bool LobattoBasisTests::testLobattoValues() {
bool success = true;
FunctionPtr x = Function::xn(1);
vector< FunctionPtr > lobattoFunctionsExpected;
// Pavel Solin's first two Lobatto functions:
// lobattoFunctionsExpected.push_back( (1 - x) / 2 );
// lobattoFunctionsExpected.push_back( (1 + x) / 2 );
// Demkowicz's:
lobattoFunctionsExpected.push_back( Function::constant(1.0) );
lobattoFunctionsExpected.push_back( x );
lobattoFunctionsExpected.push_back( (x*x - 1) / 2);
lobattoFunctionsExpected.push_back( (x*x - 1) * x / 2);
lobattoFunctionsExpected.push_back( (x*x - 1) * (5 * x * x - 1) / 8);
lobattoFunctionsExpected.push_back( (x*x - 1) * (7 * x * x - 3) * x / 8);
vector< FunctionPtr > lobattoFunctions;
bool conformingFalse = false;
int n_max = 4;
for (int n=0; n<=n_max; n++) {
lobattoFunctions.push_back( Teuchos::rcp( new LobattoFunction<>(n,conformingFalse,false) ) );
}
VarFactory varFactory;
varFactory.testVar("v", HGRAD);
varFactory.fieldVar("u", L2);
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
MeshPtr mesh = MeshFactory::quadMesh(bf, n_max);
BasisCachePtr basisCache = BasisCache::basisCacheForCell(mesh, 0);
double tol = 1e-12;
for (int n=0; n<=n_max; n++) {
if (! lobattoFunctions[n]->equals(lobattoFunctionsExpected[n], basisCache, tol) ) {
cout << "Lobatto function " << n << " does not match expected.\n";
success = false;
}
}
return success;
}
bool LobattoBasisTests::testLobattoDerivativeValues() {
bool success = true;
FunctionPtr x = Function::xn(1);
vector< FunctionPtr > legendreFunctions; // manually specified
vector< FunctionPtr > lobattoDerivatives;
FunctionPtr one = Function::constant(1);
legendreFunctions.push_back(one);
legendreFunctions.push_back(x);
legendreFunctions.push_back(0.5 * (3 * x * x - 1) );
legendreFunctions.push_back( (5 * x * x * x - 3 * x) / 2);
legendreFunctions.push_back( (1.0 / 8.0) * (35 * x * x * x * x - 30 * x * x + 3) );
legendreFunctions.push_back( (1.0 / 8.0) * (63 * x * x * x * x * x - 70 * x * x * x + 15 * x) );
bool conformingFalse = false;
int n_max = 4;
for (int n=0; n<=n_max+1; n++) {
lobattoDerivatives.push_back( Teuchos::rcp( new LobattoFunction<>(n,conformingFalse,true) ) );
}
VarFactory varFactory;
varFactory.testVar("v", HGRAD);
varFactory.fieldVar("u", L2);
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
MeshPtr mesh = MeshFactory::quadMesh(bf, n_max);
BasisCachePtr basisCache = BasisCache::basisCacheForCell(mesh, 0);
double tol = 1e-8;
for (int n=0; n<=n_max; n++) {
if (! legendreFunctions[n]->equals(lobattoDerivatives[n+1], basisCache, tol) ) {
cout << "Legendre function " << n << " != Lobatto function " << n + 1 << " derivative.\n";
cout << "L_" << n << "(0.5) = " << Function::evaluate(legendreFunctions[n],0.5) << endl;
cout << "l'_" << n+1 << "(0.5) = " << Function::evaluate(lobattoDerivatives[n+1],0.5) << endl;
success = false;
}
}
return success;
}
bool LobattoBasisTests::testLegendreValues() {
bool success = true;
FunctionPtr x = Function::xn(1);
vector< FunctionPtr > legendreFunctionsExpected;
legendreFunctionsExpected.push_back( Function::constant(1.0) );
legendreFunctionsExpected.push_back( x );
legendreFunctionsExpected.push_back( (3 * x*x - 1) / 2);
legendreFunctionsExpected.push_back( (5 * x*x*x - 3*x) / 2);
legendreFunctionsExpected.push_back( (35 * x * x * x * x - 30 * x * x + 3) / 8);
legendreFunctionsExpected.push_back( (63 * x * x * x * x * x - 70 * x * x * x + 15 * x) / 8);
vector< FunctionPtr > legendreFunctions;
int n_max = 4;
for (int n=0; n<=n_max; n++) {
legendreFunctions.push_back( Teuchos::rcp( new LegendreFunction(n) ) );
}
VarFactory varFactory;
varFactory.testVar("v", HGRAD);
varFactory.fieldVar("u", L2);
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
MeshPtr mesh = MeshFactory::quadMesh(bf, n_max);
BasisCachePtr basisCache = BasisCache::basisCacheForCell(mesh, 0);
double tol = 1e-8; // relax to make sure that failure isn't just roundoff
for (int n=0; n<=n_max; n++) {
if (! legendreFunctions[n]->equals(legendreFunctionsExpected[n], basisCache, tol) ) {
cout << "Legendre function " << n << " does not match expected.\n";
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
//////////////////// 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 );
#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 numSteps = args.Input<int>("--numSteps", "num NR steps",20);
int polyOrder = 0;
// define our manufactured solution or problem bilinear form:
bool useTriangles = false;
int pToAdd = 1;
args.Process();
int H1Order = polyOrder + 1;
////////////////////////////////////////////////////////////////////
// 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 = MeshUtilities::buildUnitQuadMesh(nCells , 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),e2(2);
e1[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 = Function::constant(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() ); // omitting term to make IP non-dependent on u
////////////////////////////////////////////////////////////////////
// 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 );
////////////////////////////////////////////////////////////////////
// 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<NullFilter> nullFilter = Teuchos::rcp(new NullFilter);
// Teuchos::RCP<HessianFilter> hessianFilter = Teuchos::rcp(new HessianFilter(hessianBF));
Teuchos::RCP< LineSearchStep > LS_Step = Teuchos::rcp(new LineSearchStep(riesz));
double NL_residual = 9e99;
for (int i = 0;i<numSteps;i++){
// write matrix to file and then resollve without hessian
/*
solution->setFilter(hessianFilter);
stringstream oss;
oss << "hessianMatrix" << i << ".dat";
solution->setWriteMatrixToFile(true,oss.str());
solution->solve(false);
solution->setFilter(nullFilter);
oss.str(""); // clear
oss << "stiffnessMatrix" << i << ".dat";
solution->setWriteMatrixToFile(false,oss.str());
*/
solution->solve(false); // do one solve to initialize things...
double stepLength = 1.0;
stepLength = LS_Step->stepSize(backgroundFlow,solution, NL_residual);
// solution->setWriteMatrixToFile(true,"stiffness.dat");
backgroundFlow->addSolution(solution,stepLength);
NL_residual = LS_Step->getNLResidual();
if (rank==0){
cout << "NL residual after adding = " << NL_residual << " with step size " << stepLength << endl;
}
double fd_gradient;
for (int dofIndex = 0;dofIndex<mesh->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;
}
}
}
VTKExporter exporter(solution, mesh, varFactory);
if (rank==0){
exporter.exportSolution("qopt");
cout << endl;
}
return 0;
}
int main(int argc, char *argv[])
{
// Process command line arguments
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr beta_n_u_hat = varFactory.fluxVar("\\widehat{\\beta \\cdot n }");
VarPtr u = varFactory.fieldVar("u");
FunctionPtr beta = Teuchos::rcp(new Beta());
//////////////////// BUILD MESH ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// define nodes for mesh
FieldContainer<double> meshBoundary(4,2);
meshBoundary(0,0) = -1.0; // x1
meshBoundary(0,1) = -1.0; // y1
meshBoundary(1,0) = 1.0;
meshBoundary(1,1) = -1.0;
meshBoundary(2,0) = 1.0;
meshBoundary(2,1) = 1.0;
meshBoundary(3,0) = -1.0;
meshBoundary(3,1) = 1.0;
int horizontalCells = 32, verticalCells = 32;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
confusionBF, H1Order, H1Order+pToAdd);
////////////////////////////////////////////////////////////////////
// INITIALIZE FLOW FUNCTIONS
////////////////////////////////////////////////////////////////////
BCPtr nullBC = Teuchos::rcp((BC*)NULL);
RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr prevTimeFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
SolutionPtr flowResidual = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
FunctionPtr u_prev_time = Teuchos::rcp( new PreviousSolutionFunction(prevTimeFlow, u) );
//////////////////// DEFINE BILINEAR FORM ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr invDt = Teuchos::rcp(new ScalarParamFunction(1.0/dt));
// v terms:
confusionBF->addTerm( beta * u, - v->grad() );
confusionBF->addTerm( beta_n_u_hat, v);
confusionBF->addTerm( u, invDt*v );
rhs->addTerm( u_prev_time * invDt * v );
//////////////////// SPECIFY RHS ///////////////////////
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// robust test norm
IPPtr ip = confusionBF->graphNorm();
// IPPtr ip = Teuchos::rcp(new IP);
// ip->addTerm(v);
// ip->addTerm(invDt*v - beta*v->grad());
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary(beta) );
FunctionPtr u0 = Teuchos::rcp( new ConstantScalarFunction(0) );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
bc->addDirichlet(beta_n_u_hat, inflowBoundary, beta*n*u0);
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
// ==================== Register Solutions ==========================
mesh->registerSolution(solution);
mesh->registerSolution(prevTimeFlow);
mesh->registerSolution(flowResidual);
// ==================== SET INITIAL GUESS ==========================
FunctionPtr u_init = Teuchos::rcp(new InitialCondition());
map<int, Teuchos::RCP<Function> > functionMap;
functionMap[u->ID()] = u_init;
prevTimeFlow->projectOntoMesh(functionMap);
//////////////////// SOLVE & REFINE ///////////////////////
// if (enforceLocalConservation) {
// // FunctionPtr parity = Teuchos::rcp<Function>( new SideParityFunction );
// // LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(parity, beta_n_u_minus_sigma_n) );
// LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(1.0, beta_n_u_minus_sigma_n) );
// LinearTermPtr sourcePart = Teuchos::rcp<LinearTerm>( new LinearTerm(invDt, u) );
// conservedQuantity->addTerm(sourcePart, true);
// solution->lagrangeConstraints()->addConstraint(conservedQuantity == u_prev_time * invDt);
// }
int timestepCount = 0;
double time_tol = 1e-8;
double L2_time_residual = 1e9;
while((L2_time_residual > time_tol) && (timestepCount < numTimeSteps))
{
solution->solve(false);
// Subtract solutions to get residual
flowResidual->setSolution(solution);
flowResidual->addSolution(prevTimeFlow, -1.0);
L2_time_residual = flowResidual->L2NormOfSolutionGlobal(u->ID());
if (rank == 0)
{
cout << endl << "Timestep: " << timestepCount << ", dt = " << dt << ", Time residual = " << L2_time_residual << endl;
stringstream outfile;
outfile << "rotatingCylinder_" << timestepCount;
solution->writeToVTK(outfile.str(), 5);
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_hat) );
FunctionPtr source = Teuchos::rcp( new PreviousSolutionFunction(flowResidual, u) );
source = invDt * source;
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, source, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
}
prevTimeFlow->setSolution(solution); // reset previous time solution to current time sol
timestepCount++;
}
return 0;
}
int main(int argc, char *argv[]) {
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int rank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
int nCells = args.Input<int>("--nCells", "num cells",2);
int numRefs = args.Input<int>("--numRefs","num adaptive refinements",0);
int numPreRefs = args.Input<int>("--numPreRefs","num preemptive adaptive refinements",0);
int order = args.Input<int>("--order","order of approximation",2);
double eps = args.Input<double>("--epsilon","diffusion parameter",1e-2);
double energyThreshold = args.Input<double>("-energyThreshold","energy thresh for adaptivity", .5);
double rampHeight = args.Input<double>("--rampHeight","ramp height at x = 2", 0.0);
double ipSwitch = args.Input<double>("--ipSwitch","point at which to switch to graph norm", 0.0); // default to 0 to remain on robust norm
bool useAnisotropy = args.Input<bool>("--useAnisotropy","aniso flag ", false);
int H1Order = order+1;
int pToAdd = args.Input<int>("--pToAdd","test space enrichment", 2);
FunctionPtr zero = Function::constant(0.0);
FunctionPtr one = Function::constant(1.0);
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
vector<double> e1,e2;
e1.push_back(1.0);e1.push_back(0.0);
e2.push_back(0.0);e2.push_back(1.0);
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
// first order term with magnitude alpha
double alpha = 0.0;
// confusionBF->addTerm(alpha * u, v);
//////////////////// BUILD MESH ///////////////////////
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);
mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));
MeshInfo meshInfo(mesh); // gets info like cell measure, etc
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
/*
// robust test norm
FunctionPtr C_h = Teuchos::rcp( new EpsilonScaling(eps) );
FunctionPtr invH = Teuchos::rcp(new InvHScaling);
FunctionPtr invSqrtH = Teuchos::rcp(new InvSqrtHScaling);
FunctionPtr sqrtH = Teuchos::rcp(new SqrtHScaling);
FunctionPtr hSwitch = Teuchos::rcp(new HSwitch(ipSwitch,mesh));
ip->addTerm(hSwitch*sqrt(eps) * v->grad() );
ip->addTerm(hSwitch*beta * v->grad() );
ip->addTerm(hSwitch*tau->div() );
// graph norm
ip->addTerm( (one-hSwitch)*((1.0/eps) * tau + v->grad()));
ip->addTerm( (one-hSwitch)*(beta * v->grad() - tau->div()));
// regularizing terms
ip->addTerm(C_h/sqrt(eps) * tau );
ip->addTerm(invSqrtH*v);
*/
// robust test norm
IPPtr robIP = Teuchos::rcp(new IP);
FunctionPtr C_h = Teuchos::rcp( new EpsilonScaling(eps) );
FunctionPtr invH = Teuchos::rcp(new InvHScaling);
FunctionPtr invSqrtH = Teuchos::rcp(new InvSqrtHScaling);
FunctionPtr sqrtH = Teuchos::rcp(new SqrtHScaling);
FunctionPtr hSwitch = Teuchos::rcp(new HSwitch(ipSwitch,mesh));
robIP->addTerm(sqrt(eps) * v->grad() );
robIP->addTerm(beta * v->grad() );
robIP->addTerm(tau->div() );
// regularizing terms
robIP->addTerm(C_h/sqrt(eps) * tau );
robIP->addTerm(invSqrtH*v);
IPPtr graphIP = confusionBF->graphNorm();
graphIP->addTerm(invSqrtH*v);
// graphIP->addTerm(C_h/sqrt(eps) * tau );
IPPtr switchIP = Teuchos::rcp(new IPSwitcher(robIP,graphIP,ipSwitch)); // rob IP for h>ipSwitch mesh size, graph norm o/w
ip = switchIP;
LinearTermPtr vVecLT = Teuchos::rcp(new LinearTerm);
LinearTermPtr tauVecLT = Teuchos::rcp(new LinearTerm);
vVecLT->addTerm(sqrt(eps)*v->grad());
tauVecLT->addTerm(C_h/sqrt(eps)*tau);
LinearTermPtr restLT = Teuchos::rcp(new LinearTerm);
restLT->addTerm(alpha*v);
restLT->addTerm(invSqrtH*v);
restLT = restLT + beta * v->grad();
restLT = restLT + tau->div();
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = zero;
// f = one;
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr Inflow = Teuchos::rcp(new LeftInflow);
SpatialFilterPtr wallBoundary = Teuchos::rcp(new WallBoundary);//MeshUtilities::rampBoundary(rampHeight);
SpatialFilterPtr freeStream = Teuchos::rcp(new FreeStreamBoundary);
bc->addDirichlet(uhat, wallBoundary, one);
// bc->addDirichlet(uhat, wallBoundary, Teuchos::rcp(new WallSmoothBC(eps)));
bc->addDirichlet(beta_n_u_minus_sigma_n, Inflow, zero);
bc->addDirichlet(beta_n_u_minus_sigma_n, freeStream, zero);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution;
solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
BCPtr nullBC = Teuchos::rcp((BC*)NULL); RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL); IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
mesh->registerSolution(backgroundFlow); // to trigger issue with p-refinements
map<int, Teuchos::RCP<Function> > functionMap; functionMap[u->ID()] = Function::constant(3.14);
backgroundFlow->projectOntoMesh(functionMap);
// lower p to p = 1 at SINGULARITY only
vector<int> ids;
/*
for (int i = 0;i<mesh->numActiveElements();i++){
bool cellIDset = false;
int cellID = mesh->activeElements()[i]->cellID();
int elemOrder = mesh->cellPolyOrder(cellID)-1;
FieldContainer<double> vv(4,2); mesh->verticesForCell(vv, cellID);
bool vertexOnWall = false; bool vertexAtSingularity = false;
for (int j = 0;j<4;j++){
if ((abs(vv(j,0)-.5) + abs(vv(j,1)))<1e-10){
vertexAtSingularity = true;
cellIDset = true;
}
}
if (!vertexAtSingularity && elemOrder<2 && !cellIDset ){
ids.push_back(cellID);
cout << "celliD = " << cellID << endl;
}
}
*/
ids.push_back(1);
ids.push_back(3);
mesh->pRefine(ids); // to put order = 1
return 0;
LinearTermPtr residual = rhs->linearTermCopy();
residual->addTerm(-confusionBF->testFunctional(solution));
RieszRepPtr rieszResidual = Teuchos::rcp(new RieszRep(mesh, ip, residual));
rieszResidual->computeRieszRep();
FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,rieszResidual));
FunctionPtr e_tau = Teuchos::rcp(new RepFunction(tau,rieszResidual));
map<int,FunctionPtr> errRepMap;
errRepMap[v->ID()] = e_v;
errRepMap[tau->ID()] = e_tau;
FunctionPtr errTau = tauVecLT->evaluate(errRepMap,false);
FunctionPtr errV = vVecLT->evaluate(errRepMap,false);
FunctionPtr errRest = restLT->evaluate(errRepMap,false);
FunctionPtr xErr = (errTau->x())*(errTau->x()) + (errV->dx())*(errV->dx());
FunctionPtr yErr = (errTau->y())*(errTau->y()) + (errV->dy())*(errV->dy());
FunctionPtr restErr = errRest*errRest;
RefinementStrategy refinementStrategy( solution, energyThreshold );
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// PRE REFINEMENTS
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
if (rank==0){
cout << "Number of pre-refinements = " << numPreRefs << endl;
}
for (int i =0;i<=numPreRefs;i++){
vector<ElementPtr> elems = mesh->activeElements();
vector<ElementPtr>::iterator elemIt;
vector<int> wallCells;
for (elemIt=elems.begin();elemIt != elems.end();elemIt++){
int cellID = (*elemIt)->cellID();
int numSides = mesh->getElement(cellID)->numSides();
FieldContainer<double> vertices(numSides,2); //for quads
mesh->verticesForCell(vertices, cellID);
bool cellIDset = false;
for (int j = 0;j<numSides;j++){
if ((abs(vertices(j,0)-.5)<1e-7) && (abs(vertices(j,1))<1e-7) && !cellIDset){ // if at singularity, i.e. if a vertex is (1,0)
wallCells.push_back(cellID);
cellIDset = true;
}
}
}
if (i<numPreRefs){
refinementStrategy.refineCells(wallCells);
}
}
double minSideLength = meshInfo.getMinCellSideLength() ;
double minCellMeasure = meshInfo.getMinCellMeasure() ;
if (rank==0){
cout << "after prerefs, sqrt min cell measure = " << sqrt(minCellMeasure) << ", min side length = " << minSideLength << endl;
}
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
VTKExporter exporter(solution, mesh, varFactory);
for (int refIndex=0;refIndex<numRefs;refIndex++){
if (rank==0){
cout << "on ref index " << refIndex << endl;
}
rieszResidual->computeRieszRep(); // in preparation to get anisotropy
vector<int> cellIDs;
refinementStrategy.getCellsAboveErrorThreshhold(cellIDs);
map<int,double> energyError = solution->energyError();
map<int,double> xErrMap = xErr->cellIntegrals(cellIDs,mesh,5,true);
map<int,double> yErrMap = yErr->cellIntegrals(cellIDs,mesh,5,true);
map<int,double> restErrMap = restErr->cellIntegrals(cellIDs,mesh,5,true);
for (vector<ElementPtr>::iterator elemIt = mesh->activeElements().begin();elemIt!=mesh->activeElements().end();elemIt++){
int cellID = (*elemIt)->cellID();
double err = xErrMap[cellID]+ yErrMap[cellID] + restErrMap[cellID];
// if (rank==0)
// cout << "err thru LT = " << sqrt(err) << ", while energy err = " << energyError[cellID] << endl;
}
/*
map<int,double> ratio,xErr,yErr;
vector<ElementPtr> elems = mesh->activeElements();
for (vector<ElementPtr>::iterator elemIt = elems.begin();elemIt!=elems.end();elemIt++){
int cellID = (*elemIt)->cellID();
ratio[cellID] = 0.0;
xErr[cellID] = 0.0;
yErr[cellID] = 0.0;
if (std::find(cellIDs.begin(),cellIDs.end(),cellID)!=cellIDs.end()){ // if this cell is above energy thresh
ratio[cellID] = yErrMap[cellID]/xErrMap[cellID];
xErr[cellID] = xErrMap[cellID];
yErr[cellID] = yErrMap[cellID];
}
}
FunctionPtr ratioFxn = Teuchos::rcp(new EnergyErrorFunction(ratio));
FunctionPtr xErrFxn = Teuchos::rcp(new EnergyErrorFunction(xErr));
FunctionPtr yErrFxn = Teuchos::rcp(new EnergyErrorFunction(yErr));
exporter.exportFunction(ratioFxn, string("ratio")+oss.str());
exporter.exportFunction(xErrFxn, string("xErr")+oss.str());
exporter.exportFunction(yErrFxn, string("yErr")+oss.str());
*/
if (useAnisotropy){
refinementStrategy.refine(rank==0,xErrMap,yErrMap); //anisotropic refinements
}else{
refinementStrategy.refine(rank==0); // no anisotropy
}
// lower p to p = 1 at SINGULARITY only
vector<int> ids;
for (int i = 0;i<mesh->numActiveElements();i++){
int cellID = mesh->activeElements()[i]->cellID();
int elemOrder = mesh->cellPolyOrder(cellID)-1;
FieldContainer<double> vv(4,2); mesh->verticesForCell(vv, cellID);
bool vertexOnWall = false; bool vertexAtSingularity = false;
for (int j = 0;j<4;j++){
if ((abs(vv(j,0)-.5) + abs(vv(j,1)))<1e-10)
vertexAtSingularity = true;
}
if (!vertexAtSingularity && elemOrder<2){
ids.push_back(cellID);
}
}
mesh->pRefine(ids); // to put order = 1
/*
if (elemOrder>1){
if (vertexAtSingularity){
vector<int> ids;
ids.push_back(cellID);
mesh->pRefine(ids,1-(elemOrder-1)); // to put order = 1
// mesh->pRefine(ids); // to put order = 1
if (rank==0)
cout << "p unrefining elem with elemOrder = " << elemOrder << endl;
}
}else{
if (!vertexAtSingularity){
vector<int> ids;
ids.push_back(cellID);
mesh->pRefine(ids,2-elemOrder);
}
}
*/
double minSideLength = meshInfo.getMinCellSideLength() ;
if (rank==0)
cout << "minSideLength is " << minSideLength << endl;
solution->condensedSolve();
std::ostringstream oss;
oss << refIndex;
}
// final solve on final mesh
solution->setWriteMatrixToFile(true,"K.mat");
solution->condensedSolve();
////////////////////////////////////////////////////////////////////////////////////////////////////////////
// CHECK CONDITIONING
////////////////////////////////////////////////////////////////////////////////////////////////////////////
bool checkConditioning = true;
if (checkConditioning){
double minSideLength = meshInfo.getMinCellSideLength() ;
StandardAssembler assembler(solution);
double maxCond = 0.0;
int maxCellID = 0;
for (int i = 0;i<mesh->numActiveElements();i++){
int cellID = mesh->getActiveElement(i)->cellID();
FieldContainer<double> ipMat = assembler.getIPMatrix(mesh->getElement(cellID));
double cond = SerialDenseWrapper::getMatrixConditionNumber(ipMat);
if (cond>maxCond){
maxCond = cond;
maxCellID = cellID;
}
}
if (rank==0){
cout << "cell ID " << maxCellID << " has minCellLength " << minSideLength << " and condition estimate " << maxCond << endl;
}
string ipMatName = string("ipMat.mat");
ElementPtr maxCondElem = mesh->getElement(maxCellID);
FieldContainer<double> ipMat = assembler.getIPMatrix(maxCondElem);
SerialDenseWrapper::writeMatrixToMatlabFile(ipMatName,ipMat);
}
//////////////////// print to file ///////////////////////
if (rank==0){
exporter.exportSolution(string("robustIP"));
cout << endl;
}
return 0;
}
int main(int argc, char *argv[])
{
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[]) {
// 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);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation");
bool steady = args.Input<bool>("--steady", "run steady rather than transient");
// Optional arguments (have defaults)
double dt = args.Input("--dt", "time step", 0.25);
int numTimeSteps = args.Input("--nt", "number of time steps", 20);
halfWidth = args.Input("--halfWidth", "half width of inlet profile", 1.0);
args.Process();
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr beta_n_u_hat = varFactory.fluxVar("\\widehat{\\beta \\cdot n }");
VarPtr u = varFactory.fieldVar("u");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// BUILD MESH ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// define nodes for mesh
FieldContainer<double> meshBoundary(4,2);
meshBoundary(0,0) = 0.0; // x1
meshBoundary(0,1) = -2.0; // y1
meshBoundary(1,0) = 4.0;
meshBoundary(1,1) = -2.0;
meshBoundary(2,0) = 4.0;
meshBoundary(2,1) = 2.0;
meshBoundary(3,0) = 0.0;
meshBoundary(3,1) = 2.0;
int horizontalCells = 8, verticalCells = 8;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
bf, H1Order, H1Order+pToAdd);
////////////////////////////////////////////////////////////////////
// INITIALIZE FLOW FUNCTIONS
////////////////////////////////////////////////////////////////////
BCPtr nullBC = Teuchos::rcp((BC*)NULL);
RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr prevTimeFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
SolutionPtr flowResidual = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
FunctionPtr u_prev_time = Teuchos::rcp( new PreviousSolutionFunction(prevTimeFlow, u) );
//////////////////// DEFINE BILINEAR FORM ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr invDt = Teuchos::rcp(new ScalarParamFunction(1.0/dt));
// v terms:
bf->addTerm( beta * u, - v->grad() );
bf->addTerm( beta_n_u_hat, v);
if (!steady)
{
bf->addTerm( u, invDt*v );
rhs->addTerm( u_prev_time * invDt * v );
}
//////////////////// SPECIFY RHS ///////////////////////
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = bf->graphNorm();
// ip->addTerm(v);
// ip->addTerm(beta*v->grad());
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr lBoundary = Teuchos::rcp( new LeftBoundary );
FunctionPtr u1 = Teuchos::rcp( new InletBC );
bc->addDirichlet(beta_n_u_hat, lBoundary, -u1);
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
// ==================== Register Solutions ==========================
mesh->registerSolution(solution);
mesh->registerSolution(prevTimeFlow);
mesh->registerSolution(flowResidual);
// ==================== SET INITIAL GUESS ==========================
double u_free = 0.0;
map<int, Teuchos::RCP<Function> > functionMap;
// functionMap[u->ID()] = Teuchos::rcp( new ConInletBC
functionMap[u->ID()] = Teuchos::rcp( new InletBC );
prevTimeFlow->projectOntoMesh(functionMap);
//////////////////// SOLVE & REFINE ///////////////////////
if (enforceLocalConservation)
{
if (steady)
{
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(beta_n_u_hat == zero);
}
else
{
// FunctionPtr parity = Teuchos::rcp<Function>( new SideParityFunction );
// LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(parity, beta_n_u_minus_sigma_n) );
LinearTermPtr conservedQuantity = Teuchos::rcp<LinearTerm>( new LinearTerm(1.0, beta_n_u_hat) );
LinearTermPtr sourcePart = Teuchos::rcp<LinearTerm>( new LinearTerm(invDt, u) );
conservedQuantity->addTerm(sourcePart, true);
solution->lagrangeConstraints()->addConstraint(conservedQuantity == u_prev_time * invDt);
}
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(solution, mesh, varFactory);
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
if (steady)
{
solution->solve(false);
if (commRank == 0)
{
stringstream outfile;
outfile << "Convection_" << refIndex;
exporter.exportSolution(outfile.str());
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_hat) );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
}
}
else
{
int timestepCount = 0;
double time_tol = 1e-8;
double L2_time_residual = 1e9;
// cout << L2_time_residual <<" "<< time_tol << timestepCount << numTimeSteps << endl;
while((L2_time_residual > time_tol) && (timestepCount < numTimeSteps))
{
solution->solve(false);
// Subtract solutions to get residual
flowResidual->setSolution(solution);
flowResidual->addSolution(prevTimeFlow, -1.0);
L2_time_residual = flowResidual->L2NormOfSolutionGlobal(u->ID());
if (commRank == 0)
{
cout << endl << "Timestep: " << timestepCount << ", dt = " << dt << ", Time residual = " << L2_time_residual << endl;
stringstream outfile;
outfile << "TransientConvection_" << refIndex << "-" << timestepCount;
exporter.exportSolution(outfile.str());
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_hat) );
FunctionPtr source = Teuchos::rcp( new PreviousSolutionFunction(flowResidual, u) );
source = -invDt * source;
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, source, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
}
prevTimeFlow->setSolution(solution); // reset previous time solution to current time sol
timestepCount++;
}
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
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;
}
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);
#endif
{
// 1D tests
CellTopoPtr line_2 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >() ) );
// let's draw a line
vector<double> v0 = makeVertex(0);
vector<double> v1 = makeVertex(1);
vector<double> v2 = makeVertex(2);
vector< vector<double> > vertices;
vertices.push_back(v0);
vertices.push_back(v1);
vertices.push_back(v2);
vector<unsigned> line1VertexList;
vector<unsigned> line2VertexList;
line1VertexList.push_back(0);
line1VertexList.push_back(1);
line2VertexList.push_back(1);
line2VertexList.push_back(2);
vector< vector<unsigned> > elementVertices;
elementVertices.push_back(line1VertexList);
elementVertices.push_back(line2VertexList);
vector< CellTopoPtr > cellTopos;
cellTopos.push_back(line_2);
cellTopos.push_back(line_2);
MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
FunctionPtr x = Function::xn(1);
FunctionPtr function = x;
FunctionPtr fbdr = Function::restrictToCellBoundary(function);
vector<FunctionPtr> functions;
functions.push_back(function);
functions.push_back(function);
vector<string> functionNames;
functionNames.push_back("function1");
functionNames.push_back("function2");
{
XDMFExporter exporter(meshTopology, "function1", false);
exporter.exportFunction(function, "function1");
}
{
XDMFExporter exporter(meshTopology, "boundary1", false);
exporter.exportFunction(fbdr, "boundary1");
}
{
XDMFExporter exporter(meshTopology, "functions1", false);
exporter.exportFunction(functions, functionNames);
}
}
{
// 2D tests
CellTopoPtr quad_4 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ) );
CellTopoPtr tri_3 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() ) );
// let's draw a little house
vector<double> v0 = makeVertex(-1,0);
vector<double> v1 = makeVertex(1,0);
vector<double> v2 = makeVertex(1,2);
vector<double> v3 = makeVertex(-1,2);
vector<double> v4 = makeVertex(0.0,3);
vector< vector<double> > vertices;
vertices.push_back(v0);
vertices.push_back(v1);
vertices.push_back(v2);
vertices.push_back(v3);
vertices.push_back(v4);
vector<unsigned> quadVertexList;
quadVertexList.push_back(0);
quadVertexList.push_back(1);
quadVertexList.push_back(2);
quadVertexList.push_back(3);
vector<unsigned> triVertexList;
triVertexList.push_back(3);
triVertexList.push_back(2);
triVertexList.push_back(4);
vector< vector<unsigned> > elementVertices;
elementVertices.push_back(quadVertexList);
elementVertices.push_back(triVertexList);
vector< CellTopoPtr > cellTopos;
cellTopos.push_back(quad_4);
cellTopos.push_back(tri_3);
MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
FunctionPtr x2 = Function::xn(2);
FunctionPtr y2 = Function::yn(2);
FunctionPtr function = x2 + y2;
FunctionPtr vect = Function::vectorize(x2, y2);
FunctionPtr fbdr = Function::restrictToCellBoundary(function);
vector<FunctionPtr> functions;
functions.push_back(function);
functions.push_back(vect);
vector<string> functionNames;
functionNames.push_back("function");
functionNames.push_back("vect");
vector<FunctionPtr> bdrfunctions;
bdrfunctions.push_back(fbdr);
bdrfunctions.push_back(fbdr);
vector<string> bdrfunctionNames;
bdrfunctionNames.push_back("bdr1");
bdrfunctionNames.push_back("bdr2");
map<int, int> cellIDToNum1DPts;
cellIDToNum1DPts[1] = 4;
{
XDMFExporter exporter(meshTopology, "Grid2D", false);
// exporter.exportFunction(function, "function2", 0, 10);
// exporter.exportFunction(vect, "vect2", 1, 10, cellIDToNum1DPts);
// exporter.exportFunction(fbdr, "boundary2", 0);
exporter.exportFunction(functions, functionNames, 1, 10);
}
{
XDMFExporter exporter(meshTopology, "BdrGrid2D", false);
// exporter.exportFunction(function, "function2", 0, 10);
// exporter.exportFunction(vect, "vect2", 1, 10, cellIDToNum1DPts);
// exporter.exportFunction(fbdr, "boundary2", 0);
exporter.exportFunction(bdrfunctions, bdrfunctionNames, 1, 10);
}
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("uhat");
VarPtr fhat = varFactory.fluxVar("fhat");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma = varFactory.fieldVar("sigma", VECTOR_L2);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( fhat, v);
//////////////////// BUILD MESH ///////////////////////
int H1Order = 4, pToAdd = 2;
Teuchos::RCP<Mesh> mesh = Teuchos::rcp( new Mesh (meshTopology, bf, H1Order, pToAdd) );
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = bf->graphNorm();
//////////////////// SPECIFY RHS ///////////////////////
RHSPtr rhs = RHS::rhs();
// Teuchos::RCP<RHS> rhs = Teuchos::rcp( new RHS );
FunctionPtr one = Function::constant(1.0);
rhs->addTerm( one * v );
//////////////////// CREATE BCs ///////////////////////
// Teuchos::RCP<BC> bc = Teuchos::rcp( new BCEasy );
BCPtr bc = BC::bc();
FunctionPtr zero = Function::zero();
SpatialFilterPtr entireBoundary = Teuchos::rcp( new EntireBoundary );
bc->addDirichlet(uhat, entireBoundary, zero);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
solution->solve(false);
RefinementStrategy refinementStrategy( solution, 0.2);
// Output solution
FunctionPtr uSoln = Function::solution(u, solution);
FunctionPtr sigmaSoln = Function::solution(sigma, solution);
FunctionPtr uhatSoln = Function::solution(uhat, solution);
FunctionPtr fhatSoln = Function::solution(fhat, solution);
{
XDMFExporter exporter(meshTopology, "Poisson", false);
exporter.exportFunction(uSoln, "u", 0, 4);
exporter.exportFunction(uSoln, "u", 1, 5);
exporter.exportFunction(uhatSoln, "uhat", 0, 4);
exporter.exportFunction(uhatSoln, "uhat", 1, 5);
// exporter.exportFunction(fhatSoln, "fhat", 0, 4);
// exporter.exportFunction(fhatSoln, "fhat", 1, 5);
}
{
XDMFExporter exporter(meshTopology, "PoissonSolution", false);
exporter.exportSolution(solution, mesh, varFactory, 0, 2, cellIDToSubdivision(mesh, 10));
refinementStrategy.refine(true);
solution->solve(false);
exporter.exportSolution(solution, mesh, varFactory, 1, 2, cellIDToSubdivision(mesh, 10));
}
// exporter.exportFunction(sigmaSoln, "Poisson-s", "sigma", 0, 5);
// exporter.exportFunction(uhatSoln, "Poisson-uhat", "uhat", 1, 6);
}
{
// 3D tests
CellTopoPtr hex = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Hexahedron<8> >() ));
// let's draw a little box
vector<double> v0 = makeVertex(0,0,0);
vector<double> v1 = makeVertex(1,0,0);
vector<double> v2 = makeVertex(1,1,0);
vector<double> v3 = makeVertex(0,1,0);
vector<double> v4 = makeVertex(0,0,1);
vector<double> v5 = makeVertex(1,0,1);
vector<double> v6 = makeVertex(1,1,1);
vector<double> v7 = makeVertex(0,1,1);
vector< vector<double> > vertices;
vertices.push_back(v0);
vertices.push_back(v1);
vertices.push_back(v2);
vertices.push_back(v3);
vertices.push_back(v4);
vertices.push_back(v5);
vertices.push_back(v6);
vertices.push_back(v7);
vector<unsigned> hexVertexList;
hexVertexList.push_back(0);
hexVertexList.push_back(1);
hexVertexList.push_back(2);
hexVertexList.push_back(3);
hexVertexList.push_back(4);
hexVertexList.push_back(5);
hexVertexList.push_back(6);
hexVertexList.push_back(7);
// vector<unsigned> triVertexList;
// triVertexList.push_back(2);
// triVertexList.push_back(3);
// triVertexList.push_back(4);
vector< vector<unsigned> > elementVertices;
elementVertices.push_back(hexVertexList);
// elementVertices.push_back(triVertexList);
vector< CellTopoPtr > cellTopos;
cellTopos.push_back(hex);
// cellTopos.push_back(tri_3);
MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
FunctionPtr x = Function::xn(1);
FunctionPtr y = Function::yn(1);
FunctionPtr z = Function::zn(1);
FunctionPtr function = x + y + z;
FunctionPtr fbdr = Function::restrictToCellBoundary(function);
FunctionPtr vect = Function::vectorize(x, y, z);
vector<FunctionPtr> functions;
functions.push_back(function);
functions.push_back(vect);
vector<string> functionNames;
functionNames.push_back("function");
functionNames.push_back("vect");
{
XDMFExporter exporter(meshTopology, "function3", false);
exporter.exportFunction(function, "function3");
}
{
XDMFExporter exporter(meshTopology, "boundary3", false);
exporter.exportFunction(fbdr, "boundary3");
}
{
XDMFExporter exporter(meshTopology, "vect3", false);
exporter.exportFunction(vect, "vect3");
}
{
XDMFExporter exporter(meshTopology, "functions3", false);
exporter.exportFunction(functions, functionNames);
}
}
}
void FunctionTests::SetUp()
{
//////////////////// 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(2.0);
beta_const.push_back(1.0);
double eps = 1e-2;
// standard confusion bilinear form
_confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
_confusionBF->addTerm(sigma1 / eps, tau->x());
_confusionBF->addTerm(sigma2 / eps, tau->y());
_confusionBF->addTerm(u, tau->div());
_confusionBF->addTerm(-uhat, tau->dot_normal());
// v terms:
_confusionBF->addTerm( sigma1, v->dx() );
_confusionBF->addTerm( sigma2, v->dy() );
_confusionBF->addTerm( beta_const * u, - v->grad() );
_confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = -1.0; // x1
quadPoints(0,1) = -1.0; // y1
quadPoints(1,0) = 1.0;
quadPoints(1,1) = -1.0;
quadPoints(2,0) = 1.0;
quadPoints(2,1) = 1.0;
quadPoints(3,0) = -1.0;
quadPoints(3,1) = 1.0;
int H1Order = 1, pToAdd = 0;
int horizontalCells = 1, verticalCells = 1;
// create a pointer to a new mesh:
_spectralConfusionMesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
_confusionBF, H1Order, H1Order+pToAdd);
// some 2D test points:
// setup test points:
static const int NUM_POINTS_1D = 10;
double x[NUM_POINTS_1D] = {-1.0,-0.8,-0.6,-.4,-.2,0,0.2,0.4,0.6,0.8};
double y[NUM_POINTS_1D] = {-0.8,-0.6,-.4,-.2,0,0.2,0.4,0.6,0.8,1.0};
_testPoints = FieldContainer<double>(NUM_POINTS_1D*NUM_POINTS_1D,2);
for (int i=0; i<NUM_POINTS_1D; i++) {
for (int j=0; j<NUM_POINTS_1D; j++) {
_testPoints(i*NUM_POINTS_1D + j, 0) = x[i];
_testPoints(i*NUM_POINTS_1D + j, 1) = y[j];
}
}
_elemType = _spectralConfusionMesh->getElement(0)->elementType();
vector<GlobalIndexType> cellIDs;
int cellID = 0;
cellIDs.push_back(cellID);
_basisCache = Teuchos::rcp( new BasisCache( _elemType, _spectralConfusionMesh ) );
_basisCache->setRefCellPoints(_testPoints);
_basisCache->setPhysicalCellNodes( _spectralConfusionMesh->physicalCellNodesForCell(cellID), cellIDs, true );
}
bool HConvergenceStudyTests::testBestApproximationErrorComputation() {
bool success = true;
bool enrichVelocity = false; // true would be for the "compliant" norm, which isn't working well yet
int minLogElements = 0, maxLogElements = minLogElements;
int numCells1D = pow(2.0,minLogElements);
int H1Order = 1;
int pToAdd = 2;
double tol = 1e-16;
double Re = 40.0;
VarFactory varFactory = VGPStokesFormulation::vgpVarFactory();
VarPtr u1_vgp = varFactory.fieldVar(VGP_U1_S);
VarPtr u2_vgp = varFactory.fieldVar(VGP_U2_S);
VarPtr sigma11_vgp = varFactory.fieldVar(VGP_SIGMA11_S);
VarPtr sigma12_vgp = varFactory.fieldVar(VGP_SIGMA12_S);
VarPtr sigma21_vgp = varFactory.fieldVar(VGP_SIGMA21_S);
VarPtr sigma22_vgp = varFactory.fieldVar(VGP_SIGMA22_S);
VarPtr p_vgp = varFactory.fieldVar(VGP_P_S);
VGPStokesFormulation stokesForm(1/Re);
int numCellsFineMesh = 20; // for computing a zero-mean pressure
int H1OrderFineMesh = 5;
// define Kovasznay domain:
FieldContainer<double> quadPointsKovasznay(4,2);
// Domain from Evans Hughes for Navier-Stokes:
quadPointsKovasznay(0,0) = 0.0; // x1
quadPointsKovasznay(0,1) = -0.5; // y1
quadPointsKovasznay(1,0) = 1.0;
quadPointsKovasznay(1,1) = -0.5;
quadPointsKovasznay(2,0) = 1.0;
quadPointsKovasznay(2,1) = 0.5;
quadPointsKovasznay(3,0) = 0.0;
quadPointsKovasznay(3,1) = 0.5;
FunctionPtr zero = Function::zero();
bool dontEnhanceFluxes = false;
VGPNavierStokesProblem zeroProblem = VGPNavierStokesProblem(Re, quadPointsKovasznay,
numCellsFineMesh, numCellsFineMesh,
H1OrderFineMesh, pToAdd,
zero, zero, zero, enrichVelocity, dontEnhanceFluxes);
FunctionPtr u1_exact, u2_exact, p_exact;
NavierStokesFormulation::setKovasznay(Re, zeroProblem.mesh(), u1_exact, u2_exact, p_exact);
VGPNavierStokesProblem problem = VGPNavierStokesProblem(Re,quadPointsKovasznay,
numCells1D,numCells1D,
H1Order, pToAdd,
u1_exact, u2_exact, p_exact, enrichVelocity, dontEnhanceFluxes);
HConvergenceStudy study(problem.exactSolution(),
problem.mesh()->bilinearForm(),
problem.exactSolution()->rhs(),
problem.backgroundFlow()->bc(),
problem.bf()->graphNorm(),
minLogElements, maxLogElements,
H1Order, pToAdd, false, false, false);
study.setReportRelativeErrors(false); // we want absolute errors
Teuchos::RCP<Mesh> mesh = problem.mesh();
int cubatureDegreeEnrichment = 10;
int L2Order = H1Order - 1;
int meshCubatureDegree = L2Order + H1Order + pToAdd;
study.setCubatureDegreeForExact(cubatureDegreeEnrichment + meshCubatureDegree);
FunctionPtr f = u1_exact;
int trialID = u1_vgp->ID();
{
double fIntegral = f->integrate(mesh,cubatureDegreeEnrichment);
// cout << "testBestApproximationErrorComputation: integral of f on whole mesh = " << fIntegral << endl;
double l2ErrorOfAverage = (Function::constant(fIntegral) - f)->l2norm(mesh,cubatureDegreeEnrichment);
// cout << "testBestApproximationErrorComputation: l2 error of fIntegral: " << l2ErrorOfAverage << endl;
ElementTypePtr elemType = mesh->elementTypes()[0];
vector<GlobalIndexType> cellIDs = mesh->cellIDsOfTypeGlobal(elemType);
bool testVsTest = false;
BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(elemType, mesh, testVsTest, cubatureDegreeEnrichment) );
basisCache->setPhysicalCellNodes(mesh->physicalCellNodesGlobal(elemType), cellIDs, false); // false: no side cache
FieldContainer<double> projectionValues(cellIDs.size());
f->integrate(projectionValues, basisCache);
FieldContainer<double> cellMeasures = basisCache->getCellMeasures();
for (int i=0; i<projectionValues.size(); i++) {
projectionValues(i) /= cellMeasures(i);
}
// since we're not worried about the actual solution values at all, just use a single zero solution:
vector< SolutionPtr > solutions;
solutions.push_back( problem.backgroundFlow() );
study.setSolutions(solutions); // this will call computeError()
double approximationError = study.bestApproximationErrors()[trialID][0]; // 0: solution/mesh index
// for a single-cell mesh, approximation error should be the same as the L^2 error of the average
double diff = abs(approximationError - l2ErrorOfAverage);
if (diff > tol) {
cout << "testBestApproximationErrorComputation: diff " << diff << " exceeds tol " << tol << endl;
success = false;
} else {
// cout << "testBestApproximationErrorComputation: diff " << diff << " is below tol " << tol << endl;
}
}
return success;
}
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;
*/
}
bool LobattoBasisTests::testSimpleStiffnessMatrix() {
bool success = true;
int rank = Teuchos::GlobalMPISession::getRank();
VarFactory varFactory;
VarPtr u = varFactory.fieldVar("u");
VarPtr un = varFactory.fluxVar("un_hat");
VarPtr v = varFactory.testVar("v", HGRAD);
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
vector<double> beta;
beta.push_back(1);
beta.push_back(1);
bf->addTerm(beta * u, v->grad());
bf->addTerm(un, v);
DofOrderingPtr trialSpace = Teuchos::rcp( new DofOrdering );
DofOrderingPtr testSpace = Teuchos::rcp( new DofOrdering );
const int numSides = 4;
const int spaceDim = 2;
int fieldOrder = 3;
int testOrder = fieldOrder+2;
BasisPtr fieldBasis = Camellia::intrepidQuadHGRAD(fieldOrder);
BasisPtr fluxBasis = Camellia::intrepidLineHGRAD(fieldOrder);
trialSpace->addEntry(u->ID(), fieldBasis, fieldBasis->rangeRank());
for (int i=0; i<numSides; i++) {
trialSpace->addEntry(un->ID(), fluxBasis, fluxBasis->rangeRank(), i);
}
BasisPtr testBasis = Camellia::lobattoQuadHGRAD(testOrder+1,false); // +1 because it lives in HGRAD
testSpace->addEntry(v->ID(), testBasis, testBasis->rangeRank());
int numTrialDofs = trialSpace->totalDofs();
int numTestDofs = testSpace->totalDofs();
int numCells = 1;
FieldContainer<double> cellNodes(numCells,numSides,spaceDim);
cellNodes(0,0,0) = 0;
cellNodes(0,0,1) = 0;
cellNodes(0,1,0) = 1;
cellNodes(0,1,1) = 0;
cellNodes(0,2,0) = 1;
cellNodes(0,2,1) = 1;
cellNodes(0,3,0) = 0;
cellNodes(0,3,1) = 1;
FieldContainer<double> stiffness(numCells,numTestDofs,numTrialDofs);
FieldContainer<double> cellSideParities(numCells,numSides);
cellSideParities.initialize(1.0);
Teuchos::RCP<shards::CellTopology> quad_4 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ) );
Teuchos::RCP<ElementType> elemType = Teuchos::rcp( new ElementType(trialSpace, testSpace, quad_4));
BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(elemType) );
vector<GlobalIndexType> cellIDs;
cellIDs.push_back(0);
basisCache->setPhysicalCellNodes(cellNodes, cellIDs, true);
bf->stiffnessMatrix(stiffness, elemType, cellSideParities, basisCache);
// TODO: finish this test
// cout << stiffness;
if (rank==0)
cout << "Warning: testSimpleStiffnessMatrix() unfinished.\n";
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;
}
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);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("uhat");
VarPtr sigma_n = varFactory.fluxVar("fhat");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("sigma1");
VarPtr sigma2 = varFactory.fieldVar("sigma2");
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma1, tau->x());
bf->addTerm(sigma2, tau->y());
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma1, v->dx() );
bf->addTerm( sigma2, v->dy() );
bf->addTerm( -sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = bf->graphNorm();
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(1.0) );
rhs->addTerm( f * v );
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
SpatialFilterPtr inflow = Teuchos::rcp( new Inflow );
bc->addDirichlet(uhat, inflow, zero);
SpatialFilterPtr leadingWedge = Teuchos::rcp( new LeadingWedge );
bc->addDirichlet(uhat, leadingWedge, zero);
SpatialFilterPtr trailingWedge = Teuchos::rcp( new TrailingWedge );
bc->addDirichlet(sigma_n, trailingWedge, zero);
// bc->addDirichlet(uhat, trailingWedge, zero);
SpatialFilterPtr top = Teuchos::rcp( new Top );
bc->addDirichlet(uhat, top, zero);
SpatialFilterPtr outflow = Teuchos::rcp( new Outflow );
bc->addDirichlet(uhat, outflow, zero);
//////////////////// BUILD MESH ///////////////////////
bool allQuads = true;
int H1Order = 3, pToAdd = 2;
// define nodes for mesh
vector< FieldContainer<double> > vertices;
FieldContainer<double> pt(2);
vector< vector<int> > elementIndices;
vector<int> q(4);
vector<int> t(3);
if (allQuads)
{
pt(0) = -halfwidth;
pt(1) = -1;
vertices.push_back(pt);
pt(0) = 0;
pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = -1;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = 0;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth;
pt(1) = halfwidth;
vertices.push_back(pt);
q[0] = 0;
q[1] = 1;
q[2] = 4;
q[3] = 5;
elementIndices.push_back(q);
q[0] = 1;
q[1] = 2;
q[2] = 3;
q[3] = 4;
elementIndices.push_back(q);
}
else
{
pt(0) = -halfwidth;
pt(1) = -1;
vertices.push_back(pt);
pt(0) = 0;
pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = -1;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = 0;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth;
pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth;
pt(1) = 0;
vertices.push_back(pt);
t[0] = 0;
t[1] = 1;
t[2] = 7;
elementIndices.push_back(t);
t[0] = 1;
t[1] = 2;
t[2] = 3;
elementIndices.push_back(t);
q[0] = 1;
q[1] = 3;
q[2] = 4;
q[3] = 5;
elementIndices.push_back(q);
q[0] = 7;
q[1] = 1;
q[2] = 5;
q[3] = 6;
elementIndices.push_back(q);
}
Teuchos::RCP<Mesh> mesh = Teuchos::rcp( new Mesh(vertices, elementIndices, bf, H1Order, pToAdd) );
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
solution->setFilter(pc);
if (enforceLocalConservation)
{
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(sigma_n == zero);
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
solution->solve(false);
if (rank==0)
{
stringstream outfile;
outfile << "poissonwedge_" << refIndex;
solution->writeToVTK(outfile.str());
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma_n) );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
}
if (refIndex < numRefs)
{
// refinementStrategy.refine(rank==0); // print to console on rank 0
vector<int> cellsToRefine;
vector<int> cells_h;
vector<int> cells_p;
refinementStrategy.getCellsAboveErrorThreshhold(cellsToRefine);
for (int i=0; i < cellsToRefine.size(); i++)
if (sqrt(mesh->getCellMeasure(cellsToRefine[i])) < 1e-3)
{
int pOrder = mesh->cellPolyOrder(cellsToRefine[i]);
if (allQuads)
cells_p.push_back(cellsToRefine[i]);
else if (pOrder < 8)
cells_p.push_back(cellsToRefine[i]);
else
cout << "Reached cell size and polynomial order limits" << endl;
// cells_h.push_back(cellsToRefine[i]);
}
else
cells_h.push_back(cellsToRefine[i]);
refinementStrategy.pRefineCells(mesh, cells_p);
refinementStrategy.hRefineCells(mesh, cells_h);
}
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
int polyOrder = 3;
int pToAdd = 2; // for tests
// define our manufactured solution or problem bilinear form:
double epsilon = 1e-2;
bool useTriangles = false;
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 1.0;
quadPoints(1,1) = 0.0;
quadPoints(2,0) = 1.0;
quadPoints(2,1) = 1.0;
quadPoints(3,0) = 0.0;
quadPoints(3,1) = 1.0;
int H1Order = polyOrder + 1;
int horizontalCells = 1, verticalCells = 1;
double energyThreshold = 0.2; // for mesh refinements
double nonlinearStepSize = 0.5;
double nonlinearRelativeEnergyTolerance = 0.015; // used to determine convergence of the nonlinear solution
////////////////////////////////////////////////////////////////////
// SET UP PROBLEM
////////////////////////////////////////////////////////////////////
Teuchos::RCP<BurgersBilinearForm> oldBurgersBF = Teuchos::rcp(new BurgersBilinearForm(epsilon));
// new-style bilinear form definition
VarFactory varFactory;
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_hat = varFactory.fluxVar("\\widehat{\\beta_n u - \\sigma_n}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
VarPtr tau = varFactory.testVar("\\tau",HDIV);
VarPtr v = varFactory.testVar("v",HGRAD);
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(quadPoints, horizontalCells, verticalCells, bf, H1Order, H1Order+pToAdd, useTriangles);
mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));
Teuchos::RCP<Solution> backgroundFlow = Teuchos::rcp(new Solution(mesh, Teuchos::rcp((BC*)NULL) , Teuchos::rcp((RHS*)NULL), Teuchos::rcp((DPGInnerProduct*)NULL))); // create null solution
oldBurgersBF->setBackgroundFlow(backgroundFlow);
// tau parts:
// 1/eps (sigma, tau)_K + (u, div tau)_K - (u_hat, tau_n)_dK
bf->addTerm(sigma1 / epsilon, tau->x());
bf->addTerm(sigma2 / epsilon, tau->y());
bf->addTerm(u, tau->div());
bf->addTerm( - uhat, tau->dot_normal() );
vector<double> e1(2); // (1,0)
e1[0] = 1;
vector<double> e2(2); // (0,1)
e2[1] = 1;
FunctionPtr u_prev = Teuchos::rcp( new PreviousSolutionFunction(backgroundFlow, u) );
FunctionPtr beta = e1 * u_prev + Teuchos::rcp( new ConstantVectorFunction( e2 ) );
// v:
// (sigma, grad v)_K - (sigma_hat_n, v)_dK - (u, beta dot grad v) + (u_hat * n dot beta, v)_dK
bf->addTerm( sigma1, v->dx() );
bf->addTerm( sigma2, v->dy() );
bf->addTerm( -u, beta * v->grad());
bf->addTerm( beta_n_u_minus_sigma_hat, v);
// ==================== SET INITIAL GUESS ==========================
mesh->registerSolution(backgroundFlow);
map<int, Teuchos::RCP<AbstractFunction> > functionMap;
functionMap[BurgersBilinearForm::U] = Teuchos::rcp(new InitialGuess());
functionMap[BurgersBilinearForm::SIGMA_1] = Teuchos::rcp(new ZeroFunction());
functionMap[BurgersBilinearForm::SIGMA_2] = Teuchos::rcp(new ZeroFunction());
backgroundFlow->projectOntoMesh(functionMap);
// ==================== END SET INITIAL GUESS ==========================
// compare stiffness matrices for first linear step:
int trialOrder = 1;
pToAdd = 0;
int testOrder = trialOrder + pToAdd;
CellTopoPtr quadTopoPtr = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ));
DofOrderingFactory dofOrderingFactory(bf);
DofOrderingPtr testOrdering = dofOrderingFactory.testOrdering(testOrder, *quadTopoPtr);
DofOrderingPtr trialOrdering = dofOrderingFactory.trialOrdering(trialOrder, *quadTopoPtr);
int numCells = 1;
// just use testOrdering for both trial and test spaces (we only use to define BasisCache)
ElementTypePtr elemType = Teuchos::rcp( new ElementType(trialOrdering, testOrdering, quadTopoPtr) );
BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(elemType) );
quadPoints.resize(1,quadPoints.dimension(0),quadPoints.dimension(1));
basisCache->setPhysicalCellNodes(quadPoints,vector<int>(1),true); // true: do create side cache
FieldContainer<double> cellSideParities(numCells,quadTopoPtr->getSideCount());
cellSideParities.initialize(1.0); // not worried here about neighbors actually having opposite parity -- just want the two BF implementations to agree...
FieldContainer<double> expectedValues(numCells, testOrdering->totalDofs(), trialOrdering->totalDofs() );
FieldContainer<double> actualValues(numCells, testOrdering->totalDofs(), trialOrdering->totalDofs() );
oldBurgersBF->stiffnessMatrix(expectedValues, elemType, cellSideParities, basisCache);
bf->stiffnessMatrix(actualValues, elemType, cellSideParities, basisCache);
// compare beta's as well
FieldContainer<double> expectedBeta = oldBurgersBF->getBeta(basisCache);
Teuchos::Array<int> dim;
expectedBeta.dimensions(dim);
FieldContainer<double> actualBeta(dim);
beta->values(actualBeta,basisCache);
double tol = 1e-14;
double maxDiff;
if (rank == 0)
{
if ( ! TestSuite::fcsAgree(expectedBeta,actualBeta,tol,maxDiff) )
{
cout << "Test failed: old Burgers beta differs from new; maxDiff " << maxDiff << ".\n";
cout << "Old beta: \n" << expectedBeta;
cout << "New beta: \n" << actualBeta;
}
else
{
cout << "Old and new Burgers beta agree!!\n";
}
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old Burgers stiffness differs from new; maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "TrialDofOrdering: \n" << *trialOrdering;
cout << "TestDofOrdering:\n" << *testOrdering;
}
else
{
cout << "Old and new Burgers stiffness agree!!\n";
}
}
// define our inner product:
// Teuchos::RCP<BurgersInnerProduct> ip = Teuchos::rcp( new BurgersInnerProduct( bf, mesh ) );
// function to scale the squared guy by epsilon/h
FunctionPtr epsilonOverHScaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
IPPtr ip = Teuchos::rcp( new IP );
ip->addTerm(tau);
ip->addTerm(tau->div());
ip->addTerm( epsilonOverHScaling * v );
ip->addTerm( sqrt(sqrt(epsilon)) * v->grad() );
ip->addTerm( beta * v->grad() );
// use old IP instead, for now...
Teuchos::RCP<BurgersInnerProduct> oldIP = Teuchos::rcp( new BurgersInnerProduct( oldBurgersBF, mesh ) );
expectedValues.resize(numCells, testOrdering->totalDofs(), testOrdering->totalDofs() );
actualValues.resize (numCells, testOrdering->totalDofs(), testOrdering->totalDofs() );
BasisCachePtr ipBasisCache = Teuchos::rcp( new BasisCache(elemType, true) ); // true: test vs. test
ipBasisCache->setPhysicalCellNodes(quadPoints,vector<int>(1),false); // false: don't create side cache
oldIP->computeInnerProductMatrix(expectedValues,testOrdering,ipBasisCache);
ip->computeInnerProductMatrix(actualValues,testOrdering,ipBasisCache);
tol = 1e-14;
maxDiff = 0.0;
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old inner product differs from new IP; maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New IP: \n" << actualValues;
cout << "testOrdering: \n" << *testOrdering;
}
else
{
cout << "Old inner product and new IP agree!!\n";
}
}
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
// the RHS as implemented by BurgersProblem divides the first component of beta by 2.0
// so we follow that. I've not done the math; just imitating the code...
Teuchos::RCP<RHSEasy> otherRHS = Teuchos::rcp( new RHSEasy );
vector<double> e1_div2 = e1;
e1_div2[0] /= 2.0;
FunctionPtr rhsBeta = (e1_div2 * beta * e1 + Teuchos::rcp( new ConstantVectorFunction( e2 ) )) * u_prev;
otherRHS->addTerm( rhsBeta * v->grad() - u_prev * tau->div() );
Teuchos::RCP<BurgersProblem> problem = Teuchos::rcp( new BurgersProblem(oldBurgersBF) );
expectedValues.resize(numCells, testOrdering->totalDofs() );
actualValues.resize (numCells, testOrdering->totalDofs() );
problem->integrateAgainstStandardBasis(expectedValues,testOrdering,basisCache);
otherRHS->integrateAgainstStandardBasis(actualValues,testOrdering,basisCache);
tol = 1e-14;
maxDiff = 0.0;
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old RHS differs from new (\"otherRHS\"); maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "testOrdering: \n" << *testOrdering;
}
else
{
cout << "Old and new RHS (\"otherRHS\") agree!!\n";
}
}
FunctionPtr u_prev_squared_div2 = 0.5 * u_prev * u_prev;
rhs->addTerm( (e1 * u_prev_squared_div2 + e2 * u_prev) * v->grad() - u_prev * tau->div());
if (! functionsAgree(e2 * u_prev,
Teuchos::rcp( new ConstantVectorFunction( e2 ) ) * u_prev,
basisCache) )
{
cout << "two like functions differ...\n";
}
FunctionPtr e1_f = Teuchos::rcp( new ConstantVectorFunction( e1 ) );
FunctionPtr e2_f = Teuchos::rcp( new ConstantVectorFunction( e2 ) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction( 1.0 ) );
if (! functionsAgree( Teuchos::rcp( new ProductFunction(e1_f, (e1_f + e2_f)) ), // e1_f * (e1_f + e2_f)
one,
basisCache) )
{
cout << "two like functions differ...\n";
}
if (! functionsAgree(u_prev_squared_div2,
(e1_div2 * beta) * u_prev,
basisCache) )
{
cout << "two like functions differ...\n";
}
if (! functionsAgree(e1 * u_prev_squared_div2,
(e1_div2 * beta * e1) * u_prev,
basisCache) )
{
cout << "two like functions differ...\n";
}
if (! functionsAgree(e1 * u_prev_squared_div2 + e2 * u_prev,
(e1_div2 * beta * e1 + Teuchos::rcp( new ConstantVectorFunction( e2 ) )) * u_prev,
basisCache) )
{
cout << "two like functions differ...\n";
}
problem->integrateAgainstStandardBasis(expectedValues,testOrdering,basisCache);
rhs->integrateAgainstStandardBasis(actualValues,testOrdering,basisCache);
tol = 1e-14;
maxDiff = 0.0;
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old RHS differs from new (\"rhs\"); maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "testOrdering: \n" << *testOrdering;
}
else
{
cout << "Old and new RHS (\"rhs\") agree!!\n";
}
}
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new TopBoundary );
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new NegatedSpatialFilter(outflowBoundary) );
Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp(new PenaltyConstraints);
LinearTermPtr sigma_hat = beta * uhat->times_normal() - beta_n_u_minus_sigma_hat;
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
pc->addConstraint(sigma_hat==zero,outflowBoundary);
FunctionPtr u0 = Teuchos::rcp( new U0 );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
Teuchos::RCP<BCEasy> inflowBC = Teuchos::rcp( new BCEasy );
FunctionPtr u0_squared_div_2 = 0.5 * u0 * u0;
inflowBC->addDirichlet(beta_n_u_minus_sigma_hat,inflowBoundary, ( e1 * u0_squared_div_2 + e2 * u0) * n );
// create a solution object
Teuchos::RCP<Solution> solution = Teuchos::rcp(new Solution(mesh, inflowBC, rhs, ip));
mesh->registerSolution(solution);
solution->setFilter(pc);
// old penalty filter:
Teuchos::RCP<LocalStiffnessMatrixFilter> penaltyBC = Teuchos::rcp(new PenaltyMethodFilter(problem));
// solution->setFilter(penaltyBC);
// compare old and new filters
elemType = mesh->getElement(0)->elementType();
trialOrdering = elemType->trialOrderPtr;
testOrdering = elemType->testOrderPtr;
// stiffness
expectedValues.resize(numCells, trialOrdering->totalDofs(), trialOrdering->totalDofs() );
actualValues.resize (numCells, trialOrdering->totalDofs(), trialOrdering->totalDofs() );
expectedValues.initialize(0.0);
actualValues.initialize(0.0);
// load
FieldContainer<double> expectedLoad(numCells, trialOrdering->totalDofs() );
FieldContainer<double> actualLoad(numCells, trialOrdering->totalDofs() );
penaltyBC->filter(expectedValues,expectedLoad,basisCache,mesh,problem);
pc->filter(actualValues,actualLoad,basisCache,mesh,problem);
maxDiff = 0.0;
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old penalty stiffness differs from new; maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "trialOrdering: \n" << *trialOrdering;
}
else
{
cout << "Old and new penalty stiffness agree!!\n";
}
}
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedLoad,actualLoad,tol,maxDiff) )
{
cout << "Test failed: old penalty load differs from new; maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "trialOrdering: \n" << *trialOrdering;
}
else
{
cout << "Old and new penalty load agree!!\n";
}
}
// define refinement strategy:
Teuchos::RCP<RefinementStrategy> refinementStrategy = Teuchos::rcp(new RefinementStrategy(solution,energyThreshold));
// =================== END INITIALIZATION CODE ==========================
// refine the spectral mesh, for comparability with the original Burgers' driver
mesh->hRefine(vector<int>(1),RefinementPattern::regularRefinementPatternQuad());
int numRefs = 5;
Teuchos::RCP<NonlinearStepSize> stepSize = Teuchos::rcp(new NonlinearStepSize(nonlinearStepSize));
Teuchos::RCP<NonlinearSolveStrategy> solveStrategy = Teuchos::rcp(
new NonlinearSolveStrategy(backgroundFlow, solution, stepSize, nonlinearRelativeEnergyTolerance)
);
for (int refIndex=0; refIndex<numRefs; refIndex++)
{
solveStrategy->solve(rank==0);
refinementStrategy->refine(rank==0); // print to console on rank 0
}
// one more nonlinear solve on refined mesh
int numNRSteps = 5;
for (int i=0; i<numNRSteps; i++)
{
solution->solve(false);
backgroundFlow->addSolution(solution,1.0);
}
if (rank==0)
{
backgroundFlow->writeFieldsToFile(BurgersBilinearForm::U, "u_ref.m");
backgroundFlow->writeFieldsToFile(BurgersBilinearForm::SIGMA_1, "sigmax.m");
backgroundFlow->writeFieldsToFile(BurgersBilinearForm::SIGMA_2, "sigmay.m");
solution->writeFluxesToFile(BurgersBilinearForm::U_HAT, "du_hat_ref.dat");
}
return 0;
}
int main(int argc, char *argv[]) {
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
bool useCompliantGraphNorm = false;
bool enforceOneIrregularity = true;
bool writeStiffnessMatrices = false;
bool writeWorstCaseGramMatrices = false;
int numRefs = 10;
// problem parameters:
double eps = 1e-8;
vector<double> beta_const;
beta_const.push_back(2.0);
beta_const.push_back(1.0);
int k = 2, delta_k = 2;
Teuchos::CommandLineProcessor cmdp(false,true); // false: don't throw exceptions; true: do return errors for unrecognized options
cmdp.setOption("polyOrder",&k,"polynomial order for field variable u");
cmdp.setOption("delta_k", &delta_k, "test space polynomial order enrichment");
cmdp.setOption("numRefs",&numRefs,"number of refinements");
cmdp.setOption("eps", &eps, "epsilon");
if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL) {
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return -1;
}
int H1Order = k + 1;
if (rank==0) {
string normChoice = useCompliantGraphNorm ? "unit-compliant graph norm" : "standard graph norm";
cout << "Using " << normChoice << "." << endl;
cout << "eps = " << eps << endl;
cout << "numRefs = " << numRefs << endl;
cout << "p = " << k << endl;
}
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u;
if (useCompliantGraphNorm) {
u = varFactory.fieldVar("u",HGRAD);
} else {
u = varFactory.fieldVar("u");
}
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(-uhat, tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( beta_const * u, - v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// mathematician's norm
IPPtr mathIP = Teuchos::rcp(new IP());
mathIP->addTerm(tau);
mathIP->addTerm(tau->div());
mathIP->addTerm(v);
mathIP->addTerm(v->grad());
// quasi-optimal norm
IPPtr qoptIP = Teuchos::rcp(new IP);
if (!useCompliantGraphNorm) {
qoptIP->addTerm( tau / eps + v->grad() );
qoptIP->addTerm( beta_const * v->grad() - tau->div() );
qoptIP->addTerm( v );
} else {
FunctionPtr h = Teuchos::rcp( new hFunction );
// here, we're aiming at optimality in 1/h^2 |u|^2 + 1/eps^2 |sigma|^2
qoptIP->addTerm( tau + eps * v->grad() );
qoptIP->addTerm( h * beta_const * v->grad() - tau->div() );
qoptIP->addTerm(v);
qoptIP->addTerm(tau);
}
//////////////////// SPECIFY RHS ///////////////////////
RHSPtr rhs = RHS::rhs();
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
BCPtr bc = BC::bc();
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary );
FunctionPtr u0 = Teuchos::rcp( new U0 );
bc->addDirichlet(uhat, outflowBoundary, u0);
bc->addDirichlet(uhat, inflowBoundary, u0);
// Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp(new PenaltyConstraints);
// pc->addConstraint(uhat==u0,inflowBoundary);
//////////////////// BUILD MESH ///////////////////////
// create a new mesh on a single-cell, unit square domain
Teuchos::RCP<Mesh> mesh = MeshFactory::quadMeshMinRule(confusionBF, H1Order, delta_k);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, qoptIP) );
// solution->setFilter(pc);
double energyThreshold = 0.2; // for mesh refinements
bool useRieszRepBasedRefStrategy = true;
if (rank==0) {
if (useRieszRepBasedRefStrategy) {
cout << "using RieszRep-based refinement strategy.\n";
} else {
cout << "using solution-based refinement strategy.\n";
}
}
Teuchos::RCP<RefinementStrategy> refinementStrategy;
if (!useRieszRepBasedRefStrategy) {
refinementStrategy = Teuchos::rcp( new RefinementStrategy( solution, energyThreshold ) );
} else {
LinearTermPtr residual = confusionBF->testFunctional(solution) - rhs->linearTerm();
refinementStrategy = Teuchos::rcp( new RefinementStrategy( mesh, residual, qoptIP, energyThreshold ) );
}
refinementStrategy->setReportPerCellErrors(true);
refinementStrategy->setEnforceOneIrregularity(enforceOneIrregularity);
for (int refIndex=0; refIndex<numRefs; refIndex++){
if (writeStiffnessMatrices) {
string stiffnessFile = fileNameForRefinement("confusion_stiffness", refIndex);
solution->setWriteMatrixToFile(true, stiffnessFile);
}
solution->solve();
if (writeWorstCaseGramMatrices) {
string gramFile = fileNameForRefinement("confusion_gram", refIndex);
bool jacobiScaling = true;
double condNum = MeshUtilities::computeMaxLocalConditionNumber(qoptIP, mesh, jacobiScaling, gramFile);
if (rank==0) {
cout << "estimated worst-case Gram matrix condition number: " << condNum << endl;
cout << "putative worst-case Gram matrix written to file " << gramFile << endl;
}
}
if (refIndex == numRefs-1) { // write out second-to-last mesh
if (rank==0)
GnuPlotUtil::writeComputationalMeshSkeleton("confusionMesh", mesh, true);
}
refinementStrategy->refine(rank==0); // print to console on rank 0
}
if (writeStiffnessMatrices) {
string stiffnessFile = fileNameForRefinement("confusion_stiffness", numRefs);
solution->setWriteMatrixToFile(true, stiffnessFile);
}
if (writeWorstCaseGramMatrices) {
string gramFile = fileNameForRefinement("confusion_gram", numRefs);
bool jacobiScaling = true;
double condNum = MeshUtilities::computeMaxLocalConditionNumber(qoptIP, mesh, jacobiScaling, gramFile);
if (rank==0) {
cout << "estimated worst-case Gram matrix condition number: " << condNum << endl;
cout << "putative worst-case Gram matrix written to file " << gramFile << endl;
}
}
// one more solve on the final refined mesh:
solution->solve();
#ifdef HAVE_EPETRAEXT_HDF5
ostringstream dir_name;
dir_name << "confusion_eps" << eps;
HDF5Exporter exporter(mesh,dir_name.str());
exporter.exportSolution(solution, varFactory, 0);
if (rank==0) cout << "wrote solution to " << dir_name.str() << endl;
#endif
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int rank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// define mathematical "constants"
vector<double> e1(2); // (1,0)
e1[0] = 1;
vector<double> e2(2); // (0,1)
e2[1] = 1;
FunctionPtr negOne = Function::constant(-1.0);
FunctionPtr one = Function::constant(1.0);
// problem params
double Re = args.Input<double>("--Re","Reynolds number",1e3);
double dt = args.Input<double>("--dt","Timestep",.25);
double Ma = args.Input<double>("--Ma","Mach number",3.0);
// solver
int nCells = args.Input<int>("--nCells", "num cells",2);
int polyOrder = args.Input<int>("--p","order of approximation",2);
int pToAdd = args.Input<int>("--pToAdd", "test space enrichment",2);
double time_tol_orig = args.Input<double>("--timeTol", "time step tolerance",1e-8);
bool useLineSearch = args.Input<bool>("--useLineSearch", "flag for line search",true); // default to zero
int maxNRIter = args.Input<int>("--maxNRIter","maximum number of NR iterations",2); // default to one per timestep
int numTimeSteps = args.Input<int>("--maxTimeSteps","max number of time steps",150); // max time steps
double minDt = args.Input<double>("--minDt","min timestep for adaptive timestepping",.01); // max time steps
double maxDt = args.Input<double>("--maxDt","max timestep for adaptive timestepping",.1); // max time steps
// adaptivity
int numUniformRefs = args.Input<int>("--numUniformRefs","num uniform refinements (pre-adaptivity)",0);
int numRefs = args.Input<int>("--numRefs","num adaptive refinements",0);
double energyThreshold = args.Input<double>("--energyThreshold", "energy thresh for adaptivity",0.25); // for mesh refinements
bool useHpStrategy = args.Input<bool>("--useHpStrategy","option to use a 'cheap' hp strategy", false);
double anisotropicThresh = args.Input<int>("--anisotropicThresh","anisotropy threshhold",10.0);
bool useAnisotropy = args.Input<bool>("--useAnisotropy","anisotropy flag",false);
bool usePointViscosity = args.Input<bool>("--usePointViscosity","use extra viscosity at plate point",false);
bool useAdaptiveTimestepping = args.Input<bool>("--useAdaptiveTimestepping","use adaptive timestepping a la Ben Kirk", false);
// conditioning for DPG
int hScaleOption = args.Input<int>("--hScaleOption","option to scale terms to offset conditioning for small h", 0);
int hScaleTauOption = args.Input<int>("--hScaleTauOption","option to scale tau terms to offset conditioning for small h", 0);
// etc - experimental
bool useHigherOrderForU = args.Input<bool>("--useHigherOrderForU","option to increase order for field vars",false); // HGRAD is one higher order
bool useConditioningCFL = args.Input<bool>("--useConditioningCFL","option to use a CFL limit for conditioning",false);
int numPreRefs = args.Input<int>("--numPreRefs","pre-refinements on singularity",0);
bool scalePlate = args.Input<bool>("--scalePlate","flag to weight plate so it matters less",false);
double ipSwitch = args.Input<double>("--ipSwitch","smallest elem thresh to switch to graph norm",0.0); // default to not changing
// IO stuff
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", "");
string solnSaveFile = args.Input<string>("--solnSaveFile", "file to which to save soln", "");
string solnLoadFile = args.Input<string>("--solnLoadFile", "file from which to load soln", "");
string dir = args.Input<string>("--dir", "dir to which we save/from which we load files","");
bool reportTimingResults = args.Input<bool>("--reportTimings", "flag to report timings of solve", false);
bool writeTimestepFiles = args.Input<bool>("--writeTimestepFiles","flag to turn on and off time step writing",false);
if (rank==0)
{
cout << "saveFile is " << dir + saveFile << endl;
cout << "saveSolnFile is " << dir + solnSaveFile << endl;
}
if (rank==0)
{
cout << "loadFile is " << dir + replayFile << endl;
cout << "loadSolnFile is " << dir + solnLoadFile << endl;
}
///////////////////////////////////////////////////////////////////////////////////////////////
// END OF INPUT ARGUMENTS
///////////////////////////////////////////////////////////////////////////////////////////////
if (useHigherOrderForU)
{
polyOrder = 1;
}
bool useTriangles = false;
FieldContainer<double> domainPoints(4,2);
domainPoints(0,0) = 0.0; // x1
domainPoints(0,1) = 0.0; // y1
domainPoints(1,0) = X_BOUNDARY;
domainPoints(1,1) = 0.0;
domainPoints(2,0) = X_BOUNDARY;
domainPoints(2,1) = YTOP;
domainPoints(3,0) = 0.0;
domainPoints(3,1) = YTOP;
int H1Order = polyOrder + 1;
// int H1Order = 2; // start with linears, and keep singularity linear at singularity
int horizontalCells = 2*nCells, verticalCells = nCells;
////////////////////////////////////////////////////////////////////
// DEFINE VARIABLES
////////////////////////////////////////////////////////////////////
// new-style bilinear form definition
// traces
VarFactory varFactory;
VarPtr u1hat = varFactory.traceVar("\\widehat{u}_1");
VarPtr u2hat = varFactory.traceVar("\\widehat{u}_2");
VarPtr That = varFactory.traceVar("\\widehat{T}");
// fluxes
VarPtr F1nhat = varFactory.fluxVar("\\widehat{F}_1n");
VarPtr F2nhat = varFactory.fluxVar("\\widehat{F}_2n");
VarPtr F3nhat = varFactory.fluxVar("\\widehat{F}_3n");
VarPtr F4nhat = varFactory.fluxVar("\\widehat{F}_4n");
// stress fields
VarPtr sigma11 = varFactory.fieldVar("\\sigma_{11}");
VarPtr sigma12 = varFactory.fieldVar("\\sigma_{12}");
VarPtr sigma22 = varFactory.fieldVar("\\sigma_{22}");
VarPtr q1 = varFactory.fieldVar("q_1");
VarPtr q2 = varFactory.fieldVar("q_2");
VarPtr omega = varFactory.fieldVar("\\omega");
VarPtr u_1,u_2,u_3,u_4;
// H1-ish fields
if (useHigherOrderForU) // HGRAD is one higher order
{
u_1 = varFactory.fieldVar("u_1",HGRAD);
u_2 = varFactory.fieldVar("u_2",HGRAD);
u_3 = varFactory.fieldVar("u_3",HGRAD);
u_4 = varFactory.fieldVar("u_4",HGRAD);
}
else
{
u_1 = varFactory.fieldVar("u_1");
u_2 = varFactory.fieldVar("u_2");
u_3 = varFactory.fieldVar("rho");
u_4 = varFactory.fieldVar("T");
}
// test fxns
VarPtr tau1 = varFactory.testVar("\\tau_1",HDIV);
VarPtr tau2 = varFactory.testVar("\\tau_2",HDIV);
VarPtr tau3 = varFactory.testVar("\\tau_3",HDIV);
VarPtr v1 = varFactory.testVar("v_1",HGRAD);
VarPtr v2 = varFactory.testVar("v_2",HGRAD);
VarPtr v3 = varFactory.testVar("v_3",HGRAD);
VarPtr v4 = varFactory.testVar("v_4",HGRAD);
////////////////////////////////////////////////////////////////////
// CREATE BILINEAR FORM PTR AND MESH
////////////////////////////////////////////////////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) ); // initialize bilinear form
// create a pointer to a new mesh:
// Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(domainPoints, horizontalCells, verticalCells, bf, H1Order, H1Order+pToAdd, useTriangles);
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildRampMesh(rampHeight,bf, H1Order, H1Order+pToAdd);
// mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));
mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("REFTREE")));
MeshInfo meshInfo(mesh); // gets info like cell measure, etc
// for writing ref history to file
Teuchos::RCP< RefinementHistory > refHistory = Teuchos::rcp( new RefinementHistory );
mesh->registerObserver(refHistory);
////////////////////////////////////////////////////////////////////
// CREATE SOLUTION OBJECT
////////////////////////////////////////////////////////////////////
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 prevTimeFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
Teuchos::RCP<Solution> solution = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP));
int enrichDegree = 2; // just for kicks.
if (rank==0)
cout << "enriching cubature by " << enrichDegree << endl;
solution->setCubatureEnrichmentDegree(enrichDegree); // double cubature enrichment
if (reportTimingResults)
{
solution->setReportTimingResults(true);
}
mesh->registerSolution(solution);
mesh->registerSolution(backgroundFlow); // u_t(i)
mesh->registerSolution(prevTimeFlow); // u_t(i-1)
// for loading refinement history
if (replayFile.length() > 0)
{
RefinementHistory refHistory;
replayFile = dir + replayFile;
refHistory.loadFromFile(replayFile);
refHistory.playback(mesh);
int numElems = mesh->numActiveElements();
if (rank==0)
{
double minSideLength = meshInfo.getMinCellSideLength() ;
cout << "after replay, num elems = " << numElems << " and min side length = " << minSideLength << endl;
}
}
if (solnLoadFile.length() > 0)
{
std::ostringstream ss;
// ss << dir << "solution_" << solnLoadFile;
// solution->readFromFile(ss.str());
ss.str("");
ss << dir << "backgroundFlow_" << solnLoadFile;
backgroundFlow->readFromFile(ss.str());
ss.str("");
ss << dir << "prevTimeFlow_" << solnLoadFile;
prevTimeFlow->readFromFile(ss.str());
}
////////////////////////////////////////////////////////////////////
// PSEUDO-TIME SOLVE STRATEGY
////////////////////////////////////////////////////////////////////
VTKExporter exporter(solution, mesh, varFactory);
VTKExporter backgroundFlowExporter(backgroundFlow, mesh, varFactory);
if (rank==0)
{
exporter.exportSolution("dU");
backgroundFlowExporter.exportSolution("U");
}
return 0;
}
int main(int argc, char *argv[]) {
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
double epsilon = args.Input<double>("--epsilon", "diffusion parameter");
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation");
int norm = args.Input<int>("--norm", "0 = graph\n 1 = robust\n 2 = modified robust");
// Optional arguments (have defaults)
halfwidth = args.Input("--halfwidth", "half the width of the wedge", 0.5);
bool allQuads = args.Input("--allQuads", "use only quads in mesh", false);
bool zeroL2 = args.Input("--zeroL2", "take L2 term on v in robust norm to zero", enforceLocalConservation);
args.Process();
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("uhat");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("fhat");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma = varFactory.fieldVar("sigma", VECTOR_L2);
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma / epsilon, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( beta * u, - v->grad() );
bf->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
// Graph norm
if (norm == 0)
{
ip = bf->graphNorm();
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
ip->addZeroMeanTerm( h2_scaling*v );
}
// Robust norm
else if (norm == 1)
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
if (!zeroL2)
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
// Weight these two terms for inflow
ip->addTerm( beta * v->grad() );
ip->addTerm( tau->div() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (zeroL2)
ip->addZeroMeanTerm( h2_scaling*v );
}
// Modified robust norm
else if (norm == 2)
{
// robust test norm
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
FunctionPtr h2_scaling = Teuchos::rcp( new ZeroMeanScaling );
if (!zeroL2)
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
ip->addTerm( tau->div() - beta*v->grad() );
ip->addTerm( ip_scaling/sqrt(epsilon) * tau );
if (zeroL2)
ip->addZeroMeanTerm( h2_scaling*v );
}
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = Teuchos::rcp( new ConstantScalarFunction(0.0) );
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
SpatialFilterPtr inflow = Teuchos::rcp( new Inflow );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
bc->addDirichlet(beta_n_u_minus_sigma_n, inflow, zero);
SpatialFilterPtr leadingWedge = Teuchos::rcp( new LeadingWedge );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
bc->addDirichlet(uhat, leadingWedge, one);
SpatialFilterPtr trailingWedge = Teuchos::rcp( new TrailingWedge );
bc->addDirichlet(beta_n_u_minus_sigma_n, trailingWedge, beta*n*one);
// bc->addDirichlet(uhat, trailingWedge, one);
SpatialFilterPtr top = Teuchos::rcp( new Top );
bc->addDirichlet(uhat, top, zero);
// bc->addDirichlet(beta_n_u_minus_sigma_n, top, zero);
SpatialFilterPtr outflow = Teuchos::rcp( new Outflow );
pc->addConstraint(beta*uhat->times_normal() - beta_n_u_minus_sigma_n == zero, outflow);
//////////////////// BUILD MESH ///////////////////////
int H1Order = 3, pToAdd = 2;
// define nodes for mesh
vector< FieldContainer<double> > vertices;
FieldContainer<double> pt(2);
vector< vector<int> > elementIndices;
vector<int> q(4);
vector<int> t(3);
if (allQuads)
{
pt(0) = -halfwidth; pt(1) = -1;
vertices.push_back(pt);
pt(0) = 0; pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth; pt(1) = -1;
vertices.push_back(pt);
pt(0) = halfwidth; pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = 0; pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth; pt(1) = halfwidth;
vertices.push_back(pt);
q[0] = 0; q[1] = 1; q[2] = 4; q[3] = 5;
elementIndices.push_back(q);
q[0] = 1; q[1] = 2; q[2] = 3; q[3] = 4;
elementIndices.push_back(q);
}
else
{
pt(0) = -halfwidth; pt(1) = -1;
vertices.push_back(pt);
pt(0) = 0; pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth; pt(1) = -1;
vertices.push_back(pt);
pt(0) = halfwidth; pt(1) = 0;
vertices.push_back(pt);
pt(0) = halfwidth; pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = 0; pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth; pt(1) = halfwidth;
vertices.push_back(pt);
pt(0) = -halfwidth; pt(1) = 0;
vertices.push_back(pt);
t[0] = 0; t[1] = 1; t[2] = 7;
elementIndices.push_back(t);
t[0] = 1; t[1] = 2; t[2] = 3;
elementIndices.push_back(t);
q[0] = 1; q[1] = 3; q[2] = 4; q[3] = 5;
elementIndices.push_back(q);
q[0] = 7; q[1] = 1; q[2] = 5; q[3] = 6;
elementIndices.push_back(q);
}
Teuchos::RCP<Mesh> mesh = Teuchos::rcp( new Mesh(vertices, elementIndices, bf, H1Order, pToAdd) );
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
solution->setFilter(pc);
if (enforceLocalConservation) {
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero);
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(solution, mesh, varFactory);
ofstream errOut;
if (commRank == 0)
errOut.open("singularwedge_err.txt");
for (int refIndex=0; refIndex<=numRefs; refIndex++){
solution->solve(false);
double energy_error = solution->energyErrorTotal();
if (commRank==0){
stringstream outfile;
outfile << "singularwedge_" << refIndex;
exporter.exportSolution(outfile.str());
// Check local conservation
FunctionPtr flux = Teuchos::rcp( new PreviousSolutionFunction(solution, beta_n_u_minus_sigma_n) );
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, varFactory, mesh);
cout << "Mass flux: Largest Local = " << fluxImbalances[0]
<< ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
errOut << mesh->numGlobalDofs() << " " << energy_error << " "
<< fluxImbalances[0] << " " << fluxImbalances[1] << " " << fluxImbalances[2] << endl;
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
if (commRank == 0)
errOut.close();
return 0;
}
int main(int argc, char *argv[]) {
// TODO: figure out the right thing to do here...
// may want to modify argc and argv before we make the following call:
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#ifdef HAVE_MPI
choice::MpiArgs args( argc, argv );
#else
choice::Args args(argc, argv );
#endif
int polyOrder, pToAdd;
try {
// read args:
polyOrder = args.Input<int>("--polyOrder", "L^2 (field) polynomial order");
pToAdd = args.Input<int>("--delta_p", "delta p for test enrichment", 2);
args.Process();
} catch ( choice::ArgException& e )
{
exit(0);
}
int H1Order = polyOrder + 1;
bool useCompliantGraphNorm = false; // weights to improve conditioning of the local problems
bool useExtendedPrecisionForOptimalTestInversion = false;
/////////////////////////// "VGP_CONFORMING" VERSION ///////////////////////
// fluxes and traces:
VarPtr u1hat, u2hat, t1n, t2n;
// fields for SGP:
VarPtr phi, p, sigma11, sigma12, sigma21, sigma22;
// fields specific to VGP:
VarPtr u1, u2;
BFPtr stokesBF;
IPPtr qoptIP;
double mu = 1;
FunctionPtr h = Teuchos::rcp( new hFunction() );
VarPtr tau1,tau2,v1,v2,q;
VarFactory varFactory;
tau1 = varFactory.testVar("\\tau_1", HDIV);
tau2 = varFactory.testVar("\\tau_2", HDIV);
v1 = varFactory.testVar("v_1", HGRAD);
v2 = varFactory.testVar("v_2", HGRAD);
q = varFactory.testVar("q", HGRAD);
u1hat = varFactory.traceVar("\\widehat{u}_1");
u2hat = varFactory.traceVar("\\widehat{u}_2");
t1n = varFactory.fluxVar("\\widehat{t_{1n}}");
t2n = varFactory.fluxVar("\\widehat{t_{2n}}");
if (!useCompliantGraphNorm) {
u1 = varFactory.fieldVar("u_1");
u2 = varFactory.fieldVar("u_2");
} else {
u1 = varFactory.fieldVar("u_1", HGRAD);
u2 = varFactory.fieldVar("u_2", HGRAD);
}
sigma11 = varFactory.fieldVar("\\sigma_11");
sigma12 = varFactory.fieldVar("\\sigma_12");
sigma21 = varFactory.fieldVar("\\sigma_21");
sigma22 = varFactory.fieldVar("\\sigma_22");
p = varFactory.fieldVar("p");
stokesBF = Teuchos::rcp( new BF(varFactory) );
// tau1 terms:
stokesBF->addTerm(u1,tau1->div());
stokesBF->addTerm(sigma11,tau1->x()); // (sigma1, tau1)
stokesBF->addTerm(sigma12,tau1->y());
stokesBF->addTerm(-u1hat, tau1->dot_normal());
// tau2 terms:
stokesBF->addTerm(u2, tau2->div());
stokesBF->addTerm(sigma21,tau2->x()); // (sigma2, tau2)
stokesBF->addTerm(sigma22,tau2->y());
stokesBF->addTerm(-u2hat, tau2->dot_normal());
// v1:
stokesBF->addTerm(mu * sigma11,v1->dx()); // (mu sigma1, grad v1)
stokesBF->addTerm(mu * sigma12,v1->dy());
stokesBF->addTerm( - p, v1->dx() );
stokesBF->addTerm( -t1n, v1);
// v2:
stokesBF->addTerm(mu * sigma21,v2->dx()); // (mu sigma2, grad v2)
stokesBF->addTerm(mu * sigma22,v2->dy());
stokesBF->addTerm( -p, v2->dy());
stokesBF->addTerm( -t2n, v2);
// q:
stokesBF->addTerm(-u1,q->dx()); // (-u, grad q)
stokesBF->addTerm(-u2,q->dy());
stokesBF->addTerm(u1hat->times_normal_x() + u2hat->times_normal_y(), q);
if (rank==0)
stokesBF->printTrialTestInteractions();
stokesBF->setUseExtendedPrecisionSolveForOptimalTestFunctions(useExtendedPrecisionForOptimalTestInversion);
mesh = MeshFactory::quadMesh(stokesBF, H1Order, pToAdd);
//////////////////// CREATE BCs ///////////////////////
BCPtr bc = BC::bc();
//////////////////// CREATE RHS ///////////////////////
RHSPtr rhs = RHS::rhs(); // zero for now...
IPPtr ip;
qoptIP = Teuchos::rcp(new IP());
if (useCompliantGraphNorm) {
qoptIP->addTerm( mu * v1->dx() + tau1->x() ); // sigma11
qoptIP->addTerm( mu * v1->dy() + tau1->y() ); // sigma12
qoptIP->addTerm( mu * v2->dx() + tau2->x() ); // sigma21
qoptIP->addTerm( mu * v2->dy() + tau2->y() ); // sigma22
qoptIP->addTerm( mu * v1->dx() + mu * v2->dy() ); // pressure
qoptIP->addTerm( h * tau1->div() - h * q->dx() ); // u1
qoptIP->addTerm( h * tau2->div() - h * q->dy()); // u2
qoptIP->addTerm( (mu / h) * v1 );
qoptIP->addTerm( (mu / h) * v2 );
qoptIP->addTerm( q );
qoptIP->addTerm( tau1 );
qoptIP->addTerm( tau2 );
} else { // standard graph norm, then
qoptIP = stokesBF->graphNorm();
}
ip = qoptIP;
if (rank==0)
ip->printInteractions();
// aim is just to answer one simple question:
// have I figured out a trial-space preimage for optimal test function (q=1, tau=0, v=0)?
SolutionPtr soln = Teuchos::rcp(new Solution(mesh));
FunctionPtr x = Function::xn();
FunctionPtr y = Function::yn();
// u1 = u1_hat = x / 2
FunctionPtr u1_exact = x / 2;
// u2 = u2_hat = y / 2
FunctionPtr u2_exact = y / 2;
// sigma = 0.5 * I
FunctionPtr sigma11_exact = Function::constant(0.5);
FunctionPtr sigma22_exact = Function::constant(0.5);
// tn_hat = 0.5 * n
FunctionPtr n = Function::normal();
FunctionPtr t1n_exact = n->x() / 2;
FunctionPtr t2n_exact = n->y() / 2;
map<int, FunctionPtr > exact_soln;
exact_soln[u1->ID()] = u1_exact;
exact_soln[u1hat->ID()] = u1_exact;
exact_soln[u2->ID()] = u2_exact;
exact_soln[u2hat->ID()] = u2_exact;
exact_soln[sigma11->ID()] = sigma11_exact;
exact_soln[sigma22->ID()] = sigma22_exact;
exact_soln[t1n->ID()] = t1n_exact;
exact_soln[t2n->ID()] = t2n_exact;
exact_soln[p->ID()] = Function::zero();
exact_soln[sigma12->ID()] = Function::zero();
exact_soln[sigma21->ID()] = Function::zero();
soln->projectOntoMesh(exact_soln);
LinearTermPtr soln_functional = stokesBF->testFunctional(soln);
RieszRepPtr rieszRep = Teuchos::rcp( new RieszRep(mesh, ip, soln_functional) );
rieszRep->computeRieszRep();
// get test functions:
FunctionPtr q_fxn = Teuchos::rcp( new RepFunction(q, rieszRep) );
FunctionPtr v1_fxn = Teuchos::rcp( new RepFunction(v1, rieszRep) );
FunctionPtr v2_fxn = Teuchos::rcp( new RepFunction(v2, rieszRep) );
FunctionPtr tau1_fxn = Teuchos::rcp( new RepFunction(tau1, rieszRep) );
FunctionPtr tau2_fxn = Teuchos::rcp( new RepFunction(tau2, rieszRep) );
cout << "L2 norm of (q-1) : " << (q_fxn - 1)->l2norm(mesh) << endl;
cout << "L2 norm of (v1) : " << (v1_fxn)->l2norm(mesh) << endl;
cout << "L2 norm of (v2) : " << (v2_fxn)->l2norm(mesh) << endl;
cout << "L2 norm of (tau1) : " << (tau1_fxn)->l2norm(mesh) << endl;
cout << "L2 norm of (tau2) : " << (tau2_fxn)->l2norm(mesh) << endl;
VTKExporter exporter(soln, mesh, varFactory);
exporter.exportSolution("conservationPreimage", H1Order*2);
cout << "Checking that the soln_functional is what I expect:\n";
FunctionPtr xyVector = Function::vectorize(x, y);
cout << "With v1 = x, integral: " << integralOverMesh(soln_functional, v1, x) << endl;
cout << "With v2 = y, integral: " << integralOverMesh(soln_functional, v2, y) << endl;
cout << "With tau1=(x,y), integral: " << integralOverMesh(soln_functional, tau1, xyVector) << endl;
cout << "With tau2=(x,y), integral: " << integralOverMesh(soln_functional, tau2, xyVector) << endl;
cout << "With q =x, integral: " << integralOverMesh(soln_functional, q, x) << endl;
cout << "(Expect 0s all around, except for q, where we expect (1,x) == 0.5.)\n";
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
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
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
int norm = args.Input<int>("--norm", "0 = graph\n 1 = robust\n 2 = coupled robust");
// Optional arguments (have defaults)
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation", false);
double Re = args.Input("--Re", "Reynolds number", 40);
double nu = 1./Re;
double lambda = Re/2.-sqrt(Re*Re/4+4*pi*pi);
int maxNewtonIterations = args.Input("--maxIterations", "maximum number of Newton iterations", 20);
int polyOrder = args.Input("--polyOrder", "polynomial order for field variables", 2);
int deltaP = args.Input("--deltaP", "how much to enrich test space", 2);
// string saveFile = args.Input<string>("--meshSaveFile", "file to which to save refinement history", "");
// string replayFile = args.Input<string>("--meshLoadFile", "file with refinement history to replay", "");
args.Process();
// if (commRank==0)
// {
// cout << "saveFile is " << saveFile << endl;
// cout << "loadFile is " << replayFile << endl;
// }
//////////////////// PROBLEM DEFINITIONS ///////////////////////
int H1Order = polyOrder+1;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
// VarPtr tau11 = varFactory.testVar("tau11", HGRAD);
// VarPtr tau12 = varFactory.testVar("tau12", HGRAD);
// VarPtr tau22 = varFactory.testVar("tau22", HGRAD);
VarPtr tau1 = varFactory.testVar("tau1", HDIV);
VarPtr tau2 = varFactory.testVar("tau2", HDIV);
VarPtr v1 = varFactory.testVar("v1", HGRAD);
VarPtr v2 = varFactory.testVar("v2", HGRAD);
VarPtr q = varFactory.testVar("q", HGRAD);
// define trial variables
VarPtr u1 = varFactory.fieldVar("u1");
VarPtr u2 = varFactory.fieldVar("u2");
// VarPtr sigma11 = varFactory.fieldVar("sigma11");
// VarPtr sigma12 = varFactory.fieldVar("sigma12");
// VarPtr sigma22 = varFactory.fieldVar("sigma22");
VarPtr sigma1 = varFactory.fieldVar("sigma1", VECTOR_L2);
VarPtr sigma2 = varFactory.fieldVar("sigma2", VECTOR_L2);
VarPtr u1hat = varFactory.traceVar("u1hat");
VarPtr u2hat = varFactory.traceVar("u2hat");
VarPtr t1hat = varFactory.fluxVar("t1hat");
VarPtr t2hat = varFactory.fluxVar("t2hat");
VarPtr p = varFactory.fieldVar("p");
//////////////////// BUILD MESH ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// define nodes for mesh
FieldContainer<double> meshBoundary(4,2);
double xmin = -0.5;
double xmax = 1.0;
double ymin = -0.5;
double ymax = 1.5;
meshBoundary(0,0) = xmin; // x1
meshBoundary(0,1) = ymin; // y1
meshBoundary(1,0) = xmax;
meshBoundary(1,1) = ymin;
meshBoundary(2,0) = xmax;
meshBoundary(2,1) = ymax;
meshBoundary(3,0) = xmin;
meshBoundary(3,1) = ymax;
int horizontalCells = 6, verticalCells = 8;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
bf, H1Order, H1Order+deltaP);
////////////////////////////////////////////////////////////////////
// INITIALIZE BACKGROUND FLOW FUNCTIONS
////////////////////////////////////////////////////////////////////
BCPtr nullBC = Teuchos::rcp((BC*)NULL);
RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
vector<double> e1(2); // (1,0)
e1[0] = 1;
vector<double> e2(2); // (0,1)
e2[1] = 1;
FunctionPtr u1_prev = Function::solution(u1, backgroundFlow);
FunctionPtr u2_prev = Function::solution(u2, backgroundFlow);
FunctionPtr sigma1_prev = Function::solution(sigma1, backgroundFlow);
FunctionPtr sigma2_prev = Function::solution(sigma2, backgroundFlow);
FunctionPtr p_prev = Function::solution(p, backgroundFlow);
// FunctionPtr sigma11_prev = Function::solution(sigma11, backgroundFlow);
// FunctionPtr sigma12_prev = Function::solution(sigma12, backgroundFlow);
// FunctionPtr sigma22_prev = Function::solution(sigma22, backgroundFlow);
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
FunctionPtr u1Exact = Teuchos::rcp( new ExactU1(lambda) );
FunctionPtr u2Exact = Teuchos::rcp( new ExactU2(lambda) );
// FunctionPtr beta = e1 * u1_prev + e2 * u2_prev;
// ==================== SET INITIAL GUESS ==========================
map<int, Teuchos::RCP<Function> > functionMap;
functionMap[u1->ID()] = u1Exact;
functionMap[u2->ID()] = u2Exact;
// functionMap[sigma1->ID()] = Function::vectorize(zero,zero);
// functionMap[sigma2->ID()] = Function::vectorize(zero,zero);
// functionMap[p->ID()] = zero;
backgroundFlow->projectOntoMesh(functionMap);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
// // stress equation
bf->addTerm( 1./nu*sigma1, tau1 );
bf->addTerm( 1./nu*sigma2, tau2 );
bf->addTerm( u1, tau1->div() );
bf->addTerm( u2, tau2->div() );
bf->addTerm( -u1hat, tau1->dot_normal() );
bf->addTerm( -u2hat, tau2->dot_normal() );
// bf->addTerm( 1./(2*nu)*sigma11, tau11 );
// bf->addTerm( 1./(2*nu)*sigma12, tau12 );
// bf->addTerm( 1./(2*nu)*sigma12, tau12 );
// bf->addTerm( 1./(2*nu)*sigma22, tau22 );
// bf->addTerm( u1, tau11->dx() );
// bf->addTerm( u1, tau12->dy() );
// bf->addTerm( u2, tau12->dx() );
// bf->addTerm( u2, tau22->dy() );
// bf->addTerm( -u1hat, tau11->times_normal_x() );
// bf->addTerm( -u1hat, tau12->times_normal_y() );
// bf->addTerm( -u2hat, tau12->times_normal_x() );
// bf->addTerm( -u2hat, tau22->times_normal_y() );
// momentum equation
bf->addTerm( -2.*u1_prev*u1, v1->dx() );
bf->addTerm( -u2_prev*u1, v1->dy() );
bf->addTerm( -u1_prev*u2, v1->dy() );
bf->addTerm( -u2_prev*u1, v2->dx() );
bf->addTerm( -u1_prev*u2, v1->dy() );
bf->addTerm( -2.*u2_prev*u2, v2->dy() );
bf->addTerm( -p, v1->dx() );
bf->addTerm( -p, v2->dy() );
// bf->addTerm( sigma11, v1->dx() );
// bf->addTerm( sigma12, v1->dy() );
// bf->addTerm( sigma12, v2->dx() );
// bf->addTerm( sigma22, v2->dy() );
bf->addTerm( sigma1, v1->grad() );
bf->addTerm( sigma2, v2->grad() );
bf->addTerm( t1hat, v1);
bf->addTerm( t2hat, v2);
// continuity equation
bf->addTerm( -u1, q->dx() );
bf->addTerm( -u2, q->dy() );
bf->addTerm( u1hat, q->times_normal_x() );
bf->addTerm( u2hat, q->times_normal_y() );
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
// stress equation
rhs->addTerm( -u1_prev * tau1->div() );
rhs->addTerm( -u2_prev * tau2->div() );
// momentum equation
rhs->addTerm( 2.*u1_prev*u1_prev * v1->dx() );
rhs->addTerm( u2_prev*u1_prev * v1->dy() );
rhs->addTerm( u1_prev*u2_prev * v1->dy() );
rhs->addTerm( u2_prev*u1_prev * v2->dx() );
rhs->addTerm( u1_prev*u2_prev * v1->dy() );
rhs->addTerm( 2.*u2_prev*u2_prev * v2->dy() );
// rhs->addTerm( p_prev * v1->dx() );
// rhs->addTerm( p_prev * v2->dy() );
// rhs->addTerm( -sigma1_prev * v1->grad() );
// rhs->addTerm( -sigma2_prev * v2->grad() );
// rhs->addTerm( -sigma11_prev * v1->dx() );
// rhs->addTerm( -sigma12_prev * v1->dy() );
// rhs->addTerm( -sigma12_prev * v2->dx() );
// rhs->addTerm( -sigma22_prev * v2->dy() );
// continuity equation
rhs->addTerm( u1_prev * q->dx() );
rhs->addTerm( u2_prev * q->dy() );
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
if (norm == 0)
{
ip = bf->graphNorm();
}
else if (norm == 1)
{
// ip = bf->l2Norm();
}
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
// Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp( new PenaltyConstraints );
SpatialFilterPtr left = Teuchos::rcp( new ConstantXBoundary(-0.5) );
SpatialFilterPtr right = Teuchos::rcp( new ConstantXBoundary(1) );
SpatialFilterPtr top = Teuchos::rcp( new ConstantYBoundary(-0.5) );
SpatialFilterPtr bottom = Teuchos::rcp( new ConstantYBoundary(1.5) );
bc->addDirichlet(u1hat, left, u1Exact);
bc->addDirichlet(u2hat, left, u2Exact);
bc->addDirichlet(u1hat, right, u1Exact);
bc->addDirichlet(u2hat, right, u2Exact);
bc->addDirichlet(u1hat, top, u1Exact);
bc->addDirichlet(u2hat, top, u2Exact);
bc->addDirichlet(u1hat, bottom, u1Exact);
bc->addDirichlet(u2hat, bottom, u2Exact);
// zero mean constraint on pressure
bc->addZeroMeanConstraint(p);
// pc->addConstraint(u1hat*u2hat-t1hat == zero, top);
// pc->addConstraint(u2hat*u2hat-t2hat == zero, top);
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
// solution->setFilter(pc);
// if (enforceLocalConservation) {
// solution->lagrangeConstraints()->addConstraint(u1hat->times_normal_x() + u2hat->times_normal_y() == zero);
// }
// ==================== Register Solutions ==========================
mesh->registerSolution(solution);
mesh->registerSolution(backgroundFlow);
// Teuchos::RCP< RefinementHistory > refHistory = Teuchos::rcp( new RefinementHistory );
// mesh->registerObserver(refHistory);
//////////////////// SOLVE & REFINE ///////////////////////
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(backgroundFlow, mesh, varFactory);
stringstream outfile;
outfile << "kovasznay" << "_" << 0;
exporter.exportSolution(outfile.str());
double nonlinearRelativeEnergyTolerance = 1e-5; // used to determine convergence of the nonlinear solution
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
double L2Update = 1e10;
int iterCount = 0;
while (L2Update > nonlinearRelativeEnergyTolerance && iterCount < maxNewtonIterations)
{
solution->solve(false);
double u1L2Update = solution->L2NormOfSolutionGlobal(u1->ID());
double u2L2Update = solution->L2NormOfSolutionGlobal(u2->ID());
L2Update = sqrt(u1L2Update*u1L2Update + u2L2Update*u2L2Update);
// Check local conservation
if (commRank == 0)
{
cout << "L2 Norm of Update = " << L2Update << endl;
// if (saveFile.length() > 0) {
// std::ostringstream oss;
// oss << string(saveFile) << refIndex ;
// cout << "on refinement " << refIndex << " saving mesh file to " << oss.str() << endl;
// refHistory->saveToFile(oss.str());
// }
}
// line search algorithm
double alpha = 1.0;
backgroundFlow->addSolution(solution, alpha);
iterCount++;
}
if (commRank == 0)
{
stringstream outfile;
outfile << "kovasznay" << "_" << refIndex+1;
exporter.exportSolution(outfile.str());
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
int norm = args.Input<int>("--norm", "0 = graph\n 1 = robust\n 2 = coupled robust");
// Optional arguments (have defaults)
int uniformRefinements = args.Input("--uniformRefinements", "number of uniform refinements", 0);
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation", false);
double radius = args.Input("--r", "cylinder radius", 0.6);
int Re = args.Input("--Re", "Reynolds number", 1);
int maxNewtonIterations = args.Input("--maxIterations", "maximum number of Newton iterations", 1);
int polyOrder = args.Input("--polyOrder", "polynomial order for field variables", 2);
int deltaP = args.Input("--deltaP", "how much to enrich test space", 2);
// string saveFile = args.Input<string>("--meshSaveFile", "file to which to save refinement history", "");
// string replayFile = args.Input<string>("--meshLoadFile", "file with refinement history to replay", "");
args.Process();
//////////////////// PROBLEM DEFINITIONS ///////////////////////
int H1Order = polyOrder+1;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau1 = varFactory.testVar("tau1", HDIV);
VarPtr tau2 = varFactory.testVar("tau2", HDIV);
VarPtr v1 = varFactory.testVar("v1", HGRAD);
VarPtr v2 = varFactory.testVar("v2", HGRAD);
VarPtr vc = varFactory.testVar("vc", HGRAD);
// define trial variables
VarPtr u1 = varFactory.fieldVar("u1");
VarPtr u2 = varFactory.fieldVar("u2");
VarPtr p = varFactory.fieldVar("p");
VarPtr u1hat = varFactory.traceVar("u1hat");
VarPtr u2hat = varFactory.traceVar("u2hat");
VarPtr t1hat = varFactory.fluxVar("t1hat");
VarPtr t2hat = varFactory.fluxVar("t2hat");
VarPtr sigma1 = varFactory.fieldVar("sigma1", VECTOR_L2);
VarPtr sigma2 = varFactory.fieldVar("sigma2", VECTOR_L2);
//////////////////// BUILD MESH ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshFactory::shiftedHemkerMesh(-1, 3, 2, radius, bf, H1Order, deltaP);
////////////////////////////////////////////////////////////////////
// INITIALIZE BACKGROUND FLOW FUNCTIONS
////////////////////////////////////////////////////////////////////
BCPtr nullBC = Teuchos::rcp((BC*)NULL);
RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
vector<double> e1(2); // (1,0)
e1[0] = 1;
vector<double> e2(2); // (0,1)
e2[1] = 1;
FunctionPtr u1_prev = Function::solution(u1, backgroundFlow);
FunctionPtr u2_prev = Function::solution(u2, backgroundFlow);
FunctionPtr sigma1_prev = Function::solution(sigma1, backgroundFlow);
FunctionPtr sigma2_prev = Function::solution(sigma2, backgroundFlow);
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
FunctionPtr beta = e1 * u1_prev + e2 * u2_prev;
// ==================== SET INITIAL GUESS ==========================
map<int, Teuchos::RCP<Function> > functionMap;
functionMap[u1->ID()] = one;
functionMap[u2->ID()] = zero;
functionMap[sigma1->ID()] = Function::vectorize(zero,zero);
functionMap[sigma2->ID()] = Function::vectorize(zero,zero);
functionMap[p->ID()] = zero;
backgroundFlow->projectOntoMesh(functionMap);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
// // stress equation
bf->addTerm( sigma1, tau1 );
bf->addTerm( sigma2, tau2 );
bf->addTerm( u1, tau1->div() );
bf->addTerm( u2, tau2->div() );
bf->addTerm( -u1hat, tau1->dot_normal() );
bf->addTerm( -u2hat, tau2->dot_normal() );
// momentum equation
// bf->addTerm( Function::xPart(sigma1_prev)*u1, v1 );
// bf->addTerm( Function::yPart(sigma1_prev)*u2, v1 );
// bf->addTerm( Function::xPart(sigma2_prev)*u1, v2 );
// bf->addTerm( Function::yPart(sigma2_prev)*u2, v2 );
// bf->addTerm( beta*sigma1, v1);
// bf->addTerm( beta*sigma2, v2);
bf->addTerm( 1./Re*sigma1, v1->grad() );
bf->addTerm( 1./Re*sigma2, v2->grad() );
bf->addTerm( t1hat, v1);
bf->addTerm( t2hat, v2);
bf->addTerm( -p, v1->dx() );
bf->addTerm( -p, v2->dy() );
// continuity equation
bf->addTerm( -u1, vc->dx() );
bf->addTerm( -u2, vc->dy() );
bf->addTerm( u1hat, vc->times_normal_x() );
bf->addTerm( u2hat, vc->times_normal_y() );
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
// stress equation
rhs->addTerm( -sigma1_prev * tau1 );
rhs->addTerm( -sigma2_prev * tau2 );
rhs->addTerm( -u1_prev * tau1->div() );
rhs->addTerm( -u2_prev * tau2->div() );
// momentum equation
// rhs->addTerm( -beta*sigma1_prev * v1 );
// rhs->addTerm( -beta*sigma2_prev * v2 );
rhs->addTerm( -1./Re*sigma1_prev * v1->grad() );
rhs->addTerm( -1./Re*sigma2_prev * v2->grad() );
// continuity equation
rhs->addTerm( u1_prev * vc->dx() );
rhs->addTerm( u2_prev * vc->dy() );
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
if (norm == 0)
{
ip = bf->graphNorm();
}
else if (norm == 1)
{
// ip = bf->l2Norm();
}
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr left = Teuchos::rcp( new ConstantXBoundary(-1) );
SpatialFilterPtr right = Teuchos::rcp( new ConstantXBoundary(3) );
SpatialFilterPtr top = Teuchos::rcp( new ConstantYBoundary(1) );
SpatialFilterPtr bottom = Teuchos::rcp( new ConstantYBoundary(-1) );
SpatialFilterPtr circle = Teuchos::rcp( new CircleBoundary(radius) );
FunctionPtr boundaryU1 = Teuchos::rcp( new BoundaryU1 );
bc->addDirichlet(u1hat, left, boundaryU1);
bc->addDirichlet(u2hat, left, zero);
bc->addDirichlet(u1hat, right, boundaryU1);
bc->addDirichlet(u2hat, right, zero);
bc->addDirichlet(u1hat, top, zero);
bc->addDirichlet(u2hat, top, zero);
bc->addDirichlet(u1hat, bottom, zero);
bc->addDirichlet(u2hat, bottom, zero);
bc->addDirichlet(u1hat, circle, zero);
bc->addDirichlet(u2hat, circle, zero);
// zero mean constraint on pressure
bc->addZeroMeanConstraint(p);
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
if (enforceLocalConservation)
{
solution->lagrangeConstraints()->addConstraint(u1hat->times_normal_x() + u2hat->times_normal_y() == zero);
}
// ==================== Register Solutions ==========================
mesh->registerSolution(solution);
mesh->registerSolution(backgroundFlow);
// Teuchos::RCP< RefinementHistory > refHistory = Teuchos::rcp( new RefinementHistory );
// mesh->registerObserver(refHistory);
//////////////////// SOLVE & REFINE ///////////////////////
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(backgroundFlow, mesh, varFactory);
ofstream errOut;
ofstream fluxOut;
if (commRank == 0)
{
errOut.open("stokeshemker_err.txt");
fluxOut.open("stokeshemker_flux.txt");
}
errOut.precision(15);
fluxOut.precision(15);
// Cell IDs for flux calculations
vector< pair<ElementPtr, int> > cellFace0;
vector< pair<ElementPtr, int> > cellFace1;
vector< pair<ElementPtr, int> > cellFace2;
vector< pair<ElementPtr, int> > cellFace3;
vector< pair<ElementPtr, int> > cellFace4;
cellFace0.push_back(make_pair(mesh->getElement(12), 3));
cellFace0.push_back(make_pair(mesh->getElement(13), 3));
cellFace0.push_back(make_pair(mesh->getElement(14), 3));
cellFace0.push_back(make_pair(mesh->getElement(15), 3));
cellFace1.push_back(make_pair(mesh->getElement(12), 1));
cellFace1.push_back(make_pair(mesh->getElement(13), 1));
cellFace1.push_back(make_pair(mesh->getElement(14), 1));
cellFace1.push_back(make_pair(mesh->getElement(15), 1));
cellFace2.push_back(make_pair(mesh->getElement(11), 1));
cellFace2.push_back(make_pair(mesh->getElement(2 ), 0));
cellFace2.push_back(make_pair(mesh->getElement(5 ), 2));
cellFace2.push_back(make_pair(mesh->getElement(16), 1));
cellFace3.push_back(make_pair(mesh->getElement(9 ), 3));
cellFace3.push_back(make_pair(mesh->getElement(8 ), 3));
cellFace3.push_back(make_pair(mesh->getElement(19), 3));
cellFace3.push_back(make_pair(mesh->getElement(18), 3));
cellFace4.push_back(make_pair(mesh->getElement(9 ), 1));
cellFace4.push_back(make_pair(mesh->getElement(8 ), 1));
cellFace4.push_back(make_pair(mesh->getElement(19), 1));
cellFace4.push_back(make_pair(mesh->getElement(18), 1));
// // for loading refinement history
// if (replayFile.length() > 0) {
// RefinementHistory refHistory;
// replayFile = replayFile;
// refHistory.loadFromFile(replayFile);
// refHistory.playback(mesh);
// int numElems = mesh->numActiveElements();
// if (commRank==0){
// double minSideLength = meshInfo.getMinCellSideLength() ;
// cout << "after replay, num elems = " << numElems << " and min side length = " << minSideLength << endl;
// }
// }
for (int i = 0; i < uniformRefinements; i++)
refinementStrategy.hRefineUniformly(mesh);
double nonlinearRelativeEnergyTolerance = 1e-5; // used to determine convergence of the nonlinear solution
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
double L2Update = 1e10;
int iterCount = 0;
while (L2Update > nonlinearRelativeEnergyTolerance && iterCount < maxNewtonIterations)
{
solution->solve(false);
double u1L2Update = solution->L2NormOfSolutionGlobal(u1->ID());
double u2L2Update = solution->L2NormOfSolutionGlobal(u2->ID());
L2Update = sqrt(u1L2Update*u1L2Update + u2L2Update*u2L2Update);
double energy_error = solution->energyErrorTotal();
// Check local conservation
if (commRank == 0)
{
FunctionPtr n = Function::normal();
FunctionPtr u1_prev = Function::solution(u1hat, solution);
FunctionPtr u2_prev = Function::solution(u2hat, solution);
FunctionPtr flux = u1_prev*n->x() + u2_prev*n->y();
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, mesh);
// cout << "Mass flux: Largest Local = " << fluxImbalances[0]
// << ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
errOut << mesh->numGlobalDofs() << " " << energy_error << " "
<< fluxImbalances[0] << " " << fluxImbalances[1] << " " << fluxImbalances[2] << endl;
double massFlux0 = computeFluxOverElementSides(u1_prev, mesh, cellFace0);
double massFlux1 = computeFluxOverElementSides(u1_prev, mesh, cellFace1);
double massFlux2 = computeFluxOverElementSides(u1_prev, mesh, cellFace2);
double massFlux3 = computeFluxOverElementSides(u1_prev, mesh, cellFace3);
double massFlux4 = computeFluxOverElementSides(u1_prev, mesh, cellFace4);
fluxOut << massFlux0 << " " << massFlux1 << " " << massFlux2 << " " << massFlux3 << " " << massFlux4 << " " << endl;
cout << "Total mass flux = " << massFlux0 << " " << massFlux1 << " " << massFlux2 << " " << massFlux3 << " " << massFlux4 << " " << endl;
// if (saveFile.length() > 0) {
// std::ostringstream oss;
// oss << string(saveFile) << refIndex ;
// cout << "on refinement " << refIndex << " saving mesh file to " << oss.str() << endl;
// refHistory->saveToFile(oss.str());
// }
}
// line search algorithm
double alpha = 1.0;
// bool useLineSearch = false;
// int posEnrich = 5; // amount of enriching of grid points on which to ensure positivity
// if (useLineSearch){ // to enforce positivity of density rho
// double lineSearchFactor = .5; double eps = .001; // arbitrary
// FunctionPtr rhoTemp = Function::solution(rho,backgroundFlow) + alpha*Function::solution(rho,solution) - Function::constant(eps);
// FunctionPtr eTemp = Function::solution(e,backgroundFlow) + alpha*Function::solution(e,solution) - Function::constant(eps);
// bool rhoIsPositive = rhoTemp->isPositive(mesh,posEnrich);
// bool eIsPositive = eTemp->isPositive(mesh,posEnrich);
// int iter = 0; int maxIter = 20;
// while (!(rhoIsPositive && eIsPositive) && iter < maxIter){
// alpha = alpha*lineSearchFactor;
// rhoTemp = Function::solution(rho,backgroundFlow) + alpha*Function::solution(rho,solution);
// eTemp = Function::solution(e,backgroundFlow) + alpha*Function::solution(e,solution);
// rhoIsPositive = rhoTemp->isPositive(mesh,posEnrich);
// eIsPositive = eTemp->isPositive(mesh,posEnrich);
// iter++;
// }
// if (commRank==0 && alpha < 1.0){
// cout << "line search factor alpha = " << alpha << endl;
// }
// }
backgroundFlow->addSolution(solution, alpha, false, true);
iterCount++;
// if (commRank == 0)
// cout << "L2 Norm of Update = " << L2Update << endl;
}
if (commRank == 0)
cout << endl;
if (commRank == 0)
{
stringstream outfile;
outfile << "stokeshemker" << uniformRefinements << "_" << refIndex;
exporter.exportSolution(outfile.str());
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
if (commRank == 0)
{
errOut.close();
fluxOut.close();
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef ENABLE_INTEL_FLOATING_POINT_EXCEPTIONS
cout << "NOTE: enabling floating point exceptions for divide by zero.\n";
_MM_SET_EXCEPTION_MASK(_MM_GET_EXCEPTION_MASK() & ~_MM_MASK_INVALID);
#endif
Teuchos::GlobalMPISession mpiSession(&argc, &argv);
int rank = Teuchos::GlobalMPISession::getRank();
#ifdef HAVE_MPI
Epetra_MpiComm Comm(MPI_COMM_WORLD);
//cout << "rank: " << rank << " of " << numProcs << endl;
#else
Epetra_SerialComm Comm;
#endif
Comm.Barrier(); // set breakpoint here to allow debugger attachment to other MPI processes than the one you automatically attached to.
Teuchos::CommandLineProcessor cmdp(false,true); // false: don't throw exceptions; true: do return errors for unrecognized options
double minTol = 1e-8;
bool use3D = false;
int refCount = 10;
int k = 4; // poly order for field variables
int delta_k = use3D ? 3 : 2; // test space enrichment
int k_coarse = 0;
bool useMumps = true;
bool useGMGSolver = true;
bool enforceOneIrregularity = true;
bool useStaticCondensation = false;
bool conformingTraces = false;
bool useDiagonalScaling = false; // of the global stiffness matrix in GMGSolver
bool printRefinementDetails = false;
bool useWeightedGraphNorm = true; // graph norm scaled according to units, more or less
int numCells = 2;
int AztecOutputLevel = 1;
int gmgMaxIterations = 10000;
int smootherOverlap = 0;
double relativeTol = 1e-6;
double D = 1.0; // characteristic length scale
cmdp.setOption("polyOrder",&k,"polynomial order for field variable u");
cmdp.setOption("delta_k", &delta_k, "test space polynomial order enrichment");
cmdp.setOption("k_coarse", &k_coarse, "polynomial order for field variables on coarse mesh");
cmdp.setOption("numRefs",&refCount,"number of refinements");
cmdp.setOption("D", &D, "domain dimension");
cmdp.setOption("useConformingTraces", "useNonConformingTraces", &conformingTraces);
cmdp.setOption("enforceOneIrregularity", "dontEnforceOneIrregularity", &enforceOneIrregularity);
cmdp.setOption("smootherOverlap", &smootherOverlap, "overlap for smoother");
cmdp.setOption("printRefinementDetails", "dontPrintRefinementDetails", &printRefinementDetails);
cmdp.setOption("azOutput", &AztecOutputLevel, "Aztec output level");
cmdp.setOption("numCells", &numCells, "number of cells in the initial mesh");
cmdp.setOption("useScaledGraphNorm", "dontUseScaledGraphNorm", &useWeightedGraphNorm);
// cmdp.setOption("gmgTol", &gmgTolerance, "tolerance for GMG convergence");
cmdp.setOption("relativeTol", &relativeTol, "Energy error-relative tolerance for iterative solver.");
cmdp.setOption("gmgMaxIterations", &gmgMaxIterations, "tolerance for GMG convergence");
bool enhanceUField = false;
cmdp.setOption("enhanceUField", "dontEnhanceUField", &enhanceUField);
cmdp.setOption("useStaticCondensation", "dontUseStaticCondensation", &useStaticCondensation);
if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL)
{
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return -1;
}
double width = D, height = D, depth = D;
VarFactory varFactory;
// fields:
VarPtr u = varFactory.fieldVar("u", L2);
VarPtr sigma = varFactory.fieldVar("\\sigma", VECTOR_L2);
FunctionPtr n = Function::normal();
// traces:
VarPtr u_hat;
if (conformingTraces)
{
u_hat = varFactory.traceVar("\\widehat{u}", u);
}
else
{
cout << "Note: using non-conforming traces.\n";
u_hat = varFactory.traceVar("\\widehat{u}", u, L2);
}
VarPtr sigma_n_hat = varFactory.fluxVar("\\widehat{\\sigma}_{n}", sigma * n);
// test functions:
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
BFPtr poissonBF = Teuchos::rcp( new BF(varFactory) );
FunctionPtr alpha = Function::constant(1); // viscosity
// tau terms:
poissonBF->addTerm(sigma / alpha, tau);
poissonBF->addTerm(-u, tau->div()); // (sigma1, tau1)
poissonBF->addTerm(u_hat, tau * n);
// v terms:
poissonBF->addTerm(- sigma, v->grad()); // (mu sigma1, grad v1)
poissonBF->addTerm( sigma_n_hat, v);
int horizontalCells = numCells, verticalCells = numCells, depthCells = numCells;
vector<double> domainDimensions;
domainDimensions.push_back(width);
domainDimensions.push_back(height);
vector<int> elementCounts;
elementCounts.push_back(horizontalCells);
elementCounts.push_back(verticalCells);
if (use3D)
{
domainDimensions.push_back(depth);
elementCounts.push_back(depthCells);
}
MeshPtr mesh, k0Mesh;
int H1Order = k + 1;
int H1Order_coarse = k_coarse + 1;
if (!use3D)
{
Teuchos::ParameterList pl;
map<int,int> trialOrderEnhancements;
if (enhanceUField)
{
trialOrderEnhancements[u->ID()] = 1;
}
BFPtr poissonBilinearForm = poissonBF;
pl.set("useMinRule", true);
pl.set("bf",poissonBilinearForm);
pl.set("H1Order", H1Order);
pl.set("delta_k", delta_k);
pl.set("horizontalElements", horizontalCells);
pl.set("verticalElements", verticalCells);
pl.set("divideIntoTriangles", false);
pl.set("useConformingTraces", conformingTraces);
pl.set("trialOrderEnhancements", &trialOrderEnhancements);
pl.set("x0",(double)0);
pl.set("y0",(double)0);
pl.set("width", width);
pl.set("height",height);
mesh = MeshFactory::quadMesh(pl);
pl.set("H1Order", H1Order_coarse);
k0Mesh = MeshFactory::quadMesh(pl);
}
else
{
mesh = MeshFactory::rectilinearMesh(poissonBF, domainDimensions, elementCounts, H1Order, delta_k);
k0Mesh = MeshFactory::rectilinearMesh(poissonBF, domainDimensions, elementCounts, H1Order_coarse, delta_k);
}
mesh->registerObserver(k0Mesh); // ensure that the k0 mesh refinements track those of the solution mesh
RHSPtr rhs = RHS::rhs(); // zero
FunctionPtr sin_pi_x = Teuchos::rcp( new Sin_ax(PI/D) );
FunctionPtr sin_pi_y = Teuchos::rcp( new Sin_ay(PI/D) );
FunctionPtr u_exact = sin_pi_x * sin_pi_y;
FunctionPtr f = -(2.0 * PI * PI / (D * D)) * sin_pi_x * sin_pi_y;
rhs->addTerm( f * v );
BCPtr bc = BC::bc();
SpatialFilterPtr boundary = SpatialFilter::allSpace();
bc->addDirichlet(u_hat, boundary, u_exact);
IPPtr graphNorm;
FunctionPtr h = Teuchos::rcp( new hFunction() );
if (useWeightedGraphNorm)
{
graphNorm = IP::ip();
graphNorm->addTerm( tau->div() ); // u
graphNorm->addTerm( (h / alpha) * tau - h * v->grad() ); // sigma
graphNorm->addTerm( v ); // boundary term (adjoint to u)
graphNorm->addTerm( h * tau );
// // new effort, with the idea that the test norm should be considered in reference space, basically
// graphNorm = IP::ip();
// graphNorm->addTerm( tau->div() ); // u
// graphNorm->addTerm( tau / h - v->grad() ); // sigma
// graphNorm->addTerm( v / h ); // boundary term (adjoint to u)
// graphNorm->addTerm( tau / h );
}
else
{
map<int, double> trialWeights; // on the squared terms in the trial space norm
trialWeights[u->ID()] = 1.0 / (D * D);
trialWeights[sigma->ID()] = 1.0;
graphNorm = poissonBF->graphNorm(trialWeights, 1.0); // 1.0: weight on the L^2 terms
}
SolutionPtr solution = Solution::solution(mesh, bc, rhs, graphNorm);
solution->setUseCondensedSolve(useStaticCondensation);
mesh->registerSolution(solution); // sign up for projection of old solution onto refined cells.
double energyThreshold = 0.2;
RefinementStrategy refinementStrategy( solution, energyThreshold );
refinementStrategy.setReportPerCellErrors(true);
refinementStrategy.setEnforceOneIrregularity(enforceOneIrregularity);
Teuchos::RCP<Solver> coarseSolver, fineSolver;
if (useMumps)
{
#ifdef HAVE_AMESOS_MUMPS
coarseSolver = Teuchos::rcp( new MumpsSolver(512, true) );
#else
cout << "useMumps=true, but MUMPS is not available!\n";
exit(0);
#endif
}
else
{
coarseSolver = Teuchos::rcp( new KluSolver );
}
GMGSolver* gmgSolver;
if (useGMGSolver)
{
double tol = relativeTol;
int maxIters = gmgMaxIterations;
BCPtr zeroBCs = bc->copyImposingZero();
gmgSolver = new GMGSolver(zeroBCs, k0Mesh, graphNorm, mesh, solution->getDofInterpreter(),
solution->getPartitionMap(), maxIters, tol, coarseSolver,
useStaticCondensation);
gmgSolver->setAztecOutput(AztecOutputLevel);
gmgSolver->setUseConjugateGradient(true);
gmgSolver->gmgOperator()->setSmootherType(GMGOperator::IFPACK_ADDITIVE_SCHWARZ);
gmgSolver->gmgOperator()->setSmootherOverlap(smootherOverlap);
fineSolver = Teuchos::rcp( gmgSolver );
}
else
{
fineSolver = coarseSolver;
}
// if (rank==0) cout << "experimentally starting by solving with MUMPS on the fine mesh.\n";
// solution->solve( Teuchos::rcp( new MumpsSolver) );
solution->solve(fineSolver);
#ifdef HAVE_EPETRAEXT_HDF5
ostringstream dir_name;
dir_name << "poissonCavityFlow_k" << k;
HDF5Exporter exporter(mesh,dir_name.str());
exporter.exportSolution(solution,varFactory,0);
#endif
#ifdef HAVE_AMESOS_MUMPS
if (useMumps) coarseSolver = Teuchos::rcp( new MumpsSolver(512, true) );
#endif
solution->reportTimings();
if (useGMGSolver) gmgSolver->gmgOperator()->reportTimings();
for (int refIndex=0; refIndex < refCount; refIndex++)
{
double energyError = solution->energyErrorTotal();
GlobalIndexType numFluxDofs = mesh->numFluxDofs();
if (rank==0)
{
cout << "Before refinement " << refIndex << ", energy error = " << energyError;
cout << " (using " << numFluxDofs << " trace degrees of freedom)." << endl;
}
bool printToConsole = printRefinementDetails && (rank==0);
refinementStrategy.refine(printToConsole);
if (useStaticCondensation)
{
CondensedDofInterpreter* condensedDofInterpreter = dynamic_cast<CondensedDofInterpreter*>(solution->getDofInterpreter().get());
if (condensedDofInterpreter != NULL)
{
condensedDofInterpreter->reinitialize();
}
}
GlobalIndexType fineDofs = mesh->globalDofCount();
GlobalIndexType coarseDofs = k0Mesh->globalDofCount();
if (rank==0)
{
cout << "After refinement, coarse mesh has " << k0Mesh->numActiveElements() << " elements and " << coarseDofs << " dofs.\n";
cout << " Fine mesh has " << mesh->numActiveElements() << " elements and " << fineDofs << " dofs.\n";
}
if (!use3D)
{
ostringstream fineMeshLocation, coarseMeshLocation;
fineMeshLocation << "poissonFineMesh_k" << k << "_ref" << refIndex;
GnuPlotUtil::writeComputationalMeshSkeleton(fineMeshLocation.str(), mesh, true); // true: label cells
coarseMeshLocation << "poissonCoarseMesh_k" << k << "_ref" << refIndex;
GnuPlotUtil::writeComputationalMeshSkeleton(coarseMeshLocation.str(), k0Mesh, true); // true: label cells
}
if (useGMGSolver) // create fresh fineSolver now that the meshes have changed:
{
#ifdef HAVE_AMESOS_MUMPS
if (useMumps) coarseSolver = Teuchos::rcp( new MumpsSolver(512, true) );
#endif
double tol = max(relativeTol * energyError, minTol);
int maxIters = gmgMaxIterations;
BCPtr zeroBCs = bc->copyImposingZero();
gmgSolver = new GMGSolver(zeroBCs, k0Mesh, graphNorm, mesh, solution->getDofInterpreter(),
solution->getPartitionMap(), maxIters, tol, coarseSolver, useStaticCondensation);
gmgSolver->setAztecOutput(AztecOutputLevel);
gmgSolver->setUseDiagonalScaling(useDiagonalScaling);
fineSolver = Teuchos::rcp( gmgSolver );
}
solution->solve(fineSolver);
solution->reportTimings();
if (useGMGSolver) gmgSolver->gmgOperator()->reportTimings();
#ifdef HAVE_EPETRAEXT_HDF5
exporter.exportSolution(solution,varFactory,refIndex+1);
#endif
}
double energyErrorTotal = solution->energyErrorTotal();
GlobalIndexType numFluxDofs = mesh->numFluxDofs();
GlobalIndexType numGlobalDofs = mesh->numGlobalDofs();
if (rank==0)
{
cout << "Final mesh has " << mesh->numActiveElements() << " elements and " << numFluxDofs << " trace dofs (";
cout << numGlobalDofs << " total dofs, including fields).\n";
cout << "Final energy error: " << energyErrorTotal << endl;
}
#ifdef HAVE_EPETRAEXT_HDF5
exporter.exportSolution(solution,varFactory,0);
#endif
if (!use3D)
{
GnuPlotUtil::writeComputationalMeshSkeleton("poissonRefinedMesh", mesh, true);
}
coarseSolver = Teuchos::rcp((Solver*) NULL); // without this when useMumps = true and running on one rank, we see a crash on exit, which may have to do with MPI being finalized before coarseSolver is deleted.
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// Required arguments
double epsilon = args.Input<double>("--epsilon", "diffusion parameter");
int numRefs = args.Input<int>("--numRefs", "number of refinement steps");
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation");
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;
}
