps + v->grad() ); qoptIP->addTerm( beta_const * v->grad() - tau->div() ); qoptIP->addTerm( v ); } else { FunctionPtr h = Teuchos::rcp( new hFunction ); // here, we're aiming at optimality in 1/h^2 |u|^2 + 1/eps^2 |sigma|^2 qoptIP->addTerm( tau + eps * v->grad() ); qoptIP->addTerm( h * beta_const * v->grad() - tau->div() ); qoptIP->addTerm(v); qoptIP->addTerm(tau); } //////////////////// SPECIFY RHS /////////////////////// RHSPtr rhs = RHS::rhs(); FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) ); rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary! //////////////////// CREATE BCs /////////////////////// BCPtr bc = BC::bc(); SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary ); SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary ); FunctionPtr u0 = Teuchos::rcp( new U0 ); bc->addDirichlet(uhat, outflowBoundary, u0); bc->addDirichlet(uhat, inflowBoundary, u0); // Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp(new PenaltyConstraints); // pc->addConstraint(uhat==u0,inflowBoundary); //////////////////// BUILD MESH /////////////////////// // create a new mesh on a single-cell, unit square domain Teuchos::RCP<Mesh> mesh = MeshFactory::quadMeshMinRule(confusionBF, H1Order, delta_k); //////////////////// SOLVE & REFINE /////////////////////// Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, qoptIP) ); // solution->setFilter(pc); double energyThreshold = 0.2; // for mesh refinements bool useRieszRepBasedRefStrategy = true; if (rank==0) { if (useRieszRepBasedRefStrategy) { cout << "using RieszRep-based refinement strategy.\n"; } else { cout << "using solution-based refinement strategy.\n"; } } Teuchos::RCP<RefinementStrategy> refinementStrategy; if (!useRieszRepBasedRefStrategy) { refinementStrategy = Teuchos::rcp( new RefinementStrategy( solution, energyThreshold ) ); } else { LinearTermPtr residual = confusionBF->testFunctional(solution) - rhs->linearTerm(); refinementStrategy = Teuchos::rcp( new RefinementStrategy( mesh, residual, qoptIP, energyThreshold ) ); } refinementStrategy->setReportPerCellErrors(true); refinementStrategy->setEnforceOneIrregularity(enforceOneIrregularity); for (int refIndex=0; refIndex<numRefs; refIndex++){ if (writeStiffnessMatrices) { string stiffnessFile = fileNameForRefinement("confusion_stiffness", refIndex); solution->setWriteMatrixToFile(true, stiffnessFile); } solution->solve(); if (writeWorstCaseGramMatrices) { string gramFile = fileNameForRefinement("confusion_gram", refIndex); bool jacobiScaling = true; double condNum = MeshUtilities::computeMaxLocalConditionNumber(qoptIP, mesh, jacobiScaling, gramFile); if (rank==0) { cout << "estimated worst-case Gram matrix condition number: " << condNum << endl; cout << "putative worst-case Gram matrix written to file " << gramFile << endl; } } if (refIndex == numRefs-1) { // write out second-to-last mesh if (rank==0) GnuPlotUtil::writeComputationalMeshSkeleton("confusionMesh", mesh, true); } refinementStrategy->refine(rank==0); // print to console on rank 0 } if (writeStiffnessMatrices) { string stiffnessFile = fileNameForRefinement("confusion_stiffness", numRefs); solution->setWriteMatrixToFile(true, stiffnessFile); } if (writeWorstCaseGramMatrices) { string gramFile = fileNameForRefinement("confusion_gram", numRefs); bool jacobiScaling = true; double condNum = MeshUtilities::computeMaxLocalConditionNumber(qoptIP, mesh, jacobiScaling, gramFile); if (rank==0) { cout << "estimated worst-case Gram matrix condition number: " << condNum << endl; cout << "putative worst-case Gram matrix written to file " << gramFile << endl; } } // one more solve on the final refined mesh: solution->solve(); #ifdef HAVE_EPETRAEXT_HDF5 ostringstream dir_name; dir_name << "confusion_eps" << eps; HDF5Exporter exporter(mesh,dir_name.str()); exporter.exportSolution(solution, varFactory, 0); if (rank==0) cout << "wrote solution to " << dir_name.str() << endl; #endif return 0; }
// tests to make sure that the rieszNorm computed via matrices is the same as the one computed thru direct integration bool ScratchPadTests::testRieszIntegration() { double tol = 1e-11; bool success = true; int nCells = 2; double eps = .25; //////////////////// DECLARE VARIABLES /////////////////////// // define test variables VarFactoryPtr varFactory = VarFactory::varFactory(); VarPtr tau = varFactory->testVar("\\tau", HDIV); VarPtr v = varFactory->testVar("v", HGRAD); // define trial variables VarPtr uhat = varFactory->traceVar("\\widehat{u}"); VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}"); VarPtr u = varFactory->fieldVar("u"); VarPtr sigma1 = varFactory->fieldVar("\\sigma_1"); VarPtr sigma2 = varFactory->fieldVar("\\sigma_2"); vector<double> beta; beta.push_back(1.0); beta.push_back(0.0); //////////////////// DEFINE BILINEAR FORM /////////////////////// BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) ); // tau terms: confusionBF->addTerm(sigma1 / eps, tau->x()); confusionBF->addTerm(sigma2 / eps, tau->y()); confusionBF->addTerm(u, tau->div()); confusionBF->addTerm(uhat, -tau->dot_normal()); // v terms: confusionBF->addTerm( sigma1, v->dx() ); confusionBF->addTerm( sigma2, v->dy() ); confusionBF->addTerm( -u, beta * v->grad() ); confusionBF->addTerm( beta_n_u_minus_sigma_n, v); //////////////////// DEFINE INNER PRODUCT(S) /////////////////////// // robust test norm IPPtr ip = Teuchos::rcp(new IP); // just H1 projection ip->addTerm(v->grad()); ip->addTerm(v); ip->addTerm(tau); ip->addTerm(tau->div()); //////////////////// SPECIFY RHS AND HELPFUL FUNCTIONS /////////////////////// FunctionPtr n = Function::normal(); vector<double> e1,e2; e1.push_back(1.0); e1.push_back(0.0); e2.push_back(0.0); e2.push_back(1.0); FunctionPtr one = Function::constant(1.0); FunctionPtr zero = Function::constant(0.0); RHSPtr rhs = RHS::rhs(); FunctionPtr f = one; rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary! //////////////////// CREATE BCs /////////////////////// BCPtr bc = BC::bc(); SpatialFilterPtr squareBoundary = Teuchos::rcp( new SquareBoundary ); bc->addDirichlet(uhat, squareBoundary, zero); //////////////////// BUILD MESH /////////////////////// // define nodes for mesh int order = 2; int H1Order = order+1; int pToAdd = 2; // create a pointer to a new mesh: Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd); //////////////////// SOLVE & REFINE /////////////////////// LinearTermPtr lt = Teuchos::rcp(new LinearTerm); FunctionPtr fxn = Function::xn(1); // fxn = x lt->addTerm(fxn*v + fxn->grad()*v->grad()); lt->addTerm(fxn*tau->x() + fxn*tau->y() + (fxn->dx() + fxn->dy())*tau->div()); Teuchos::RCP<RieszRep> rieszLT = Teuchos::rcp(new RieszRep(mesh, ip, lt)); rieszLT->computeRieszRep(); double rieszNorm = rieszLT->getNorm(); FunctionPtr e_v = RieszRep::repFunction(v,rieszLT); FunctionPtr e_tau = RieszRep::repFunction(tau,rieszLT); map<int,FunctionPtr> repFxns; repFxns[v->ID()] = e_v; repFxns[tau->ID()] = e_tau; double integratedNorm = sqrt((lt->evaluate(repFxns,false))->integrate(mesh,5,true)); success = abs(rieszNorm-integratedNorm)<tol; if (success==false) { cout << "Failed testRieszIntegration; riesz norm is computed to be = " << rieszNorm << ", while using integration it's computed to be " << integratedNorm << endl; return success; } return success; }
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 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; }
void Projector::projectFunctionOntoBasis(FieldContainer<double> &basisCoefficients, FunctionPtr fxn, BasisPtr basis, BasisCachePtr basisCache) { VarFactory varFactory; VarPtr var; if (! basisCache->isSideCache()) { if (fxn->rank()==0) { var = varFactory.fieldVar("dummyField"); } else if (fxn->rank()==1) { var = varFactory.fieldVar("dummyField",VECTOR_L2); } else { TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "projectFunctionOntoBasis does not yet support functions of rank > 1."); } } else { // for present purposes, distinction between trace and flux doesn't really matter, // except that parities come into the IP computation for fluxes (even though they'll cancel), // and since basisCache doesn't necessarily have parities defined (especially in tests), // it's simpler all around to use traces. var = varFactory.traceVar("dummyTrace"); } IPPtr ip = Teuchos::rcp( new IP ); ip->addTerm(var); // simple L^2 IP projectFunctionOntoBasis(basisCoefficients, fxn, basis, basisCache, ip, var); /* // TODO: rewrite this to use the version above (define L2 inner product for a dummy variable, then pass in this ip and varPtr) shards::CellTopology cellTopo = basis->domainTopology(); DofOrderingPtr dofOrderPtr = Teuchos::rcp(new DofOrdering()); // assume only L2 projections IntrepidExtendedTypes::EOperatorExtended op = IntrepidExtendedTypes::OP_VALUE; // have information, build inner product matrix int numDofs = basis->getCardinality(); const FieldContainer<double> *cubPoints = &(basisCache->getPhysicalCubaturePoints()); constFCPtr basisValues = basisCache->getTransformedValues(basis, op); constFCPtr testBasisValues = basisCache->getTransformedWeightedValues(basis, op); int numCells = cubPoints->dimension(0); int numPts = cubPoints->dimension(1); FieldContainer<double> functionValues(numCells,numPts); fxn->values(functionValues, basisCache); FieldContainer<double> gramMatrix(numCells,numDofs,numDofs); FieldContainer<double> ipVector(numCells,numDofs); FunctionSpaceTools::integrate<double>(gramMatrix,*basisValues,*testBasisValues,COMP_BLAS); FunctionSpaceTools::integrate<double>(ipVector,functionValues,*testBasisValues,COMP_BLAS); basisCoefficients.resize(numCells,numDofs); for (int cellIndex=0; cellIndex<numCells; cellIndex++){ Epetra_SerialDenseSolver solver; Epetra_SerialDenseMatrix A(Copy, &gramMatrix(cellIndex,0,0), gramMatrix.dimension(2), gramMatrix.dimension(2), gramMatrix.dimension(1)); // stride -- fc stores in row-major order (a.o.t. SDM) Epetra_SerialDenseVector b(Copy, &ipVector(cellIndex,0), ipVector.dimension(1)); Epetra_SerialDenseVector x(gramMatrix.dimension(1)); if (cellIndex==0) { cout << "legacy projectFunctionOntoBasis: matrix A for cellIndex 0 = " << endl; for (int i=0;i<gramMatrix.dimension(2);i++){ for (int j=0;j<gramMatrix.dimension(1);j++){ cout << A(i,j) << " "; } cout << endl; } cout << endl; cout << "legacy projectFunctionOntoBasis: vector B for cellIndex 0 = " << endl; for (int i=0;i<ipVector.dimension(1);i++){ cout << b(i) << endl; } } solver.SetMatrix(A); int info = solver.SetVectors(x,b); if (info!=0){ cout << "projectFunctionOntoBasis: failed to SetVectors with error " << info << endl; } bool equilibrated = false; if (solver.ShouldEquilibrate()){ solver.EquilibrateMatrix(); solver.EquilibrateRHS(); equilibrated = true; } info = solver.Solve(); if (info!=0){ cout << "projectFunctionOntoBasis: failed to solve with error " << info << endl; } if (equilibrated) { int successLocal = solver.UnequilibrateLHS(); if (successLocal != 0) { cout << "projection: unequilibration FAILED with error: " << successLocal << endl; } } for (int i=0;i<numDofs;i++){ basisCoefficients(cellIndex,i) = x(i); } }*/ }
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; }