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;
}
bool LinearTermTests::testIntegration()
{
// for now, we just check the consistency: for LinearTerm a = b + c, does a->integrate
// give the same values as b->integrate + c->integrate ?
bool success = true;
// VarPtr v1, v2, v3; // HGRAD members (test variables)
// VarPtr q1, q2, q3; // HDIV members (test variables)
// VarPtr u1, u2, u3; // L2 members (trial variables)
// VarPtr u1_hat, u2_hat; // trace variables
// VarPtr u3_hat_n; // flux variable
//
// FunctionPtr sine_x;
if ( ! checkLTSumConsistency(1 * v1, 1 * v2, testOrder, basisCache) )
{
cout << "(v1 + v2)->integrate not consistent with sum of summands integration.\n";
success = false;
}
if ( ! checkLTSumConsistency(sine_x * v1, 1 * v2, testOrder, basisCache) )
{
cout << "(sine_x * v1 + v2)->integrate not consistent with sum of summands integration.\n";
success = false;
}
if ( ! checkLTSumConsistency(1 * q1->div(), 1 * q2->x(), testOrder, basisCache) )
{
cout << "(q1->div() + q2->x())->integrate not consistent with sum of summands integration.\n";
success = false;
}
if ( ! checkLTSumConsistency(1 * u1, 1 * u2, trialOrder, basisCache) )
{
cout << "(u1 + u2)->integrate not consistent with sum of summands integration.\n";
success = false;
}
if ( ! checkLTSumConsistency(1 * u1, sine_x * u2, trialOrder, basisCache) )
{
cout << "(u1 + sine_x * u2)->integrate not consistent with sum of summands integration.\n";
success = false;
}
// now, same thing, but with boundary-value-only functions in the mix:
// this next is a fairly complex test; may want to add a more granular one above...
IPPtr ip = Teuchos::rcp(new IP);
RHSPtr rhs = RHS::rhs();
BCPtr bc = BC::bc();
SolutionPtr solution = Teuchos::rcp( new Solution(mesh,bc,rhs,ip) );
// project some functions onto solution, so that something interesting is there:
FunctionPtr u1_proj = sine_x;
FunctionPtr u2_proj = cos_y;
FunctionPtr u3_proj = u1_proj * u2_proj;
map<int, FunctionPtr> solnToProject;
solnToProject[u1->ID()] = u1_proj;
solnToProject[u2->ID()] = u2_proj;
solnToProject[u3->ID()] = u3_proj;
solnToProject[u1_hat->ID()] = u1_proj;
solnToProject[u2_hat->ID()] = u2_proj;
// u3_hat_n isn't too much like a 'real' bilinear form, in that u3 itself is a scalar
// this is just a test, so I'm not worried about it...
solnToProject[u3_hat_n->ID()] = u3_proj;
solution->projectOntoMesh(solnToProject);
LinearTermPtr bfTestFunctional = bf->testFunctional(solution);
// bf->addTerm(u1, q1->x());
// bf->addTerm(u2, q1->y());
// bf->addTerm(u3, v1);
// bf->addTerm(u1_hat, q1->dot_normal());
// bf->addTerm(u3_hat_n, v1);
LinearTermPtr testFunctionalNoBoundaryValues = u1_proj * q1->x() + u2_proj * q1->y() + u3_proj * v1;
FunctionPtr u1_hat_prev = Teuchos::rcp( new PreviousSolutionFunction<double>(solution, u1_hat) );
FunctionPtr u2_hat_prev = Teuchos::rcp( new PreviousSolutionFunction<double>(solution, u2_hat) );
FunctionPtr u3_hat_prev = Teuchos::rcp( new PreviousSolutionFunction<double>(solution, u3_hat_n) );
LinearTermPtr testFunctionalBoundaryValues = u1_hat_prev * q1->dot_normal() + u3_hat_prev * v1;
if ( ! checkLTSumConsistency(testFunctionalNoBoundaryValues, testFunctionalBoundaryValues,
testOrder, basisCache) )
{
cout << "bfTestFunctional->integrate not consistent with sum of summands integration.\n";
success = false;
}
if ( ! checkLTSumConsistency(testFunctionalBoundaryValues, bfTestFunctional - testFunctionalBoundaryValues,
testOrder, basisCache) )
{
cout << "bfTestFunctional->integrate not consistent with sum of summands integration.\n";
success = false;
}
if ( ! checkLTSumConsistency(testFunctionalNoBoundaryValues, bfTestFunctional - testFunctionalNoBoundaryValues,
testOrder, basisCache) )
{
cout << "bfTestFunctional->integrate not consistent with sum of summands integration.\n";
success = false;
}
return success;
}
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 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 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[]) {
// 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[]) {
// 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");
int norm = args.Input<int>("--norm", "0 = graph\n 1 = robust\n 2 = coupled robust");
// Optional arguments (have defaults)
int uniformRefinements = args.Input("--uniformRefinements", "number of uniform refinements", 0);
bool enforceLocalConservation = args.Input<bool>("--conserve", "enforce local conservation", false);
double radius = args.Input("--r", "cylinder radius", 0.6);
int Re = args.Input("--Re", "Reynolds number", 1);
int maxNewtonIterations = args.Input("--maxIterations", "maximum number of Newton iterations", 1);
int polyOrder = args.Input("--polyOrder", "polynomial order for field variables", 2);
int deltaP = args.Input("--deltaP", "how much to enrich test space", 2);
// string saveFile = args.Input<string>("--meshSaveFile", "file to which to save refinement history", "");
// string replayFile = args.Input<string>("--meshLoadFile", "file with refinement history to replay", "");
args.Process();
//////////////////// PROBLEM DEFINITIONS ///////////////////////
int H1Order = polyOrder+1;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau1 = varFactory.testVar("tau1", HDIV);
VarPtr tau2 = varFactory.testVar("tau2", HDIV);
VarPtr v1 = varFactory.testVar("v1", HGRAD);
VarPtr v2 = varFactory.testVar("v2", HGRAD);
VarPtr vc = varFactory.testVar("vc", HGRAD);
// define trial variables
VarPtr u1 = varFactory.fieldVar("u1");
VarPtr u2 = varFactory.fieldVar("u2");
VarPtr p = varFactory.fieldVar("p");
VarPtr u1hat = varFactory.traceVar("u1hat");
VarPtr u2hat = varFactory.traceVar("u2hat");
VarPtr t1hat = varFactory.fluxVar("t1hat");
VarPtr t2hat = varFactory.fluxVar("t2hat");
VarPtr sigma1 = varFactory.fieldVar("sigma1", VECTOR_L2);
VarPtr sigma2 = varFactory.fieldVar("sigma2", VECTOR_L2);
//////////////////// BUILD MESH ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshFactory::shiftedHemkerMesh(-1, 3, 2, radius, bf, H1Order, deltaP);
////////////////////////////////////////////////////////////////////
// INITIALIZE BACKGROUND FLOW FUNCTIONS
////////////////////////////////////////////////////////////////////
BCPtr nullBC = Teuchos::rcp((BC*)NULL);
RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
vector<double> e1(2); // (1,0)
e1[0] = 1;
vector<double> e2(2); // (0,1)
e2[1] = 1;
FunctionPtr u1_prev = Function::solution(u1, backgroundFlow);
FunctionPtr u2_prev = Function::solution(u2, backgroundFlow);
FunctionPtr sigma1_prev = Function::solution(sigma1, backgroundFlow);
FunctionPtr sigma2_prev = Function::solution(sigma2, backgroundFlow);
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction(1.0) );
FunctionPtr beta = e1 * u1_prev + e2 * u2_prev;
// ==================== SET INITIAL GUESS ==========================
map<int, Teuchos::RCP<Function> > functionMap;
functionMap[u1->ID()] = one;
functionMap[u2->ID()] = zero;
functionMap[sigma1->ID()] = Function::vectorize(zero,zero);
functionMap[sigma2->ID()] = Function::vectorize(zero,zero);
functionMap[p->ID()] = zero;
backgroundFlow->projectOntoMesh(functionMap);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
// // stress equation
bf->addTerm( sigma1, tau1 );
bf->addTerm( sigma2, tau2 );
bf->addTerm( u1, tau1->div() );
bf->addTerm( u2, tau2->div() );
bf->addTerm( -u1hat, tau1->dot_normal() );
bf->addTerm( -u2hat, tau2->dot_normal() );
// momentum equation
// bf->addTerm( Function::xPart(sigma1_prev)*u1, v1 );
// bf->addTerm( Function::yPart(sigma1_prev)*u2, v1 );
// bf->addTerm( Function::xPart(sigma2_prev)*u1, v2 );
// bf->addTerm( Function::yPart(sigma2_prev)*u2, v2 );
// bf->addTerm( beta*sigma1, v1);
// bf->addTerm( beta*sigma2, v2);
bf->addTerm( 1./Re*sigma1, v1->grad() );
bf->addTerm( 1./Re*sigma2, v2->grad() );
bf->addTerm( t1hat, v1);
bf->addTerm( t2hat, v2);
bf->addTerm( -p, v1->dx() );
bf->addTerm( -p, v2->dy() );
// continuity equation
bf->addTerm( -u1, vc->dx() );
bf->addTerm( -u2, vc->dy() );
bf->addTerm( u1hat, vc->times_normal_x() );
bf->addTerm( u2hat, vc->times_normal_y() );
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
// stress equation
rhs->addTerm( -sigma1_prev * tau1 );
rhs->addTerm( -sigma2_prev * tau2 );
rhs->addTerm( -u1_prev * tau1->div() );
rhs->addTerm( -u2_prev * tau2->div() );
// momentum equation
// rhs->addTerm( -beta*sigma1_prev * v1 );
// rhs->addTerm( -beta*sigma2_prev * v2 );
rhs->addTerm( -1./Re*sigma1_prev * v1->grad() );
rhs->addTerm( -1./Re*sigma2_prev * v2->grad() );
// continuity equation
rhs->addTerm( u1_prev * vc->dx() );
rhs->addTerm( u2_prev * vc->dy() );
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
if (norm == 0)
{
ip = bf->graphNorm();
}
else if (norm == 1)
{
// ip = bf->l2Norm();
}
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr left = Teuchos::rcp( new ConstantXBoundary(-1) );
SpatialFilterPtr right = Teuchos::rcp( new ConstantXBoundary(3) );
SpatialFilterPtr top = Teuchos::rcp( new ConstantYBoundary(1) );
SpatialFilterPtr bottom = Teuchos::rcp( new ConstantYBoundary(-1) );
SpatialFilterPtr circle = Teuchos::rcp( new CircleBoundary(radius) );
FunctionPtr boundaryU1 = Teuchos::rcp( new BoundaryU1 );
bc->addDirichlet(u1hat, left, boundaryU1);
bc->addDirichlet(u2hat, left, zero);
bc->addDirichlet(u1hat, right, boundaryU1);
bc->addDirichlet(u2hat, right, zero);
bc->addDirichlet(u1hat, top, zero);
bc->addDirichlet(u2hat, top, zero);
bc->addDirichlet(u1hat, bottom, zero);
bc->addDirichlet(u2hat, bottom, zero);
bc->addDirichlet(u1hat, circle, zero);
bc->addDirichlet(u2hat, circle, zero);
// zero mean constraint on pressure
bc->addZeroMeanConstraint(p);
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
if (enforceLocalConservation)
{
solution->lagrangeConstraints()->addConstraint(u1hat->times_normal_x() + u2hat->times_normal_y() == zero);
}
// ==================== Register Solutions ==========================
mesh->registerSolution(solution);
mesh->registerSolution(backgroundFlow);
// Teuchos::RCP< RefinementHistory > refHistory = Teuchos::rcp( new RefinementHistory );
// mesh->registerObserver(refHistory);
//////////////////// SOLVE & REFINE ///////////////////////
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
VTKExporter exporter(backgroundFlow, mesh, varFactory);
ofstream errOut;
ofstream fluxOut;
if (commRank == 0)
{
errOut.open("stokeshemker_err.txt");
fluxOut.open("stokeshemker_flux.txt");
}
errOut.precision(15);
fluxOut.precision(15);
// Cell IDs for flux calculations
vector< pair<ElementPtr, int> > cellFace0;
vector< pair<ElementPtr, int> > cellFace1;
vector< pair<ElementPtr, int> > cellFace2;
vector< pair<ElementPtr, int> > cellFace3;
vector< pair<ElementPtr, int> > cellFace4;
cellFace0.push_back(make_pair(mesh->getElement(12), 3));
cellFace0.push_back(make_pair(mesh->getElement(13), 3));
cellFace0.push_back(make_pair(mesh->getElement(14), 3));
cellFace0.push_back(make_pair(mesh->getElement(15), 3));
cellFace1.push_back(make_pair(mesh->getElement(12), 1));
cellFace1.push_back(make_pair(mesh->getElement(13), 1));
cellFace1.push_back(make_pair(mesh->getElement(14), 1));
cellFace1.push_back(make_pair(mesh->getElement(15), 1));
cellFace2.push_back(make_pair(mesh->getElement(11), 1));
cellFace2.push_back(make_pair(mesh->getElement(2 ), 0));
cellFace2.push_back(make_pair(mesh->getElement(5 ), 2));
cellFace2.push_back(make_pair(mesh->getElement(16), 1));
cellFace3.push_back(make_pair(mesh->getElement(9 ), 3));
cellFace3.push_back(make_pair(mesh->getElement(8 ), 3));
cellFace3.push_back(make_pair(mesh->getElement(19), 3));
cellFace3.push_back(make_pair(mesh->getElement(18), 3));
cellFace4.push_back(make_pair(mesh->getElement(9 ), 1));
cellFace4.push_back(make_pair(mesh->getElement(8 ), 1));
cellFace4.push_back(make_pair(mesh->getElement(19), 1));
cellFace4.push_back(make_pair(mesh->getElement(18), 1));
// // for loading refinement history
// if (replayFile.length() > 0) {
// RefinementHistory refHistory;
// replayFile = replayFile;
// refHistory.loadFromFile(replayFile);
// refHistory.playback(mesh);
// int numElems = mesh->numActiveElements();
// if (commRank==0){
// double minSideLength = meshInfo.getMinCellSideLength() ;
// cout << "after replay, num elems = " << numElems << " and min side length = " << minSideLength << endl;
// }
// }
for (int i = 0; i < uniformRefinements; i++)
refinementStrategy.hRefineUniformly(mesh);
double nonlinearRelativeEnergyTolerance = 1e-5; // used to determine convergence of the nonlinear solution
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
double L2Update = 1e10;
int iterCount = 0;
while (L2Update > nonlinearRelativeEnergyTolerance && iterCount < maxNewtonIterations)
{
solution->solve(false);
double u1L2Update = solution->L2NormOfSolutionGlobal(u1->ID());
double u2L2Update = solution->L2NormOfSolutionGlobal(u2->ID());
L2Update = sqrt(u1L2Update*u1L2Update + u2L2Update*u2L2Update);
double energy_error = solution->energyErrorTotal();
// Check local conservation
if (commRank == 0)
{
FunctionPtr n = Function::normal();
FunctionPtr u1_prev = Function::solution(u1hat, solution);
FunctionPtr u2_prev = Function::solution(u2hat, solution);
FunctionPtr flux = u1_prev*n->x() + u2_prev*n->y();
Teuchos::Tuple<double, 3> fluxImbalances = checkConservation(flux, zero, mesh);
// cout << "Mass flux: Largest Local = " << fluxImbalances[0]
// << ", Global = " << fluxImbalances[1] << ", Sum Abs = " << fluxImbalances[2] << endl;
errOut << mesh->numGlobalDofs() << " " << energy_error << " "
<< fluxImbalances[0] << " " << fluxImbalances[1] << " " << fluxImbalances[2] << endl;
double massFlux0 = computeFluxOverElementSides(u1_prev, mesh, cellFace0);
double massFlux1 = computeFluxOverElementSides(u1_prev, mesh, cellFace1);
double massFlux2 = computeFluxOverElementSides(u1_prev, mesh, cellFace2);
double massFlux3 = computeFluxOverElementSides(u1_prev, mesh, cellFace3);
double massFlux4 = computeFluxOverElementSides(u1_prev, mesh, cellFace4);
fluxOut << massFlux0 << " " << massFlux1 << " " << massFlux2 << " " << massFlux3 << " " << massFlux4 << " " << endl;
cout << "Total mass flux = " << massFlux0 << " " << massFlux1 << " " << massFlux2 << " " << massFlux3 << " " << massFlux4 << " " << endl;
// if (saveFile.length() > 0) {
// std::ostringstream oss;
// oss << string(saveFile) << refIndex ;
// cout << "on refinement " << refIndex << " saving mesh file to " << oss.str() << endl;
// refHistory->saveToFile(oss.str());
// }
}
// line search algorithm
double alpha = 1.0;
// bool useLineSearch = false;
// int posEnrich = 5; // amount of enriching of grid points on which to ensure positivity
// if (useLineSearch){ // to enforce positivity of density rho
// double lineSearchFactor = .5; double eps = .001; // arbitrary
// FunctionPtr rhoTemp = Function::solution(rho,backgroundFlow) + alpha*Function::solution(rho,solution) - Function::constant(eps);
// FunctionPtr eTemp = Function::solution(e,backgroundFlow) + alpha*Function::solution(e,solution) - Function::constant(eps);
// bool rhoIsPositive = rhoTemp->isPositive(mesh,posEnrich);
// bool eIsPositive = eTemp->isPositive(mesh,posEnrich);
// int iter = 0; int maxIter = 20;
// while (!(rhoIsPositive && eIsPositive) && iter < maxIter){
// alpha = alpha*lineSearchFactor;
// rhoTemp = Function::solution(rho,backgroundFlow) + alpha*Function::solution(rho,solution);
// eTemp = Function::solution(e,backgroundFlow) + alpha*Function::solution(e,solution);
// rhoIsPositive = rhoTemp->isPositive(mesh,posEnrich);
// eIsPositive = eTemp->isPositive(mesh,posEnrich);
// iter++;
// }
// if (commRank==0 && alpha < 1.0){
// cout << "line search factor alpha = " << alpha << endl;
// }
// }
backgroundFlow->addSolution(solution, alpha, false, true);
iterCount++;
// if (commRank == 0)
// cout << "L2 Norm of Update = " << L2Update << endl;
}
if (commRank == 0)
cout << endl;
if (commRank == 0)
{
stringstream outfile;
outfile << "stokeshemker" << uniformRefinements << "_" << refIndex;
exporter.exportSolution(outfile.str());
}
if (refIndex < numRefs)
refinementStrategy.refine(commRank==0); // print to console on commRank 0
}
if (commRank == 0)
{
errOut.close();
fluxOut.close();
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int 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
int polyOrder = 2;
// define our manufactured solution or problem bilinear form:
double epsilon = 1e-3;
bool useTriangles = false;
int pToAdd = 2;
int nCells = 2;
if ( argc > 1)
{
nCells = atoi(argv[1]);
if (rank==0)
{
cout << "numCells = " << nCells << endl;
}
}
int numSteps = 20;
if ( argc > 2)
{
numSteps = atoi(argv[2]);
if (rank==0)
{
cout << "num NR steps = " << numSteps << endl;
}
}
int useHessian = 0; // defaults to "not use"
if ( argc > 3)
{
useHessian = atoi(argv[3]);
if (rank==0)
{
cout << "useHessian = " << useHessian << endl;
}
}
int thresh = numSteps; // threshhold for when to apply linesearch/hessian
if ( argc > 4)
{
thresh = atoi(argv[4]);
if (rank==0)
{
cout << "thresh = " << thresh << endl;
}
}
int H1Order = polyOrder + 1;
double energyThreshold = 0.2; // for mesh refinements
double nonlinearStepSize = 0.5;
double nonlinearRelativeEnergyTolerance = 1e-8; // used to determine convergence of the nonlinear solution
////////////////////////////////////////////////////////////////////
// DEFINE VARIABLES
////////////////////////////////////////////////////////////////////
// new-style bilinear form definition
VarFactory varFactory;
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_hat = varFactory.fluxVar("\\widehat{\\beta_n u - \\sigma_n}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
VarPtr tau = varFactory.testVar("\\tau",HDIV);
VarPtr v = varFactory.testVar("v",HGRAD);
BFPtr bf = Teuchos::rcp( new BF(varFactory) ); // initialize bilinear form
////////////////////////////////////////////////////////////////////
// CREATE MESH
////////////////////////////////////////////////////////////////////
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells, bf, H1Order, H1Order+pToAdd);
mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));
////////////////////////////////////////////////////////////////////
// INITIALIZE BACKGROUND FLOW FUNCTIONS
////////////////////////////////////////////////////////////////////
BCPtr nullBC = Teuchos::rcp((BC*)NULL);
RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC,
nullRHS, nullIP) );
vector<double> e1(2); // (1,0)
e1[0] = 1;
vector<double> e2(2); // (0,1)
e2[1] = 1;
FunctionPtr u_prev = Teuchos::rcp( new PreviousSolutionFunction(backgroundFlow, u) );
FunctionPtr beta = e1 * u_prev + Teuchos::rcp( new ConstantVectorFunction( e2 ) );
////////////////////////////////////////////////////////////////////
// DEFINE BILINEAR FORM
////////////////////////////////////////////////////////////////////
// tau parts:
// 1/eps (sigma, tau)_K + (u, div tau)_K - (u_hat, tau_n)_dK
bf->addTerm(sigma1 / epsilon, tau->x());
bf->addTerm(sigma2 / epsilon, tau->y());
bf->addTerm(u, tau->div());
bf->addTerm( - uhat, tau->dot_normal() );
// v:
// (sigma, grad v)_K - (sigma_hat_n, v)_dK - (u, beta dot grad v) + (u_hat * n dot beta, v)_dK
bf->addTerm( sigma1, v->dx() );
bf->addTerm( sigma2, v->dy() );
bf->addTerm( -u, beta * v->grad());
bf->addTerm( beta_n_u_minus_sigma_hat, v);
// ==================== SET INITIAL GUESS ==========================
mesh->registerSolution(backgroundFlow);
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr u0 = Teuchos::rcp( new U0 );
map<int, Teuchos::RCP<Function> > functionMap;
functionMap[u->ID()] = u0;
functionMap[sigma1->ID()] = zero;
functionMap[sigma2->ID()] = zero;
backgroundFlow->projectOntoMesh(functionMap);
// ==================== END SET INITIAL GUESS ==========================
////////////////////////////////////////////////////////////////////
// DEFINE INNER PRODUCT
////////////////////////////////////////////////////////////////////
// function to scale the squared guy by epsilon/h
FunctionPtr epsilonOverHScaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
IPPtr ip = Teuchos::rcp( new IP );
ip->addTerm( epsilonOverHScaling * (1.0/sqrt(epsilon))* tau);
ip->addTerm( tau->div());
// ip->addTerm( epsilonOverHScaling * v );
ip->addTerm( v );
ip->addTerm( sqrt(epsilon) * v->grad() );
ip->addTerm(v->grad());
// ip->addTerm( beta * v->grad() );
////////////////////////////////////////////////////////////////////
// DEFINE RHS
////////////////////////////////////////////////////////////////////
RHSPtr rhs = RHS::rhs();
FunctionPtr u_prev_squared_div2 = 0.5 * u_prev * u_prev;
rhs->addTerm((e1 * u_prev_squared_div2 + e2 * u_prev) * v->grad() - u_prev * tau->div());
////////////////////////////////////////////////////////////////////
// DEFINE DIRICHLET BC
////////////////////////////////////////////////////////////////////
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new TopBoundary);
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new NegatedSpatialFilter(outflowBoundary) );
BCPtr inflowBC = BC::bc();
FunctionPtr u0_squared_div_2 = 0.5 * u0 * u0;
inflowBC->addDirichlet(beta_n_u_minus_sigma_hat,inflowBoundary,
( e1 * u0_squared_div_2 + e2 * u0) * n );
////////////////////////////////////////////////////////////////////
// CREATE SOLUTION OBJECT
////////////////////////////////////////////////////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp(new Solution(mesh, inflowBC, rhs, ip));
mesh->registerSolution(solution);
////////////////////////////////////////////////////////////////////
// WARNING: UNFINISHED HESSIAN BIT
////////////////////////////////////////////////////////////////////
VarFactory hessianVars = varFactory.getBubnovFactory(VarFactory::BUBNOV_TRIAL);
VarPtr du = hessianVars.test(u->ID());
BFPtr hessianBF = Teuchos::rcp( new BF(hessianVars) ); // initialize bilinear form
// FunctionPtr e_v = Function::constant(1.0); // dummy error rep function for now - should do nothing
FunctionPtr u_current = Teuchos::rcp( new PreviousSolutionFunction(solution, u) );
FunctionPtr sig1_prev = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma1) );
FunctionPtr sig2_prev = Teuchos::rcp( new PreviousSolutionFunction(solution, sigma2) );
FunctionPtr sig_prev = (e1*sig1_prev + e2*sig2_prev);
FunctionPtr fnhat = Teuchos::rcp(new PreviousSolutionFunction(solution,beta_n_u_minus_sigma_hat));
FunctionPtr uhat_prev = Teuchos::rcp(new PreviousSolutionFunction(solution,uhat));
LinearTermPtr residual = Teuchos::rcp(new LinearTerm);// residual
residual->addTerm(fnhat*v - (e1 * (u_prev_squared_div2 - sig1_prev) + e2 * (u_prev - sig2_prev)) * v->grad());
residual->addTerm((1/epsilon)*sig_prev * tau + u_prev * tau->div() - uhat_prev*tau->dot_normal());
LinearTermPtr Bdu = Teuchos::rcp(new LinearTerm);// residual
Bdu->addTerm( u_current*tau->div() - u_current*(beta*v->grad()));
Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ip, residual));
Teuchos::RCP<RieszRep> duRiesz = Teuchos::rcp(new RieszRep(mesh, ip, Bdu));
riesz->computeRieszRep();
FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,riesz));
e_v->writeValuesToMATLABFile(mesh, "e_v.m");
FunctionPtr posErrPart = Teuchos::rcp(new PositivePart(e_v->dx()));
hessianBF->addTerm(e_v->dx()*u,du);
// hessianBF->addTerm(posErrPart*u,du);
Teuchos::RCP<HessianFilter> hessianFilter = Teuchos::rcp(new HessianFilter(hessianBF));
if (useHessian)
{
solution->setWriteMatrixToFile(true,"hessianStiffness.dat");
}
else
{
solution->setWriteMatrixToFile(true,"stiffness.dat");
}
Teuchos::RCP< LineSearchStep > LS_Step = Teuchos::rcp(new LineSearchStep(riesz));
ofstream out;
out.open("Burgers.txt");
double NL_residual = 9e99;
for (int i = 0; i<numSteps; i++)
{
solution->solve(false); // do one solve to initialize things...
double stepLength = 1.0;
stepLength = LS_Step->stepSize(backgroundFlow,solution, NL_residual);
if (useHessian)
{
solution->setFilter(hessianFilter);
}
backgroundFlow->addSolution(solution,stepLength);
NL_residual = LS_Step->getNLResidual();
if (rank==0)
{
cout << "NL residual after adding = " << NL_residual << " with step size " << stepLength << endl;
out << NL_residual << endl; // saves initial NL error
}
}
out.close();
////////////////////////////////////////////////////////////////////
// DEFINE REFINEMENT STRATEGY
////////////////////////////////////////////////////////////////////
Teuchos::RCP<RefinementStrategy> refinementStrategy;
refinementStrategy = Teuchos::rcp(new RefinementStrategy(solution,energyThreshold));
int numRefs = 0;
Teuchos::RCP<NonlinearStepSize> stepSize = Teuchos::rcp(new NonlinearStepSize(nonlinearStepSize));
Teuchos::RCP<NonlinearSolveStrategy> solveStrategy;
solveStrategy = Teuchos::rcp( new NonlinearSolveStrategy(backgroundFlow, solution, stepSize,
nonlinearRelativeEnergyTolerance));
////////////////////////////////////////////////////////////////////
// SOLVE
////////////////////////////////////////////////////////////////////
for (int refIndex=0; refIndex<numRefs; refIndex++)
{
solveStrategy->solve(rank==0); // print to console on rank 0
refinementStrategy->refine(rank==0); // print to console on rank 0
}
// solveStrategy->solve(rank==0);
if (rank==0)
{
backgroundFlow->writeToVTK("Burgers.vtu",min(H1Order+1,4));
solution->writeFluxesToFile(uhat->ID(), "burgers.dat");
cout << "wrote solution files" << endl;
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
int polyOrder = 3;
int pToAdd = 2; // for tests
// define our manufactured solution or problem bilinear form:
bool useTriangles = false;
FieldContainer<double> meshPoints(4,2);
meshPoints(0,0) = 0.0; // x1
meshPoints(0,1) = 0.0; // y1
meshPoints(1,0) = 1.0;
meshPoints(1,1) = 0.0;
meshPoints(2,0) = 1.0;
meshPoints(2,1) = 1.0;
meshPoints(3,0) = 0.0;
meshPoints(3,1) = 1.0;
int H1Order = polyOrder + 1;
int horizontalCells = 4, verticalCells = 4;
double energyThreshold = 0.2; // for mesh refinements
double nonlinearStepSize = 0.5;
double nonlinearRelativeEnergyTolerance = 1e-8; // used to determine convergence of the nonlinear solution
////////////////////////////////////////////////////////////////////
// DEFINE VARIABLES
////////////////////////////////////////////////////////////////////
// new-style bilinear form definition
VarFactory varFactory;
VarPtr fhat = varFactory.fluxVar("\\widehat{f}");
VarPtr u = varFactory.fieldVar("u");
VarPtr v = varFactory.testVar("v",HGRAD);
BFPtr bf = Teuchos::rcp( new BF(varFactory) ); // initialize bilinear form
////////////////////////////////////////////////////////////////////
// CREATE MESH
////////////////////////////////////////////////////////////////////
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(meshPoints, horizontalCells,
verticalCells, bf, H1Order,
H1Order+pToAdd, useTriangles);
mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));
////////////////////////////////////////////////////////////////////
// INITIALIZE BACKGROUND FLOW FUNCTIONS
////////////////////////////////////////////////////////////////////
BCPtr nullBC = Teuchos::rcp((BC*)NULL);
RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL);
IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC,
nullRHS, nullIP) );
vector<double> e1(2); // (1,0)
e1[0] = 1;
vector<double> e2(2); // (0,1)
e2[1] = 1;
FunctionPtr u_prev = Teuchos::rcp( new PreviousSolutionFunction(backgroundFlow, u) );
FunctionPtr beta = e1 * u_prev + Teuchos::rcp( new ConstantVectorFunction( e2 ) );
////////////////////////////////////////////////////////////////////
// DEFINE BILINEAR FORM
////////////////////////////////////////////////////////////////////
// v:
// (sigma, grad v)_K - (sigma_hat_n, v)_dK - (u, beta dot grad v) + (u_hat * n dot beta, v)_dK
bf->addTerm( -u, beta * v->grad());
bf->addTerm( fhat, v);
// ==================== SET INITIAL GUESS ==========================
mesh->registerSolution(backgroundFlow);
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
FunctionPtr u0 = Teuchos::rcp( new U0 );
map<int, Teuchos::RCP<Function> > functionMap;
functionMap[u->ID()] = u0;
backgroundFlow->projectOntoMesh(functionMap);
// ==================== END SET INITIAL GUESS ==========================
////////////////////////////////////////////////////////////////////
// DEFINE INNER PRODUCT
////////////////////////////////////////////////////////////////////
IPPtr ip = Teuchos::rcp( new IP );
ip->addTerm( v );
ip->addTerm( beta * v->grad() );
////////////////////////////////////////////////////////////////////
// DEFINE RHS
////////////////////////////////////////////////////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr u_prev_squared_div2 = 0.5 * u_prev * u_prev;
rhs->addTerm( (e1 * u_prev_squared_div2 + e2 * u_prev) * v->grad());
////////////////////////////////////////////////////////////////////
// DEFINE DIRICHLET BC
////////////////////////////////////////////////////////////////////
Teuchos::RCP<BCEasy> inflowBC = Teuchos::rcp( new BCEasy );
// Create spatial filters
SpatialFilterPtr bottomBoundary = Teuchos::rcp( new BottomBoundary );
SpatialFilterPtr leftBoundary = Teuchos::rcp( new LeftBoundary );
SpatialFilterPtr rightBoundary = Teuchos::rcp( new LeftBoundary );
// Create BCs
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
FunctionPtr u0_squared_div_2 = 0.5 * u0 * u0;
SimpleFunction* u0Ptr = static_cast<SimpleFunction *>(u0.get());
double u0Left = u0Ptr->value(0,0);
double u0Right = u0Ptr->value(1.0,0);
FunctionPtr leftVal = Teuchos::rcp( new ConstantScalarFunction( -0.5*u0Left*u0Left ) );
FunctionPtr rightVal = Teuchos::rcp( new ConstantScalarFunction( 0.5*u0Right*u0Right ) );
inflowBC->addDirichlet(fhat, bottomBoundary, -u0 );
inflowBC->addDirichlet(fhat, leftBoundary, leftVal );
inflowBC->addDirichlet(fhat, rightBoundary, rightVal );
////////////////////////////////////////////////////////////////////
// CREATE SOLUTION OBJECT
////////////////////////////////////////////////////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp(new Solution(mesh, inflowBC, rhs, ip));
mesh->registerSolution(solution);
if (enforceLocalConservation)
{
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(fhat == zero);
}
////////////////////////////////////////////////////////////////////
// DEFINE REFINEMENT STRATEGY
////////////////////////////////////////////////////////////////////
Teuchos::RCP<RefinementStrategy> refinementStrategy;
refinementStrategy = Teuchos::rcp(new RefinementStrategy(solution,energyThreshold));
////////////////////////////////////////////////////////////////////
// SOLVE
////////////////////////////////////////////////////////////////////
for (int refIndex=0; refIndex<=numRefs; refIndex++)
{
double L2Update = 1e7;
int iterCount = 0;
while (L2Update > nonlinearRelativeEnergyTolerance && iterCount < maxNewtonIterations)
{
solution->solve();
L2Update = solution->L2NormOfSolutionGlobal(u->ID());
cout << "L2 Norm of Update = " << L2Update << endl;
// backgroundFlow->clear();
backgroundFlow->addSolution(solution, newtonStepSize);
iterCount++;
}
cout << endl;
// check conservation
VarPtr testOne = varFactory.testVar("1", CONSTANT_SCALAR);
// Create a fake bilinear form for the testing
BFPtr fakeBF = Teuchos::rcp( new BF(varFactory) );
// Define our mass flux
FunctionPtr massFlux = Teuchos::rcp( new PreviousSolutionFunction(solution, fhat) );
LinearTermPtr massFluxTerm = massFlux * testOne;
Teuchos::RCP<shards::CellTopology> quadTopoPtr = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ));
DofOrderingFactory dofOrderingFactory(fakeBF);
int fakeTestOrder = H1Order;
DofOrderingPtr testOrdering = dofOrderingFactory.testOrdering(fakeTestOrder, *quadTopoPtr);
int testOneIndex = testOrdering->getDofIndex(testOne->ID(),0);
vector< ElementTypePtr > elemTypes = mesh->elementTypes(); // global element types
map<int, double> massFluxIntegral; // cellID -> integral
double maxMassFluxIntegral = 0.0;
double totalMassFlux = 0.0;
double totalAbsMassFlux = 0.0;
for (vector< ElementTypePtr >::iterator elemTypeIt = elemTypes.begin(); elemTypeIt != elemTypes.end(); elemTypeIt++)
{
ElementTypePtr elemType = *elemTypeIt;
vector< ElementPtr > elems = mesh->elementsOfTypeGlobal(elemType);
vector<int> cellIDs;
for (int i=0; i<elems.size(); i++)
{
cellIDs.push_back(elems[i]->cellID());
}
FieldContainer<double> physicalCellNodes = mesh->physicalCellNodesGlobal(elemType);
BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(elemType,mesh) );
basisCache->setPhysicalCellNodes(physicalCellNodes,cellIDs,true); // true: create side caches
FieldContainer<double> cellMeasures = basisCache->getCellMeasures();
FieldContainer<double> fakeRHSIntegrals(elems.size(),testOrdering->totalDofs());
massFluxTerm->integrate(fakeRHSIntegrals,testOrdering,basisCache,true); // true: force side evaluation
for (int i=0; i<elems.size(); i++)
{
int cellID = cellIDs[i];
// pick out the ones for testOne:
massFluxIntegral[cellID] = fakeRHSIntegrals(i,testOneIndex);
}
// find the largest:
for (int i=0; i<elems.size(); i++)
{
int cellID = cellIDs[i];
maxMassFluxIntegral = max(abs(massFluxIntegral[cellID]), maxMassFluxIntegral);
}
for (int i=0; i<elems.size(); i++)
{
int cellID = cellIDs[i];
maxMassFluxIntegral = max(abs(massFluxIntegral[cellID]), maxMassFluxIntegral);
totalMassFlux += massFluxIntegral[cellID];
totalAbsMassFlux += abs( massFluxIntegral[cellID] );
}
}
if (rank==0)
{
cout << endl;
cout << "largest mass flux: " << maxMassFluxIntegral << endl;
cout << "total mass flux: " << totalMassFlux << endl;
cout << "sum of mass flux absolute value: " << totalAbsMassFlux << endl;
cout << endl;
stringstream outfile;
outfile << "burgers_" << refIndex;
backgroundFlow->writeToVTK(outfile.str(), 5);
}
if (refIndex < numRefs)
refinementStrategy->refine(rank==0); // print to console on rank 0
}
return 0;
}
