void RHSTests::setup()
{
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 1.0;
quadPoints(1,1) = 0.0;
quadPoints(2,0) = 1.0;
quadPoints(2,1) = 1.0;
quadPoints(3,0) = 0.0;
quadPoints(3,1) = 1.0;
int H1Order = 3;
int delta_p = 3; // for test functions
int horizontalCells = 2;
int verticalCells = 2;
double eps = 1.0; // not really testing for sharp gradients right now--just want to see if things basically work
double beta_x = 1.0;
double beta_y = 1.0;
BFPtr confusionBF = ConfusionBilinearForm::confusionBF(eps,beta_x,beta_y);
Teuchos::RCP<ConfusionProblemLegacy> confusionProblem = Teuchos::rcp( new ConfusionProblemLegacy(confusionBF, beta_x, beta_y) );
_rhs = confusionProblem;
_mesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells, confusionBF, H1Order, H1Order+delta_p);
_mesh->setUsePatchBasis(false);
VarFactoryPtr varFactory = confusionBF->varFactory(); // Create test IDs that match the enum in ConfusionBilinearForm
_tau = varFactory->testVar(ConfusionBilinearForm::S_TAU,HDIV);
_v = varFactory->testVar(ConfusionBilinearForm::S_V,HGRAD);
_rhsEasy = RHS::rhs();
_rhsEasy->addTerm( _v );
}
VarPtr PoissonFormulation::tau()
{
VarFactoryPtr vf = _poissonBF->varFactory();
if (_spaceDim > 1)
return vf->testVar(S_TAU, HDIV);
else
return vf->testVar(S_TAU, HGRAD);
}
bool LinearTermTests::testLinearTermEvaluation()
{
bool success = true;
double eps = .1;
FunctionPtr one = Function::constant(1.0);
vector<double> e1,e2;
e1.push_back(1.0);
e1.push_back(0.0);
e2.push_back(0.0);
e2.push_back(1.0);
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr tau = varFactory->testVar("\\tau", HDIV);
VarPtr v = varFactory->testVar("v", HGRAD);
// define a couple LinearTerms
LinearTermPtr vVecLT = Teuchos::rcp(new LinearTerm);
LinearTermPtr tauVecLT = Teuchos::rcp(new LinearTerm);
vVecLT->addTerm(sqrt(eps)*v->grad());
tauVecLT->addTerm((1/sqrt(eps))*tau);
//////////////////// evaluate LinearTerms /////////////////
map<int,FunctionPtr> errRepMap;
errRepMap[v->ID()] = one;
errRepMap[tau->ID()] = one*e1+one*e2; // vector valued fxn (1,1)
FunctionPtr errTau = tauVecLT->evaluate(errRepMap,false);
FunctionPtr errV = vVecLT->evaluate(errRepMap,false);
try
{
bool xTauZero = errTau->x()->isZero();
bool yTauZero = errTau->y()->isZero();
bool xVZero = errV->dx()->isZero();
bool yVZero = errV->dy()->isZero();
}
catch (...)
{
cout << "testLinearTermEvaluation: Caught exception.\n";
success = false;
}
/*
FunctionPtr xErr = (errTau->x())*(errTau->x()) + (errV->dx())*(errV->dx());
FunctionPtr yErr = (errTau->y())*(errTau->y()) + (errV->dy())*(errV->dy());
double xErrVal = xErr->integrate(mesh,15,true);
*/
// if we don't crash, return success
return success;
}
void PoissonExactSolution::setUseSinglePointBCForPHI(bool useSinglePointBCForPhi, IndexType vertexIndexForZeroValue)
{
FunctionPtr phi_exact = phi();
VarFactoryPtr vf = _bf->varFactory();
VarPtr psi_hat_n = vf->fluxVar(PoissonBilinearForm::S_PSI_HAT_N);
VarPtr q = vf->testVar(PoissonBilinearForm::S_Q, HGRAD);
VarPtr phi = vf->fieldVar(PoissonBilinearForm::S_PHI);
SpatialFilterPtr wholeBoundary = SpatialFilter::allSpace();
FunctionPtr n = Function::normal();
FunctionPtr psi_n_exact = phi_exact->grad() * n;
_bc = BC::bc();
_bc->addDirichlet(psi_hat_n, wholeBoundary, psi_n_exact);
if (!useSinglePointBCForPhi)
{
_bc->addZeroMeanConstraint(phi);
}
else
{
std::vector<double> point = getPointForBCImposition();
double value = Function::evaluate(phi_exact, point[0], point[1]);
// cout << "PoissonExactSolution: imposing phi = " << value << " at (" << point[0] << ", " << point[1] << ")\n";
_bc->addSpatialPointBC(phi->ID(), value, point);
}
}
VarPtr PressurelessStokesFormulation::v(int i)
{
if (i > _spaceDim)
{
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "i must be less than or equal to _spaceDim");
}
VarFactoryPtr vf = _stokesBF->varFactory();
switch (i)
{
case 1:
return vf->testVar(S_V1, HGRAD);
case 2:
return vf->testVar(S_V2, HGRAD);
case 3:
return vf->testVar(S_V3, HGRAD);
}
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "unhandled i value");
}
BFPtr TestBilinearFormDx::bf()
{
VarFactoryPtr vf = VarFactory::varFactory();
VarPtr u = vf->fieldVar("u",HGRAD);
VarPtr v = vf->testVar("v",HGRAD);
BFPtr bf = BF::bf(vf);
bf->addTerm(u->dx(), v->dx());
return bf;
}
bool LobattoBasisTests::testLobattoValues()
{
bool success = true;
FunctionPtr x = Function::xn(1);
vector< FunctionPtr > lobattoFunctionsExpected;
// Pavel Solin's first two Lobatto functions:
// lobattoFunctionsExpected.push_back( (1 - x) / 2 );
// lobattoFunctionsExpected.push_back( (1 + x) / 2 );
// Demkowicz's:
lobattoFunctionsExpected.push_back( Function::constant(1.0) );
lobattoFunctionsExpected.push_back( x );
lobattoFunctionsExpected.push_back( (x*x - 1) / 2);
lobattoFunctionsExpected.push_back( (x*x - 1) * x / 2);
lobattoFunctionsExpected.push_back( (x*x - 1) * (5 * x * x - 1) / 8);
lobattoFunctionsExpected.push_back( (x*x - 1) * (7 * x * x - 3) * x / 8);
vector< FunctionPtr > lobattoFunctions;
bool conformingFalse = false;
int n_max = 4;
for (int n=0; n<=n_max; n++)
{
lobattoFunctions.push_back( Teuchos::rcp( new LobattoFunction<>(n,conformingFalse,false) ) );
}
VarFactoryPtr varFactory = VarFactory::varFactory();
varFactory->testVar("v", HGRAD);
varFactory->fieldVar("u", L2);
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
MeshPtr mesh = MeshFactory::quadMesh(bf, n_max);
BasisCachePtr basisCache = BasisCache::basisCacheForCell(mesh, 0);
double tol = 1e-12;
for (int n=0; n<=n_max; n++)
{
if (! lobattoFunctions[n]->equals(lobattoFunctionsExpected[n], basisCache, tol) )
{
cout << "Lobatto function " << n << " does not match expected.\n";
success = false;
}
}
return success;
}
ConfusionManufacturedSolution::ConfusionManufacturedSolution(double epsilon, double beta_x, double beta_y)
{
_epsilon = epsilon;
_beta_x = beta_x;
_beta_y = beta_y;
// set the class variables from ExactSolution:
// _bc = Teuchos::rcp(this,false); // false: don't let the RCP own the memory
// _rhs = Teuchos::rcp(this,false);
BFPtr bf = ConfusionBilinearForm::confusionBF(epsilon,beta_x,beta_y);
_bilinearForm = bf;
VarFactoryPtr vf = bf->varFactory();
VarPtr u = vf->fieldVar(ConfusionBilinearForm::S_U);
VarPtr sigma1 = vf->fieldVar(ConfusionBilinearForm::S_SIGMA_1);
VarPtr sigma2 = vf->fieldVar(ConfusionBilinearForm::S_SIGMA_2);
_u_hat = vf->traceVar(ConfusionBilinearForm::S_U_HAT);
_beta_n_u_minus_sigma_hat = vf->fluxVar(ConfusionBilinearForm::S_BETA_N_U_MINUS_SIGMA_HAT);
_v = vf->testVar(ConfusionBilinearForm::S_V, HGRAD);
FunctionPtr u_exact = this->u();
FunctionPtr sigma_exact = epsilon * u_exact->grad();
FunctionPtr u_exact_laplacian = u_exact->dx()->dx() + u_exact->dy()->dy();
_rhs = RHS::rhs();
FunctionPtr f = - _epsilon * u_exact_laplacian + _beta_x * u_exact->dx() + _beta_y * u_exact->dy();
_rhs->addTerm( f * _v );
_bc = BC::bc();
_bc->addDirichlet(_u_hat, SpatialFilter::allSpace(), u_exact);
FunctionPtr beta = Function::vectorize(Function::constant(_beta_x), Function::constant(_beta_y));
FunctionPtr n = Function::normal();
FunctionPtr one_skeleton = Function::meshSkeletonCharacteristic(); // allows restriction to skeleton
FunctionPtr sigma_flux_exact = beta * ( n * u_exact - sigma_exact * one_skeleton);
this->setSolutionFunction(u, u_exact);
this->setSolutionFunction(sigma1, sigma_exact->x());
this->setSolutionFunction(sigma2, sigma_exact->y());
this->setSolutionFunction(_u_hat, u_exact);
this->setSolutionFunction(_beta_n_u_minus_sigma_hat, sigma_flux_exact);
}
bool LobattoBasisTests::testLobattoDerivativeValues()
{
bool success = true;
FunctionPtr x = Function::xn(1);
vector< FunctionPtr > legendreFunctions; // manually specified
vector< FunctionPtr > lobattoDerivatives;
FunctionPtr one = Function::constant(1);
legendreFunctions.push_back(one);
legendreFunctions.push_back(x);
legendreFunctions.push_back(0.5 * (3 * x * x - 1) );
legendreFunctions.push_back( (5 * x * x * x - 3 * x) / 2);
legendreFunctions.push_back( (1.0 / 8.0) * (35 * x * x * x * x - 30 * x * x + 3) );
legendreFunctions.push_back( (1.0 / 8.0) * (63 * x * x * x * x * x - 70 * x * x * x + 15 * x) );
bool conformingFalse = false;
int n_max = 4;
for (int n=0; n<=n_max+1; n++)
{
lobattoDerivatives.push_back( Teuchos::rcp( new LobattoFunction<>(n,conformingFalse,true) ) );
}
VarFactoryPtr varFactory = VarFactory::varFactory();
varFactory->testVar("v", HGRAD);
varFactory->fieldVar("u", L2);
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
MeshPtr mesh = MeshFactory::quadMesh(bf, n_max);
BasisCachePtr basisCache = BasisCache::basisCacheForCell(mesh, 0);
double tol = 1e-8;
for (int n=0; n<=n_max; n++)
{
if (! legendreFunctions[n]->equals(lobattoDerivatives[n+1], basisCache, tol) )
{
cout << "Legendre function " << n << " != Lobatto function " << n + 1 << " derivative.\n";
cout << "L_" << n << "(0.5) = " << Function::evaluate(legendreFunctions[n],0.5) << endl;
cout << "l'_" << n+1 << "(0.5) = " << Function::evaluate(lobattoDerivatives[n+1],0.5) << endl;
success = false;
}
}
return success;
}
bool LobattoBasisTests::testLegendreValues()
{
bool success = true;
FunctionPtr x = Function::xn(1);
vector< FunctionPtr > legendreFunctionsExpected;
legendreFunctionsExpected.push_back( Function::constant(1.0) );
legendreFunctionsExpected.push_back( x );
legendreFunctionsExpected.push_back( (3 * x*x - 1) / 2);
legendreFunctionsExpected.push_back( (5 * x*x*x - 3*x) / 2);
legendreFunctionsExpected.push_back( (35 * x * x * x * x - 30 * x * x + 3) / 8);
legendreFunctionsExpected.push_back( (63 * x * x * x * x * x - 70 * x * x * x + 15 * x) / 8);
vector< FunctionPtr > legendreFunctions;
int n_max = 4;
for (int n=0; n<=n_max; n++)
{
legendreFunctions.push_back( Teuchos::rcp( new LegendreFunction(n) ) );
}
VarFactoryPtr varFactory = VarFactory::varFactory();
varFactory->testVar("v", HGRAD);
varFactory->fieldVar("u", L2);
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
MeshPtr mesh = MeshFactory::quadMesh(bf, n_max);
BasisCachePtr basisCache = BasisCache::basisCacheForCell(mesh, 0);
double tol = 1e-8; // relax to make sure that failure isn't just roundoff
for (int n=0; n<=n_max; n++)
{
if (! legendreFunctions[n]->equals(legendreFunctionsExpected[n], basisCache, tol) )
{
cout << "Legendre function " << n << " does not match expected.\n";
success = false;
}
}
return success;
}
PoissonExactSolution::PoissonExactSolution(PoissonExactSolutionType type, int polyOrder, bool useConformingTraces)
{
// poly order here means that of phi
_polyOrder = polyOrder;
_type = type;
_bf = PoissonBilinearForm::poissonBilinearForm(useConformingTraces);
this->_bilinearForm = _bf;
FunctionPtr phi_exact = phi();
VarFactoryPtr vf = _bf->varFactory();
VarPtr psi_hat_n = vf->fluxVar(PoissonBilinearForm::S_PSI_HAT_N);
VarPtr phi_hat = vf->traceVar(PoissonBilinearForm::S_PHI_HAT);
VarPtr phi = vf->fieldVar(PoissonBilinearForm::S_PHI);
VarPtr psi_1 = vf->fieldVar(PoissonBilinearForm::S_PSI_1);
VarPtr psi_2 = vf->fieldVar(PoissonBilinearForm::S_PSI_2);
VarPtr q = vf->testVar(PoissonBilinearForm::S_Q, HGRAD);
FunctionPtr psi_exact = phi_exact->grad();
FunctionPtr n = Function::normal();
this->setSolutionFunction(phi, phi_exact);
this->setSolutionFunction(psi_1, psi_exact->x());
this->setSolutionFunction(psi_2, psi_exact->y());
this->setSolutionFunction(phi_hat, phi_exact);
this->setSolutionFunction(psi_hat_n, psi_exact * n);
SpatialFilterPtr wholeBoundary = SpatialFilter::allSpace();
_rhs = RHS::rhs();
FunctionPtr f = phi_exact->dx()->dx() + phi_exact->dy()->dy();
_rhs->addTerm(f * q);
setUseSinglePointBCForPHI(false, -1); // sets _bc
}
// test variables:
VarPtr PressurelessStokesFormulation::tau(int i, int j)
{
if (i > j) // swap them
{
int k = i;
i = j;
j = k;
}
if (j > _spaceDim)
{
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "i and j must be less than or equal to _spaceDim");
}
VarFactoryPtr vf = _stokesBF->varFactory();
switch (i)
{
case 1:
switch (j)
{
case 1:
return vf->testVar(S_TAU11, HGRAD);
case 2:
return vf->testVar(S_TAU12, HGRAD);
case 3:
return vf->testVar(S_TAU13, HGRAD);
}
case 2:
switch (j)
{
case 2:
return vf->testVar(S_TAU22, HGRAD);
case 3:
return vf->testVar(S_TAU23, HGRAD);
}
case 3:
switch (j)
{
case 3:
return vf->testVar(S_TAU23, HGRAD);
}
}
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "unhandled (i,j) pair");
}
bool LinearTermTests::testIntegrateMixedBasis()
{
bool success = true;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = 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(1.0);
//////////////////// DEFINE BILINEAR FORM/Mesh ///////////////////////
BFPtr convectionBF = Teuchos::rcp( new BF(varFactory) );
// v terms:
convectionBF->addTerm( -u, beta * v->grad() );
convectionBF->addTerm( beta_n_u_hat, v);
convectionBF->addTerm( u, v);
// build CONSTANT SINGLE ELEMENT MESH
int order = 0;
int H1Order = order+1;
int pToAdd = 1;
int nCells = 2; // along a side
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,convectionBF, H1Order, H1Order+pToAdd);
ElementTypePtr elemType = mesh->getElement(0)->elementType();
BasisCachePtr basisCache = Teuchos::rcp(new BasisCache(elemType, mesh));
vector<GlobalIndexType> cellIDs;
vector< ElementPtr > allElems = mesh->activeElements();
vector< ElementPtr >::iterator elemIt;
for (elemIt=allElems.begin(); elemIt!=allElems.end(); elemIt++)
{
cellIDs.push_back((*elemIt)->cellID());
}
bool createSideCacheToo = true;
basisCache->setPhysicalCellNodes(mesh->physicalCellNodesGlobal(elemType), cellIDs, createSideCacheToo);
int numTrialDofs = elemType->trialOrderPtr->totalDofs();
int numCells = mesh->numActiveElements();
double areaPerCell = 1.0 / numCells;
FieldContainer<double> integrals(numCells,numTrialDofs);
FieldContainer<double> expectedIntegrals(numCells,numTrialDofs);
double sidelengthOfCell = 1.0 / nCells;
DofOrderingPtr trialOrdering = elemType->trialOrderPtr;
int dofForField = trialOrdering->getDofIndex(u->ID(), 0);
vector<int> dofsForFlux;
const vector<int>* sidesForFlux = &trialOrdering->getSidesForVarID(beta_n_u_hat->ID());
for (vector<int>::const_iterator sideIt = sidesForFlux->begin(); sideIt != sidesForFlux->end(); sideIt++)
{
int sideIndex = *sideIt;
dofsForFlux.push_back(trialOrdering->getDofIndex(beta_n_u_hat->ID(), 0, sideIndex));
}
for (int cellIndex = 0; cellIndex < numCells; cellIndex++)
{
expectedIntegrals(cellIndex, dofForField) = areaPerCell;
for (vector<int>::iterator dofIt = dofsForFlux.begin(); dofIt != dofsForFlux.end(); dofIt++)
{
int fluxDofIndex = *dofIt;
expectedIntegrals(cellIndex, fluxDofIndex) = sidelengthOfCell;
}
}
// cout << "expectedIntegrals:\n" << expectedIntegrals;
// setup: with constant degrees of freedom, we expect that the integral of int_dK (flux) + int_K (field) will be ones for each degree of freedom, assuming the basis functions for these constants field/flux variables are just C = 1.0.
//
//On a unit square, int_K (constant) = 1.0, and int_dK (u_i) = 1, for i = 0,...,3.
LinearTermPtr lt = 1.0 * beta_n_u_hat;
LinearTermPtr field = 1.0 * u;
lt->addTerm(field,true);
lt->integrate(integrals, elemType->trialOrderPtr, basisCache);
double tol = 1e-12;
double maxDiff;
success = TestSuite::fcsAgree(integrals,expectedIntegrals,tol,maxDiff);
if (success==false)
{
cout << "Failed testIntegrateMixedBasis with maxDiff = " << maxDiff << endl;
}
return success;
}
int main(int argc, char *argv[])
{
Teuchos::GlobalMPISession mpiSession(&argc, &argv, 0);
int spaceDim = 2;
int meshWidth = 2;
bool conformingTraces = true;
int H1Order = 2, delta_k = 3;
double domainWidth = 1.0e-3;
bool diagScaling = false;
double h = domainWidth / meshWidth;
double weight = h / 4.0; // ratio of area of square with sidelength h to its perimeter
double sigma_weight = 1.0; // h / 4.0; // sigma = sigma_weight * u->grad()
Space uHatSpace = conformingTraces ? HGRAD : L2;
VarFactoryPtr vf = VarFactory::varFactory();
// fields
VarPtr u = vf->fieldVar("u");
VarPtr sigma = vf->fieldVar("sigma", VECTOR_L2);
// traces
VarPtr u_hat = vf->traceVar("u_hat", uHatSpace);
VarPtr sigma_n = vf->fluxVar("sigma_n");
// tests
VarPtr v = vf->testVar("v", HGRAD);
VarPtr tau = vf->testVar("tau", HDIV);
BFPtr bf = BF::bf(vf);
// standard BF:
// bf->addTerm(sigma, v->grad());
// bf->addTerm(sigma_n, v);
//
// bf->addTerm(sigma, tau);
// bf->addTerm(u, tau->div());
// bf->addTerm(-u_hat, tau->dot_normal());
// weighted BF:
bf->addTerm(sigma, v->grad());
bf->addTerm(weight * sigma_n, v);
bf->addTerm(sigma, tau);
bf->addTerm(sigma_weight * u, tau->div());
bf->addTerm(- sigma_weight * weight * u_hat, tau->dot_normal());
IPPtr ip = IP::ip();
// standard IP:
ip->addTerm(tau + v->grad());
ip->addTerm(tau->div());
ip->addTerm(v);
ip->addTerm(tau);
// weighted IP:
// ip->addTerm(tau + v->grad());
// ip->addTerm(sigma_weight * tau->div());
// ip->addTerm(max(sigma_weight,1e-3) * v);
// ip->addTerm(sigma_weight * weight * tau);
BCPtr bc = BC::bc();
bc->addDirichlet(u_hat, SpatialFilter::allSpace(), Function::zero());
RHSPtr rhs = RHS::rhs();
rhs->addTerm(1.0 * sigma_weight * v);
vector<double> dimensions(spaceDim,domainWidth);
vector<int> elementCounts(spaceDim,meshWidth);
MeshPtr mesh = MeshFactory::rectilinearMesh(bf, dimensions, elementCounts, H1Order, delta_k);
SolutionPtr soln = Solution::solution(mesh, bc, rhs, ip);
soln->setUseCondensedSolve(true);
soln->initializeLHSVector();
soln->initializeStiffnessAndLoad();
soln->populateStiffnessAndLoad();
Teuchos::RCP<Epetra_RowMatrix> stiffness = soln->getStiffnessMatrix();
double condNumber = conditionNumberLAPACK(*stiffness, diagScaling);
cout << "condest (1-norm): " << condNumber << endl;
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
#endif
int commRank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
// {
// // 1D tests
// CellTopoPtrLegacy line_2 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Line<2> >() ) );
// // let's draw a line
// vector<double> v0 = makeVertex(0);
// vector<double> v1 = makeVertex(1);
// vector<double> v2 = makeVertex(2);
// vector< vector<double> > vertices;
// vertices.push_back(v0);
// vertices.push_back(v1);
// vertices.push_back(v2);
// vector<unsigned> line1VertexList;
// vector<unsigned> line2VertexList;
// line1VertexList.push_back(0);
// line1VertexList.push_back(1);
// line2VertexList.push_back(1);
// line2VertexList.push_back(2);
// vector< vector<unsigned> > elementVertices;
// elementVertices.push_back(line1VertexList);
// elementVertices.push_back(line2VertexList);
// vector< CellTopoPtrLegacy > cellTopos;
// cellTopos.push_back(line_2);
// cellTopos.push_back(line_2);
// MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
// MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
// FunctionPtr x = Function::xn(1);
// FunctionPtr function = x;
// FunctionPtr fbdr = Function::restrictToCellBoundary(function);
// vector<FunctionPtr> functions;
// functions.push_back(function);
// functions.push_back(function);
// vector<string> functionNames;
// functionNames.push_back("function1");
// functionNames.push_back("function2");
// // {
// // HDF5Exporter exporter(mesh, "function1", false);
// // exporter.exportFunction(function, "function1");
// // }
// // {
// // HDF5Exporter exporter(mesh, "boundary1", false);
// // exporter.exportFunction(fbdr, "boundary1");
// // }
// // {
// // HDF5Exporter exporter(mesh, "functions1", false);
// // exporter.exportFunction(functions, functionNames);
// // }
// }
{
// 2D tests
// CellTopoPtrLegacy quad_4 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ) );
// CellTopoPtrLegacy tri_3 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Triangle<3> >() ) );
CellTopoPtr quad_4 = CellTopology::quad();
CellTopoPtr tri_3 = CellTopology::triangle();
// let's draw a little house
vector<double> v0 = makeVertex(-1,0);
vector<double> v1 = makeVertex(1,0);
vector<double> v2 = makeVertex(1,2);
vector<double> v3 = makeVertex(-1,2);
vector<double> v4 = makeVertex(0.0,3);
vector< vector<double> > vertices;
vertices.push_back(v0);
vertices.push_back(v1);
vertices.push_back(v2);
vertices.push_back(v3);
vertices.push_back(v4);
vector<unsigned> quadVertexList;
quadVertexList.push_back(0);
quadVertexList.push_back(1);
quadVertexList.push_back(2);
quadVertexList.push_back(3);
vector<unsigned> triVertexList;
triVertexList.push_back(3);
triVertexList.push_back(2);
triVertexList.push_back(4);
vector< vector<unsigned> > elementVertices;
elementVertices.push_back(quadVertexList);
elementVertices.push_back(triVertexList);
// vector< CellTopoPtrLegacy > cellTopos;
vector< CellTopoPtr> cellTopos;
cellTopos.push_back(quad_4);
cellTopos.push_back(tri_3);
MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr vf = VarFactory::varFactory();
VarPtr tau = vf->testVar("tau", HDIV);
VarPtr v = vf->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = vf->traceVar("uhat");
VarPtr fhat = vf->fluxVar("fhat");
VarPtr u = vf->fieldVar("u");
VarPtr sigma = vf->fieldVar("sigma", VECTOR_L2);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(vf) );
// tau terms:
bf->addTerm(sigma, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( fhat, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = bf->graphNorm();
//////////////////// SPECIFY RHS ///////////////////////
RHSPtr rhs = RHS::rhs();
FunctionPtr one = Function::constant(1.0);
rhs->addTerm( one * v );
//////////////////// CREATE BCs ///////////////////////
BCPtr bc = BC::bc();
FunctionPtr zero = Function::zero();
SpatialFilterPtr entireBoundary = SpatialFilter::allSpace();
bc->addDirichlet(uhat, entireBoundary, zero);
//////////////////// SOLVE & REFINE ///////////////////////
// Output solution
Intrepid::FieldContainer<GlobalIndexType> savedCellPartition;
Teuchos::RCP<Epetra_FEVector> savedLHSVector;
{
//////////////////// BUILD MESH ///////////////////////
int H1Order = 4, pToAdd = 2;
Teuchos::RCP<Mesh> mesh = Teuchos::rcp( new Mesh (meshTopology, bf, H1Order, pToAdd) );
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
solution->solve(false);
RefinementStrategy refinementStrategy( solution, 0.2);
HDF5Exporter exporter(mesh, "Poisson");
// exporter.exportSolution(solution, vf, 0, 2, cellIDToSubdivision(mesh, 4));
exporter.exportSolution(solution, 0, 2);
mesh->saveToHDF5("MeshSave.h5");
solution->saveToHDF5("SolnSave.h5");
solution->save("PoissonProblem");
// int numRefs = 1;
// for (int ref = 1; ref <= numRefs; ref++)
// {
// refinementStrategy.refine(commRank==0);
// solution->solve(false);
// mesh->saveToHDF5("MeshSave.h5");
// solution->saveToHDF5("SolnSave.h5");
// exporter.exportSolution(solution, vf, ref, 2, cellIDToSubdivision(mesh, 4));
// }
mesh->globalDofAssignment()->getPartitions(savedCellPartition);
savedLHSVector = solution->getLHSVector();
}
{
SolutionPtr loadedSolution = Solution::load(bf, "PoissonProblem");
HDF5Exporter exporter(loadedSolution->mesh(), "ProblemLoaded");
// exporter.exportSolution(loadedSolution, vf, 0, 2, cellIDToSubdivision(loadedSolution->mesh(), 4));
exporter.exportSolution(loadedSolution, 0, 2);
}
// {
// MeshPtr loadedMesh = MeshFactory::loadFromHDF5(bf, "Test0.h5");
// Teuchos::RCP<Solution> loadedSolution = Teuchos::rcp( new Solution(loadedMesh, bc, rhs, ip) );
// loadedSolution->solve(false);
// HDF5Exporter exporter(loadedMesh, "MeshLoaded");
// exporter.exportSolution(loadedSolution, vf, 0, 2, cellIDToSubdivision(loadedMesh, 4));
// }
{
MeshPtr loadedMesh = MeshFactory::loadFromHDF5(bf, "MeshSave.h5");
Intrepid::FieldContainer<GlobalIndexType> loadedCellPartition;
loadedMesh->globalDofAssignment()->getPartitions(loadedCellPartition);
if (loadedCellPartition.size() != savedCellPartition.size())
{
cout << "Error: the loaded partition has different size/shape than the saved one.\n";
cout << "loaded size: " << loadedCellPartition.size() << "; saved size: " << savedCellPartition.size() << endl;
}
else
{
bool partitionsMatch = true;
for (int i=0; i<loadedCellPartition.size(); i++)
{
if (loadedCellPartition[i] != savedCellPartition[i])
{
partitionsMatch = false;
break;
}
}
if (partitionsMatch) cout << "Saved and loaded cell partitions match!\n";
else
{
cout << "Saved and loaded cell partitions differ.\n";
cout << "saved:\n" << savedCellPartition;
cout << "loaded:\n" << loadedCellPartition;
}
}
Teuchos::RCP<Solution> loadedSolution = Teuchos::rcp( new Solution(loadedMesh, bc, rhs, ip) );
loadedSolution->loadFromHDF5("SolnSave.h5");
Teuchos::RCP<Epetra_FEVector> loadedLHSVector = loadedSolution->getLHSVector();
if (loadedLHSVector->Map().MinLID() != savedLHSVector->Map().MinLID())
{
cout << "On rank " << commRank << ", loaded min LID = " << loadedLHSVector->Map().MinLID();
cout << ", but saved min LID = " << savedLHSVector->Map().MinLID() << endl;
}
else if (loadedLHSVector->Map().MaxLID() != savedLHSVector->Map().MaxLID())
{
cout << "On rank " << commRank << ", loaded max LID = " << loadedLHSVector->Map().MaxLID();
cout << ", but saved max LID = " << savedLHSVector->Map().MaxLID() << endl;
}
else
{
bool globalIDsMatch = true;
for (int lid = loadedLHSVector->Map().MinLID(); lid <= loadedLHSVector->Map().MaxLID(); lid++)
{
if (loadedLHSVector->Map().GID(lid) != savedLHSVector->Map().GID(lid))
{
globalIDsMatch = false;
}
}
if (! globalIDsMatch)
{
cout << "On rank " << commRank << ", loaded and saved solution vector maps differ in their global IDs.\n";
}
else
{
cout << "On rank " << commRank << ", loaded and saved solution vector maps match in their global IDs.\n";
}
bool entriesMatch = true;
double tol = 1e-16;
if (loadedLHSVector->Map().MinLID() != loadedLHSVector->Map().MaxLID())
{
for (int lid = loadedLHSVector->Map().MinLID(); lid <= loadedLHSVector->Map().MaxLID(); lid++)
{
double loadedValue = (*loadedLHSVector)[0][lid];
double savedValue = (*savedLHSVector)[0][lid];
double diff = abs( loadedValue - savedValue );
if (diff > tol)
{
entriesMatch = false;
cout << "On rank " << commRank << ", loaded and saved solution vectors differ in entry with lid " << lid;
cout << "; loaded value = " << loadedValue << "; saved value = " << savedValue << ".\n";
}
}
if (entriesMatch)
{
cout << "On rank " << commRank << ", loaded and saved solution vectors match!\n";
}
else
{
cout << "On rank " << commRank << ", loaded and saved solution vectors do not match.\n";
}
}
}
HDF5Exporter exporter(loadedMesh, "SolutionLoaded");
// exporter.exportSolution(loadedSolution, vf, 0, 2, cellIDToSubdivision(loadedMesh, 4));
exporter.exportSolution(loadedSolution, 0, 2);
}
}
// {
// // 3D tests
// CellTopoPtrLegacy hex = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Hexahedron<8> >() ));
// // let's draw a little box
// vector<double> v0 = makeVertex(0,0,0);
// vector<double> v1 = makeVertex(1,0,0);
// vector<double> v2 = makeVertex(1,1,0);
// vector<double> v3 = makeVertex(0,1,0);
// vector<double> v4 = makeVertex(0,0,1);
// vector<double> v5 = makeVertex(1,0,1);
// vector<double> v6 = makeVertex(1,1,1);
// vector<double> v7 = makeVertex(0,1,1);
// vector< vector<double> > vertices;
// vertices.push_back(v0);
// vertices.push_back(v1);
// vertices.push_back(v2);
// vertices.push_back(v3);
// vertices.push_back(v4);
// vertices.push_back(v5);
// vertices.push_back(v6);
// vertices.push_back(v7);
// vector<unsigned> hexVertexList;
// hexVertexList.push_back(0);
// hexVertexList.push_back(1);
// hexVertexList.push_back(2);
// hexVertexList.push_back(3);
// hexVertexList.push_back(4);
// hexVertexList.push_back(5);
// hexVertexList.push_back(6);
// hexVertexList.push_back(7);
// // vector<unsigned> triVertexList;
// // triVertexList.push_back(2);
// // triVertexList.push_back(3);
// // triVertexList.push_back(4);
// vector< vector<unsigned> > elementVertices;
// elementVertices.push_back(hexVertexList);
// // elementVertices.push_back(triVertexList);
// vector< CellTopoPtrLegacy > cellTopos;
// cellTopos.push_back(hex);
// // cellTopos.push_back(tri_3);
// MeshGeometryPtr meshGeometry = Teuchos::rcp( new MeshGeometry(vertices, elementVertices, cellTopos) );
// MeshTopologyPtr meshTopology = Teuchos::rcp( new MeshTopology(meshGeometry) );
// FunctionPtr x = Function::xn(1);
// FunctionPtr y = Function::yn(1);
// FunctionPtr z = Function::zn(1);
// FunctionPtr function = x + y + z;
// FunctionPtr fbdr = Function::restrictToCellBoundary(function);
// FunctionPtr vect = Function::vectorize(x, y, z);
// vector<FunctionPtr> functions;
// functions.push_back(function);
// functions.push_back(vect);
// vector<string> functionNames;
// functionNames.push_back("function");
// functionNames.push_back("vect");
// // {
// // HDF5Exporter exporter(mesh, "function3", false);
// // exporter.exportFunction(function, "function3");
// // }
// // {
// // HDF5Exporter exporter(mesh, "boundary3", false);
// // exporter.exportFunction(fbdr, "boundary3");
// // }
// // {
// // HDF5Exporter exporter(mesh, "vect3", false);
// // exporter.exportFunction(vect, "vect3");
// // }
// // {
// // HDF5Exporter exporter(mesh, "functions3", false);
// // exporter.exportFunction(functions, functionNames);
// // }
// }
}
PressurelessStokesFormulation::PressurelessStokesFormulation(int spaceDim)
{
_spaceDim = spaceDim;
if ((spaceDim != 2) && (spaceDim != 3))
{
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "spaceDim must be 2 or 3");
}
// declare all possible variables -- will only create the ones we need for spaceDim
// fields
VarPtr u1, u2, u3;
VarPtr sigma11, sigma12, sigma13;
VarPtr sigma22, sigma23;
VarPtr sigma33;
// traces
VarPtr u1_hat, u2_hat, u3_hat;
VarPtr t1n, t2n, t3n;
// tests
VarPtr v1, v2, v3;
VarPtr tau11, tau12, tau13;
VarPtr tau22, tau23;
VarPtr tau33;
VarFactoryPtr vf = VarFactory::varFactory();
u1 = vf->fieldVar(S_U1);
u2 = vf->fieldVar(S_U2);
if (spaceDim==3) u3 = vf->fieldVar(S_U3);
sigma11 = vf->fieldVar(S_SIGMA11);
sigma12 = vf->fieldVar(S_SIGMA12);
sigma22 = vf->fieldVar(S_SIGMA22);
if (spaceDim==3)
{
sigma13 = vf->fieldVar(S_SIGMA13);
sigma23 = vf->fieldVar(S_SIGMA23);
sigma33 = vf->fieldVar(S_SIGMA33);
}
u1_hat = vf->traceVar(S_U1_HAT, 1.0 * u1, L2);
u2_hat = vf->traceVar(S_U2_HAT, 1.0 * u2, L2);
if (spaceDim==3) u3_hat = vf->traceVar(S_U3_HAT, 1.0 * u3, L2);
TFunctionPtr<double> n = TFunction<double>::normal();
LinearTermPtr sigma1n, sigma2n, sigma3n;
if (spaceDim==2)
{
sigma1n = sigma11 * n->x() + sigma12 * n->y();
sigma2n = sigma12 * n->x() + sigma22 * n->y();
}
else
{
sigma1n = sigma11 * n->x() + sigma12 * n->y() + sigma13 * n->z();
sigma2n = sigma12 * n->x() + sigma22 * n->y() + sigma23 * n->z();
sigma3n = sigma13 * n->x() + sigma23 * n->y() + sigma33 * n->z();
}
t1n = vf->fluxVar(S_TN1_HAT, sigma1n);
t2n = vf->fluxVar(S_TN2_HAT, sigma2n);
if (spaceDim==3) t3n = vf->fluxVar(S_TN3_HAT, sigma3n);
v1 = vf->testVar(S_V1, HGRAD);
v2 = vf->testVar(S_V2, HGRAD);
if (spaceDim==3) v3 = vf->testVar(S_V3, HGRAD);
tau11 = vf->testVar(S_TAU11, HGRAD);
tau12 = vf->testVar(S_TAU12, HGRAD);
tau22 = vf->testVar(S_TAU22, HGRAD);
if (spaceDim==3)
{
tau13 = vf->testVar(S_TAU13, HGRAD);
tau23 = vf->testVar(S_TAU23, HGRAD);
tau33 = vf->testVar(S_TAU33, HGRAD);
}
_stokesBF = Teuchos::rcp( new BF(vf) );
// v1
_stokesBF->addTerm(-sigma11, v1->dx());
_stokesBF->addTerm(-sigma12, v1->dy());
if (spaceDim==3)
{
_stokesBF->addTerm(-sigma13, v1->dz());
}
_stokesBF->addTerm(t1n, v1);
// v2
_stokesBF->addTerm(-sigma12, v2->dx());
_stokesBF->addTerm(-sigma22, v2->dy());
if (spaceDim==3)
{
_stokesBF->addTerm(-sigma23, v2->dz());
}
_stokesBF->addTerm(t2n, v2);
// v3
if (spaceDim==3)
{
_stokesBF->addTerm(-sigma13, v3->dx());
_stokesBF->addTerm(-sigma23, v3->dy());
_stokesBF->addTerm(-sigma33, v3->dz());
_stokesBF->addTerm(t3n, v3);
}
LinearTermPtr p; // pressure term, the negative weighted trace of tensor sigma
if (spaceDim==2)
{
p = -0.5 * sigma11 + -0.5 * sigma22;
}
else
{
p = -(1.0/3.0) * sigma11 + -(1.0/3.0) * sigma22 + -(1.0/3.0) * sigma33;
}
LinearTermPtr tau1n, tau2n, tau3n;
LinearTermPtr div_tau1, div_tau2, div_tau3;
if (spaceDim==2)
{
tau1n = tau11 * n->x() + tau12 * n->y();
tau2n = tau12 * n->x() + tau22 * n->y();
div_tau1 = tau11->dx() + tau12->dy();
div_tau2 = tau12->dx() + tau22->dy();
}
else
{
tau1n = tau11 * n->x() + tau12 * n->y() + tau13 * n->z();
tau2n = tau12 * n->x() + tau22 * n->y() + tau23 * n->z();
tau3n = tau13 * n->x() + tau23 * n->y() + tau33 * n->z();
div_tau1 = tau11->dx() + tau12->dy() + tau13->dz();
div_tau2 = tau12->dx() + tau22->dy() + tau23->dz();
div_tau3 = tau13->dx() + tau23->dy() + tau33->dz();
}
// tau1j
_stokesBF->addTerm(sigma11, tau11);
_stokesBF->addTerm(sigma12, tau12);
if (spaceDim==3) _stokesBF->addTerm(sigma13, tau13);
_stokesBF->addTerm(2 * u1, div_tau1);
_stokesBF->addTerm(-2 * u1_hat, tau1n);
_stokesBF->addTerm(p, tau11);
// tau2j
_stokesBF->addTerm(sigma12, tau12);
_stokesBF->addTerm(sigma22, tau22);
if (spaceDim==3) _stokesBF->addTerm(sigma23, tau23);
_stokesBF->addTerm(2 * u2, div_tau2);
_stokesBF->addTerm(-2 * u2_hat, tau2n);
_stokesBF->addTerm(p, tau22);
// tau3j
if (spaceDim==3)
{
_stokesBF->addTerm(sigma13, tau13);
_stokesBF->addTerm(sigma23, tau23);
_stokesBF->addTerm(sigma33, tau33);
_stokesBF->addTerm(2 * u3, div_tau3);
_stokesBF->addTerm(-2 * u3_hat, tau3n);
_stokesBF->addTerm(p, tau33);
}
}
// tests Riesz inversion by integration by parts
bool LinearTermTests::testRieszInversion()
{
bool success = true;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr tau = varFactory->testVar("\\tau", HDIV);
VarPtr v = varFactory->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory->traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory->fieldVar("u");
VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
double eps = .01;
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = 1;
int pToAdd = 1;
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 1.0;
quadPoints(1,1) = 0.0;
quadPoints(2,0) = 1.0;
quadPoints(2,1) = 1.0;
quadPoints(3,0) = 0.0;
quadPoints(3,1) = 1.0;
int nCells = 1;
int horizontalCells = nCells, verticalCells = nCells;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> myMesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
confusionBF, H1Order, H1Order+pToAdd);
ElementTypePtr elemType = myMesh->getElement(0)->elementType();
BasisCachePtr basisCache = Teuchos::rcp(new BasisCache(elemType, myMesh));
vector<GlobalIndexType> cellIDs;
vector<ElementPtr> elems = myMesh->activeElements();
vector<ElementPtr>::iterator elemIt;
for (elemIt=elems.begin(); elemIt!=elems.end(); elemIt++)
{
int cellID = (*elemIt)->cellID();
cellIDs.push_back(cellID);
}
bool createSideCacheToo = true;
basisCache->setPhysicalCellNodes(myMesh->physicalCellNodesGlobal(elemType), cellIDs, createSideCacheToo);
LinearTermPtr integrand = Teuchos::rcp(new LinearTerm);// residual
LinearTermPtr integrandIBP = Teuchos::rcp(new LinearTerm);// residual
vector<double> e1(2); // (1,0)
vector<double> e2(2); // (0,1)
e1[0] = 1;
e2[1] = 1;
FunctionPtr n = Function::normal();
FunctionPtr X = Function::xn(1);
FunctionPtr Y = Function::yn(1);
FunctionPtr testFxn1 = X;
FunctionPtr testFxn2 = Y;
FunctionPtr divTestFxn = testFxn1->dx() + testFxn2->dy();
FunctionPtr vectorTest = testFxn1*e1 + testFxn2*e2;
integrand->addTerm(divTestFxn*v);
integrandIBP->addTerm(vectorTest*n*v - vectorTest*v->grad()); // boundary term
IPPtr sobolevIP = Teuchos::rcp(new IP);
sobolevIP->addTerm(v);
sobolevIP->addTerm(tau);
Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(myMesh, sobolevIP, integrand));
// riesz->setPrintOption(true);
riesz->computeRieszRep();
Teuchos::RCP<RieszRep> rieszIBP = Teuchos::rcp(new RieszRep(myMesh, sobolevIP, integrandIBP));
riesz->setFunctional(integrandIBP);
// rieszIBP->setPrintOption(true);
rieszIBP->computeRieszRep();
FunctionPtr rieszOrigFxn = RieszRep::repFunction(v,riesz);
FunctionPtr rieszIBPFxn = RieszRep::repFunction(v,rieszIBP);
int numCells = basisCache->getPhysicalCubaturePoints().dimension(0);
int numPts = basisCache->getPhysicalCubaturePoints().dimension(1);
FieldContainer<double> valOriginal( numCells, numPts);
FieldContainer<double> valIBP( numCells, numPts);
rieszOrigFxn->values(valOriginal,basisCache);
rieszIBPFxn->values(valIBP,basisCache);
double maxDiff;
double tol = 1e-14;
success = TestSuite::fcsAgree(valOriginal,valIBP,tol,maxDiff);
if (success==false)
{
cout << "Failed TestRieszInversion with maxDiff = " << maxDiff << endl;
}
return success;
}
bool LinearTermTests::testRieszInversionAsProjection()
{
bool success = true;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr tau = varFactory->testVar("\\tau", HDIV);
VarPtr v = varFactory->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory->traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory->fieldVar("u");
VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
double eps = .01;
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = 2;
int pToAdd = 2;
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 1.0;
quadPoints(1,1) = 0.0;
quadPoints(2,0) = 1.0;
quadPoints(2,1) = 1.0;
quadPoints(3,0) = 0.0;
quadPoints(3,1) = 1.0;
int nCells = 2;
int horizontalCells = nCells, verticalCells = nCells;
// create a new mesh:
MeshPtr myMesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells, confusionBF, H1Order, H1Order+pToAdd);
ElementTypePtr elemType = myMesh->getElement(0)->elementType();
BasisCachePtr basisCache = Teuchos::rcp(new BasisCache(elemType, myMesh));
vector<GlobalIndexType> cellIDs = myMesh->cellIDsOfTypeGlobal(elemType);
bool createSideCacheToo = true;
basisCache->setPhysicalCellNodes(myMesh->physicalCellNodesGlobal(elemType), cellIDs, createSideCacheToo);
LinearTermPtr integrand = Teuchos::rcp(new LinearTerm); // residual
FunctionPtr x = Function::xn(1);
FunctionPtr y = Function::yn(1);
FunctionPtr testFxn1 = x;
FunctionPtr testFxn2 = y;
FunctionPtr fxnToProject = x * y + 1.0;
integrand->addTerm(fxnToProject * v);
IPPtr ip_L2 = Teuchos::rcp(new IP);
ip_L2->addTerm(v);
ip_L2->addTerm(tau);
Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(myMesh, ip_L2, integrand));
riesz->computeRieszRep();
FunctionPtr rieszFxn = RieszRep::repFunction(v,riesz);
int numCells = basisCache->getPhysicalCubaturePoints().dimension(0);
int numPts = basisCache->getPhysicalCubaturePoints().dimension(1);
FieldContainer<double> valProject( numCells, numPts );
FieldContainer<double> valExpected( numCells, numPts );
rieszFxn->values(valProject,basisCache);
fxnToProject->values(valExpected,basisCache);
// int rank = Teuchos::GlobalMPISession::getRank();
// if (rank==0) cout << "physicalCubaturePoints:\n" << basisCache->getPhysicalCubaturePoints();
double maxDiff;
double tol = 1e-12;
success = TestSuite::fcsAgree(valProject,valExpected,tol,maxDiff);
if (success==false)
{
cout << "Failed Riesz Inversion Projection test with maxDiff = " << maxDiff << endl;
serializeOutput("valExpected", valExpected);
serializeOutput("valProject", valProject);
serializeOutput("physicalPoints", basisCache->getPhysicalCubaturePoints());
}
return allSuccess(success);
}
bool ScratchPadTests::testGalerkinOrthogonality()
{
double tol = 1e-11;
bool success = true;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr v = varFactory->testVar("v", HGRAD);
vector<double> beta;
beta.push_back(1.0);
beta.push_back(1.0);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// robust test norm
IPPtr ip = Teuchos::rcp(new IP);
ip->addTerm(v);
ip->addTerm(beta*v->grad());
// define trial variables
VarPtr beta_n_u = varFactory->fluxVar("\\widehat{\\beta \\cdot n }");
VarPtr u = varFactory->fieldVar("u");
//////////////////// BUILD MESH ///////////////////////
BFPtr convectionBF = Teuchos::rcp( new BF(varFactory) );
FunctionPtr n = Function::normal();
// v terms:
convectionBF->addTerm( -u, beta * v->grad() );
convectionBF->addTerm( beta_n_u, v);
// define nodes for mesh
int order = 2;
int H1Order = order+1;
int pToAdd = 1;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(4, convectionBF, H1Order, H1Order+pToAdd);
//////////////////// SOLVE ///////////////////////
RHSPtr rhs = RHS::rhs();
BCPtr bc = BC::bc();
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new NegatedSpatialFilter(inflowBoundary) );
FunctionPtr uIn;
uIn = Teuchos::rcp(new Uinflow); // uses a discontinuous piecewise-constant basis function on left and bottom sides of square
bc->addDirichlet(beta_n_u, inflowBoundary, beta*n*uIn);
Teuchos::RCP<Solution> solution;
solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
solution->solve(false);
FunctionPtr uFxn = Function::solution(u, solution);
FunctionPtr fnhatFxn = Function::solution(beta_n_u,solution);
// make residual for riesz representation function
LinearTermPtr residual = Teuchos::rcp(new LinearTerm);// residual
FunctionPtr parity = Function::sideParity();
residual->addTerm(-fnhatFxn*v + (beta*uFxn)*v->grad());
Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ip, residual));
riesz->computeRieszRep();
map<int,FunctionPtr> err_rep_map;
err_rep_map[v->ID()] = RieszRep::repFunction(v,riesz);
//////////////////// GET BOUNDARY CONDITION DATA ///////////////////////
FieldContainer<GlobalIndexType> bcGlobalIndices;
FieldContainer<double> bcGlobalValues;
mesh->boundary().bcsToImpose(bcGlobalIndices,bcGlobalValues,*(solution->bc()), NULL);
set<int> bcInds;
for (int i=0; i<bcGlobalIndices.dimension(0); i++)
{
bcInds.insert(bcGlobalIndices(i));
}
//////////////////// CHECK GALERKIN ORTHOGONALITY ///////////////////////
BCPtr nullBC;
RHSPtr nullRHS;
IPPtr nullIP;
SolutionPtr solnPerturbation = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
map< int, vector<DofInfo> > infoMap = constructGlobalDofToLocalDofInfoMap(mesh);
for (map< int, vector<DofInfo> >::iterator mapIt = infoMap.begin();
mapIt != infoMap.end(); mapIt++)
{
int dofIndex = mapIt->first;
vector< DofInfo > dofInfoVector = mapIt->second; // all the local dofs that map to dofIndex
// create perturbation in direction du
solnPerturbation->clear(); // clear all solns
// set each corresponding local dof to 1.0
for (vector< DofInfo >::iterator dofInfoIt = dofInfoVector.begin();
dofInfoIt != dofInfoVector.end(); dofInfoIt++)
{
DofInfo info = *dofInfoIt;
FieldContainer<double> solnCoeffs(info.basisCardinality);
solnCoeffs(info.basisOrdinal) = 1.0;
solnPerturbation->setSolnCoeffsForCellID(solnCoeffs, info.cellID, info.trialID, info.sideIndex);
}
// solnPerturbation->setSolnCoeffForGlobalDofIndex(1.0,dofIndex);
LinearTermPtr b_du = convectionBF->testFunctional(solnPerturbation);
FunctionPtr gradient = b_du->evaluate(err_rep_map, TestingUtilities::isFluxOrTraceDof(mesh,dofIndex)); // use boundary part only if flux
double grad = gradient->integrate(mesh,10);
if (!TestingUtilities::isFluxOrTraceDof(mesh,dofIndex) && abs(grad)>tol) // if we're not single-precision zero FOR FIELDS
{
// int cellID = mesh->getGlobalToLocalMap()[dofIndex].first;
cout << "Failed testGalerkinOrthogonality() for fields with diff " << abs(grad) << " at dof " << dofIndex << "; info:" << endl;
cout << dofInfoString(infoMap[dofIndex]);
success = false;
}
}
FieldContainer<double> errorJumps(mesh->numGlobalDofs()); //initialized to zero
// just test fluxes ON INTERNAL SKELETON here
set<GlobalIndexType> activeCellIDs = mesh->getActiveCellIDsGlobal();
for (GlobalIndexType activeCellID : activeCellIDs)
{
ElementPtr elem = mesh->getElement(activeCellID);
for (int sideIndex = 0; sideIndex < 4; sideIndex++)
{
ElementTypePtr elemType = elem->elementType();
vector<int> localDofIndices = elemType->trialOrderPtr->getDofIndices(beta_n_u->ID(), sideIndex);
for (int i = 0; i<localDofIndices.size(); i++)
{
int globalDofIndex = mesh->globalDofIndex(elem->cellID(), localDofIndices[i]);
vector< DofInfo > dofInfoVector = infoMap[globalDofIndex];
solnPerturbation->clear();
TestingUtilities::setSolnCoeffForGlobalDofIndex(solnPerturbation,1.0,globalDofIndex);
// also add in BCs
for (int i = 0; i<bcGlobalIndices.dimension(0); i++)
{
TestingUtilities::setSolnCoeffForGlobalDofIndex(solnPerturbation,bcGlobalValues(i),bcGlobalIndices(i));
}
LinearTermPtr b_du = convectionBF->testFunctional(solnPerturbation);
FunctionPtr gradient = b_du->evaluate(err_rep_map, TestingUtilities::isFluxOrTraceDof(mesh,globalDofIndex)); // use boundary part only if flux
double jump = gradient->integrate(mesh,10);
errorJumps(globalDofIndex) += jump;
}
}
}
for (int i = 0; i<mesh->numGlobalDofs(); i++)
{
if (abs(errorJumps(i))>tol)
{
cout << "Failing Galerkin orthogonality test for fluxes with diff " << errorJumps(i) << " at dof " << i << endl;
cout << dofInfoString(infoMap[i]);
success = false;
}
}
return success;
}
// tests to make sure that the rieszNorm computed via matrices is the same as the one computed thru direct integration
bool ScratchPadTests::testRieszIntegration()
{
double tol = 1e-11;
bool success = true;
int nCells = 2;
double eps = .25;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr tau = varFactory->testVar("\\tau", HDIV);
VarPtr v = varFactory->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory->traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory->fieldVar("u");
VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// robust test norm
IPPtr ip = Teuchos::rcp(new IP);
// just H1 projection
ip->addTerm(v->grad());
ip->addTerm(v);
ip->addTerm(tau);
ip->addTerm(tau->div());
//////////////////// SPECIFY RHS AND HELPFUL FUNCTIONS ///////////////////////
FunctionPtr n = Function::normal();
vector<double> e1,e2;
e1.push_back(1.0);
e1.push_back(0.0);
e2.push_back(0.0);
e2.push_back(1.0);
FunctionPtr one = Function::constant(1.0);
FunctionPtr zero = Function::constant(0.0);
RHSPtr rhs = RHS::rhs();
FunctionPtr f = one;
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
BCPtr bc = BC::bc();
SpatialFilterPtr squareBoundary = Teuchos::rcp( new SquareBoundary );
bc->addDirichlet(uhat, squareBoundary, zero);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int order = 2;
int H1Order = order+1;
int pToAdd = 2;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);
//////////////////// SOLVE & REFINE ///////////////////////
LinearTermPtr lt = Teuchos::rcp(new LinearTerm);
FunctionPtr fxn = Function::xn(1); // fxn = x
lt->addTerm(fxn*v + fxn->grad()*v->grad());
lt->addTerm(fxn*tau->x() + fxn*tau->y() + (fxn->dx() + fxn->dy())*tau->div());
Teuchos::RCP<RieszRep> rieszLT = Teuchos::rcp(new RieszRep(mesh, ip, lt));
rieszLT->computeRieszRep();
double rieszNorm = rieszLT->getNorm();
FunctionPtr e_v = RieszRep::repFunction(v,rieszLT);
FunctionPtr e_tau = RieszRep::repFunction(tau,rieszLT);
map<int,FunctionPtr> repFxns;
repFxns[v->ID()] = e_v;
repFxns[tau->ID()] = e_tau;
double integratedNorm = sqrt((lt->evaluate(repFxns,false))->integrate(mesh,5,true));
success = abs(rieszNorm-integratedNorm)<tol;
if (success==false)
{
cout << "Failed testRieszIntegration; riesz norm is computed to be = " << rieszNorm << ", while using integration it's computed to be " << integratedNorm << endl;
return success;
}
return success;
}
bool VectorizedBasisTestSuite::testPoisson()
{
bool success = true;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr tau = varFactory->testVar("\\tau", HDIV);
VarPtr v = varFactory->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory->traceVar("\\widehat{u}");
VarPtr sigma_n = varFactory->fluxVar("\\widehat{\\sigma_{n}}");
VarPtr u = varFactory->fieldVar("u");
VarPtr sigma = varFactory->fieldVar("\\sigma", VECTOR_L2);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// tau terms:
bf->addTerm(sigma, tau);
bf->addTerm(u, tau->div());
bf->addTerm(-uhat, tau->dot_normal());
// v terms:
bf->addTerm( sigma, v->grad() );
bf->addTerm( -sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = bf->graphNorm();
//////////////////// SPECIFY RHS ///////////////////////
RHSPtr rhs = RHS::rhs();
FunctionPtr f = Function::constant(1.0);
rhs->addTerm( f * v );
//////////////////// CREATE BCs ///////////////////////
BCPtr bc = BC::bc();
SpatialFilterPtr boundary = SpatialFilter::allSpace();
FunctionPtr zero = Function::zero();
bc->addDirichlet(uhat, boundary, zero);
//////////////////// BUILD MESH ///////////////////////
int H1Order = 3, pToAdd = 2;
// define nodes for mesh
FieldContainer<double> meshBoundary(4,2);
meshBoundary(0,0) = 0.0; // x1
meshBoundary(0,1) = 0.0; // y1
meshBoundary(1,0) = 1.0;
meshBoundary(1,1) = 0.0;
meshBoundary(2,0) = 1.0;
meshBoundary(2,1) = 1.0;
meshBoundary(3,0) = 0.0;
meshBoundary(3,1) = 1.0;
int horizontalCells = 1, verticalCells = 1;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshFactory::buildQuadMesh(meshBoundary, horizontalCells, verticalCells,
bf, H1Order, H1Order+pToAdd, false);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
#ifdef USE_VTK
VTKExporter exporter(solution, mesh, varFactory);
#endif
for (int refIndex=0; refIndex<=4; refIndex++)
{
solution->solve(false);
#ifdef USE_VTK
// output commented out because it's not properly part of the test.
// stringstream outfile;
// outfile << "test_" << refIndex;
// exporter.exportSolution(outfile.str());
#endif
if (refIndex < 4)
refinementStrategy.refine(false); // don't print to console
}
return success;
}
bool FunctionTests::testValuesDottedWithTensor()
{
bool success = true;
vector< FunctionPtr > vectorFxns;
double xValue = 3, yValue = 4;
FunctionPtr simpleVector = Function::vectorize(Function::constant(xValue), Function::constant(yValue));
vectorFxns.push_back(simpleVector);
FunctionPtr x = Function::xn(1);
FunctionPtr y = Function::yn(1);
vectorFxns.push_back( Function::vectorize(x*x, x*y) );
VGPStokesFormulation vgpStokes = VGPStokesFormulation(1.0);
BFPtr bf = vgpStokes.bf();
int h1Order = 1;
MeshPtr mesh = MeshFactory::quadMesh(bf, h1Order);
int cellID=0; // the only cell
BasisCachePtr basisCache = BasisCache::basisCacheForCell(mesh, cellID);
for (int i=0; i<vectorFxns.size(); i++)
{
FunctionPtr vectorFxn_i = vectorFxns[i];
for (int j=0; j<vectorFxns.size(); j++)
{
FunctionPtr vectorFxn_j = vectorFxns[j];
FunctionPtr dotProduct = vectorFxn_i * vectorFxn_j;
FunctionPtr expectedDotProduct = vectorFxn_i->x() * vectorFxn_j->x() + vectorFxn_i->y() * vectorFxn_j->y();
if (! expectedDotProduct->equals(dotProduct, basisCache))
{
cout << "testValuesDottedWithTensor() failed: expected dot product does not match dotProduct.\n";
success = false;
double tol = 1e-14;
reportFunctionValueDifferences(dotProduct, expectedDotProduct, basisCache, tol);
}
}
}
// now, let's try the same thing, but for a LinearTerm dot product
VarFactoryPtr vf = VarFactory::varFactory();
VarPtr v = vf->testVar("v", HGRAD);
DofOrderingPtr dofOrdering = Teuchos::rcp( new DofOrdering(CellTopology::quad()) );
shards::CellTopology quad_4(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
BasisPtr basis = BasisFactory::basisFactory()->getBasis(h1Order, quad_4.getKey(), Camellia::FUNCTION_SPACE_HGRAD);
dofOrdering->addEntry(v->ID(), basis, v->rank());
int numCells = 1;
int numFields = basis->getCardinality();
for (int i=0; i<vectorFxns.size(); i++)
{
FunctionPtr f_i = vectorFxns[i];
LinearTermPtr lt_i = f_i * v;
LinearTermPtr lt_i_x = f_i->x() * v;
LinearTermPtr lt_i_y = f_i->y() * v;
for (int j=0; j<vectorFxns.size(); j++)
{
FunctionPtr f_j = vectorFxns[j];
LinearTermPtr lt_j = f_j * v;
LinearTermPtr lt_j_x = f_j->x() * v;
LinearTermPtr lt_j_y = f_j->y() * v;
FieldContainer<double> values(numCells,numFields,numFields);
lt_i->integrate(values, dofOrdering, lt_j, dofOrdering, basisCache);
FieldContainer<double> values_expected(numCells,numFields,numFields);
lt_i_x->integrate(values_expected,dofOrdering,lt_j_x,dofOrdering,basisCache);
lt_i_y->integrate(values_expected,dofOrdering,lt_j_y,dofOrdering,basisCache);
double tol = 1e-14;
double maxDiff = 0;
if (!fcsAgree(values, values_expected, tol, maxDiff))
{
cout << "FunctionTests::testValuesDottedWithTensor: ";
cout << "dot product and sum of the products of scalar components differ by maxDiff " << maxDiff;
cout << " in LinearTerm::integrate().\n";
success = false;
}
}
}
// // finally, let's try the same sort of thing, but now with a vector-valued basis
// BasisPtr vectorBasisTemp = BasisFactory::basisFactory()->getBasis(h1Order, quad_4.getKey(), Camellia::FUNCTION_SPACE_VECTOR_HGRAD);
// VectorBasisPtr vectorBasis = Teuchos::rcp( (VectorizedBasis<double, FieldContainer<double> > *)vectorBasisTemp.get(),false);
//
// BasisPtr compBasis = vectorBasis->getComponentBasis();
//
// // create a new v, and a new dofOrdering
// VarPtr v_vector = vf->testVar("v_vector", VECTOR_HGRAD);
// dofOrdering = Teuchos::rcp( new DofOrdering );
// dofOrdering->addEntry(v_vector->ID(), vectorBasis, v_vector->rank());
//
// DofOrderingPtr dofOrderingComp = Teuchos::rcp( new DofOrdering );
// dofOrderingComp->addEntry(v->ID(), compBasis, v->rank());
//
return success;
}
void FunctionTests::setup()
{
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr tau = varFactory->testVar("\\tau", HDIV);
VarPtr v = varFactory->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory->traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory->fieldVar("u");
VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");
vector<double> beta_const;
beta_const.push_back(2.0);
beta_const.push_back(1.0);
double eps = 1e-2;
// standard confusion bilinear form
_confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
_confusionBF->addTerm(sigma1 / eps, tau->x());
_confusionBF->addTerm(sigma2 / eps, tau->y());
_confusionBF->addTerm(u, tau->div());
_confusionBF->addTerm(-uhat, tau->dot_normal());
// v terms:
_confusionBF->addTerm( sigma1, v->dx() );
_confusionBF->addTerm( sigma2, v->dy() );
_confusionBF->addTerm( beta_const * u, - v->grad() );
_confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = -1.0; // x1
quadPoints(0,1) = -1.0; // y1
quadPoints(1,0) = 1.0;
quadPoints(1,1) = -1.0;
quadPoints(2,0) = 1.0;
quadPoints(2,1) = 1.0;
quadPoints(3,0) = -1.0;
quadPoints(3,1) = 1.0;
int H1Order = 1, pToAdd = 0;
int horizontalCells = 1, verticalCells = 1;
// create a pointer to a new mesh:
_spectralConfusionMesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
_confusionBF, H1Order, H1Order+pToAdd);
// some 2D test points:
// setup test points:
static const int NUM_POINTS_1D = 10;
double x[NUM_POINTS_1D] = {-1.0,-0.8,-0.6,-.4,-.2,0,0.2,0.4,0.6,0.8};
double y[NUM_POINTS_1D] = {-0.8,-0.6,-.4,-.2,0,0.2,0.4,0.6,0.8,1.0};
_testPoints = FieldContainer<double>(NUM_POINTS_1D*NUM_POINTS_1D,2);
for (int i=0; i<NUM_POINTS_1D; i++)
{
for (int j=0; j<NUM_POINTS_1D; j++)
{
_testPoints(i*NUM_POINTS_1D + j, 0) = x[i];
_testPoints(i*NUM_POINTS_1D + j, 1) = y[j];
}
}
_elemType = _spectralConfusionMesh->getElementType(0);
vector<GlobalIndexType> cellIDs;
GlobalIndexType cellID = 0;
cellIDs.push_back(cellID);
_basisCache = Teuchos::rcp( new BasisCache( _elemType, _spectralConfusionMesh ) );
_basisCache->setRefCellPoints(_testPoints);
_basisCache->setPhysicalCellNodes( _spectralConfusionMesh->physicalCellNodesForCell(cellID), cellIDs, true );
}
int main(int argc, char *argv[])
{
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
int spaceDim = 2;
#ifdef HAVE_MPI
choice::MpiArgs args( argc, argv );
#else
choice::Args args(argc, argv );
#endif
int minPolyOrder = args.Input<int>("--minPolyOrder", "L^2 (field) minimum polynomial order",0);
int maxPolyOrder = args.Input<int>("--maxPolyOrder", "L^2 (field) maximum polynomial order",1);
int minLogElements = args.Input<int>("--minLogElements", "base 2 log of the minimum number of elements in one mesh direction", 0);
int maxLogElements = args.Input<int>("--maxLogElements", "base 2 log of the maximum number of elements in one mesh direction", 4);
double Re = args.Input<double>("--Re", "Reynolds number", 40);
// bool outputStiffnessMatrix = args.Input<bool>("--writeFinalStiffnessToDisk", "write the final stiffness matrix to disk.", false);
bool computeMaxConditionNumber = args.Input<bool>("--computeMaxConditionNumber", "compute the maximum Gram matrix condition number for final mesh.", false);
int maxIters = args.Input<int>("--maxIters", "maximum number of Newton-Raphson iterations to take to try to match tolerance", 50);
double minL2Increment = args.Input<double>("--NRtol", "Newton-Raphson tolerance, L^2 norm of increment", 1e-12);
string normChoice = args.Input<string>("--norm", "norm choice: graph, compliantGraph, stokesGraph, or stokesCompliantGraph", "graph");
bool useCondensedSolve = args.Input<bool>("--useCondensedSolve", "use static condensation", true);
double dt = args.Input<double>("--timeStep", "time step (0 for none)", 0);
double zmcRho = args.Input<double>("--zmcRho", "zero-mean constraint rho (stabilization parameter)", -1);
// string replayFile = args.Input<string>("--replayFile", "file with refinement history to replay", "");
// string saveFile = args.Input<string>("--saveReplay", "file to which to save refinement history", "");
args.Process();
int pToAdd = 2; // for optimal test function approximation
bool useLineSearch = false;
bool computeRelativeErrors = true; // we'll say false when one of the exact solution components is 0
bool useEnrichedTraces = true; // enriched traces are the right choice, mathematically speaking
BasisFactory::basisFactory()->setUseEnrichedTraces(useEnrichedTraces);
// parse args:
bool useTriangles = false, useGraphNorm = false, useCompliantNorm = false, useStokesCompliantNorm = false, useStokesGraphNorm = false;
if (normChoice=="graph")
{
useGraphNorm = true;
}
else if (normChoice=="compliantGraph")
{
useCompliantNorm = true;
}
else if (normChoice=="stokesGraph")
{
useStokesGraphNorm = true;
}
else if (normChoice=="stokesCompliantGraph")
{
useStokesCompliantNorm = true;
}
else
{
if (rank==0) cout << "unknown norm choice. Exiting.\n";
exit(-1);
}
bool artificialTimeStepping = (dt > 0);
if (rank == 0)
{
cout << "pToAdd = " << pToAdd << endl;
cout << "useTriangles = " << (useTriangles ? "true" : "false") << "\n";
cout << "norm = " << normChoice << endl;
}
// define Kovasznay domain:
FieldContainer<double> quadPointsKovasznay(4,2);
// domain from Cockburn Kanschat for Stokes:
quadPointsKovasznay(0,0) = -0.5; // x1
quadPointsKovasznay(0,1) = 0.0; // y1
quadPointsKovasznay(1,0) = 1.5;
quadPointsKovasznay(1,1) = 0.0;
quadPointsKovasznay(2,0) = 1.5;
quadPointsKovasznay(2,1) = 2.0;
quadPointsKovasznay(3,0) = -0.5;
quadPointsKovasznay(3,1) = 2.0;
// Domain from Evans Hughes for Navier-Stokes:
// quadPointsKovasznay(0,0) = 0.0; // x1
// quadPointsKovasznay(0,1) = -0.5; // y1
// quadPointsKovasznay(1,0) = 1.0;
// quadPointsKovasznay(1,1) = -0.5;
// quadPointsKovasznay(2,0) = 1.0;
// quadPointsKovasznay(2,1) = 0.5;
// quadPointsKovasznay(3,0) = 0.0;
// quadPointsKovasznay(3,1) = 0.5;
// double Re = 10.0; // Cockburn Kanschat Stokes
// double Re = 40.0; // Evans Hughes Navier-Stokes
// double Re = 1000.0;
string formulationTypeStr = "vgp";
FunctionPtr u1_exact, u2_exact, p_exact;
int numCellsFineMesh = 20; // for computing a zero-mean pressure
int H1OrderFineMesh = 5;
// VGPNavierStokesProblem(double Re, Intrepid::FieldContainer<double> &quadPoints, int horizontalCells,
// int verticalCells, int H1Order, int pToAdd,
// TFunctionPtr<double> u1_0, TFunctionPtr<double> u2_0, TFunctionPtr<double> f1, TFunctionPtr<double> f2,
// bool enrichVelocity = false, bool enhanceFluxes = false)
FunctionPtr zero = Function::zero();
VGPNavierStokesProblem zeroProblem = VGPNavierStokesProblem(Re, quadPointsKovasznay,
numCellsFineMesh, numCellsFineMesh,
H1OrderFineMesh, pToAdd,
zero, zero, zero, useCompliantNorm || useStokesCompliantNorm);
VarFactoryPtr varFactory = VGPStokesFormulation::vgpVarFactory();
VarPtr u1_vgp = varFactory->fieldVar(VGP_U1_S);
VarPtr u2_vgp = varFactory->fieldVar(VGP_U2_S);
VarPtr sigma11_vgp = varFactory->fieldVar(VGP_SIGMA11_S);
VarPtr sigma12_vgp = varFactory->fieldVar(VGP_SIGMA12_S);
VarPtr sigma21_vgp = varFactory->fieldVar(VGP_SIGMA21_S);
VarPtr sigma22_vgp = varFactory->fieldVar(VGP_SIGMA22_S);
VarPtr p_vgp = varFactory->fieldVar(VGP_P_S);
VarPtr v1_vgp = varFactory->testVar(VGP_V1_S, HGRAD);
VarPtr v2_vgp = varFactory->testVar(VGP_V2_S, HGRAD);
// if (rank==0) {
// cout << "bilinear form with zero background flow:\n";
// zeroProblem.bf()->printTrialTestInteractions();
// }
VGPStokesFormulation stokesForm(1/Re);
NavierStokesFormulation::setKovasznay(Re, zeroProblem.mesh(), u1_exact, u2_exact, p_exact);
// if (rank==0) cout << "Stokes bilinearForm: " << stokesForm.bf()->displayString() << endl;
map< string, string > convergenceDataForMATLAB; // key: field file name
for (int polyOrder = minPolyOrder; polyOrder <= maxPolyOrder; polyOrder++)
{
int H1Order = polyOrder + 1;
int numCells1D = pow(2.0,minLogElements);
if (rank==0)
{
cout << "L^2 order: " << polyOrder << endl;
cout << "Re = " << Re << endl;
}
int kovasznayCubatureEnrichment = 20; // 20 is better than 10 for accurately measuring error on the coarser meshes.
vector< VGPNavierStokesProblem > problems;
do
{
VGPNavierStokesProblem problem = VGPNavierStokesProblem(Re,quadPointsKovasznay,
numCells1D,numCells1D,
H1Order, pToAdd,
u1_exact, u2_exact, p_exact, useCompliantNorm || useStokesCompliantNorm);
problem.backgroundFlow()->setCubatureEnrichmentDegree(kovasznayCubatureEnrichment);
problem.solutionIncrement()->setCubatureEnrichmentDegree(kovasznayCubatureEnrichment);
problem.backgroundFlow()->setZeroMeanConstraintRho(zmcRho);
problem.solutionIncrement()->setZeroMeanConstraintRho(zmcRho);
FunctionPtr dt_inv;
if (artificialTimeStepping)
{
// // LHS gets u_inc / dt:
BFPtr bf = problem.bf();
dt_inv = ParameterFunction::parameterFunction(1.0 / dt); //Teuchos::rcp( new ConstantScalarFunction(1.0 / dt, "\\frac{1}{dt}") );
bf->addTerm(-dt_inv * u1_vgp, v1_vgp);
bf->addTerm(-dt_inv * u2_vgp, v2_vgp);
problem.setIP( bf->graphNorm() ); // graph norm has changed...
}
else
{
dt_inv = Function::zero();
}
problems.push_back(problem);
if ( useCompliantNorm )
{
problem.setIP(problem.vgpNavierStokesFormulation()->scaleCompliantGraphNorm(dt_inv));
}
else if (useStokesCompliantNorm)
{
VGPStokesFormulation stokesForm(1.0); // pretend Re = 1 in the graph norm
problem.setIP(stokesForm.scaleCompliantGraphNorm());
}
else if (useStokesGraphNorm)
{
VGPStokesFormulation stokesForm(1.0); // pretend Re = 1 in the graph norm
problem.setIP(stokesForm.graphNorm());
}
else if (! useGraphNorm )
{
// then use the naive:
problem.setIP(problem.bf()->naiveNorm(spaceDim));
}
if (rank==0)
{
cout << numCells1D << " x " << numCells1D << ": " << problem.mesh()->numGlobalDofs() << " dofs " << endl;
}
numCells1D *= 2;
}
while (pow(2.0,maxLogElements) >= numCells1D);
// note that rhs and bilinearForm aren't really going to be right here, since they
// involve a background flow which varies over the various problems...
HConvergenceStudy study(problems[0].exactSolution(),
problems[0].mesh()->bilinearForm(),
problems[0].exactSolution()->rhs(),
problems[0].backgroundFlow()->bc(),
problems[0].bf()->graphNorm(),
minLogElements, maxLogElements,
H1Order, pToAdd, false, useTriangles, false);
study.setReportRelativeErrors(computeRelativeErrors);
study.setCubatureDegreeForExact(kovasznayCubatureEnrichment);
vector< SolutionPtr > solutions;
numCells1D = pow(2.0,minLogElements);
for (vector< VGPNavierStokesProblem >::iterator problem = problems.begin();
problem != problems.end(); problem++)
{
SolutionPtr solnIncrement = problem->solutionIncrement();
FunctionPtr u1_incr = Function::solution(u1_vgp, solnIncrement);
FunctionPtr u2_incr = Function::solution(u2_vgp, solnIncrement);
FunctionPtr sigma11_incr = Function::solution(sigma11_vgp, solnIncrement);
FunctionPtr sigma12_incr = Function::solution(sigma12_vgp, solnIncrement);
FunctionPtr sigma21_incr = Function::solution(sigma21_vgp, solnIncrement);
FunctionPtr sigma22_incr = Function::solution(sigma22_vgp, solnIncrement);
FunctionPtr p_incr = Function::solution(p_vgp, solnIncrement);
// LinearTermPtr rhsLT = problem->backgroundFlow()->rhs()->linearTerm();
// if (rank==0) cout << "bilinearForm: " << problems[0].mesh()->bilinearForm()->displayString() << endl;
// if (rank==0) cout << "RHS: " << rhsLT->displayString() << endl;
FunctionPtr l2_incr = u1_incr * u1_incr + u2_incr * u2_incr + p_incr * p_incr
+ sigma11_incr * sigma11_incr + sigma12_incr * sigma12_incr
+ sigma21_incr * sigma21_incr + sigma22_incr * sigma22_incr;
double weight = 1.0;
do
{
weight = problem->iterate(useLineSearch, useCondensedSolve);
LinearTermPtr rhsLT = problem->backgroundFlow()->rhs()->linearTerm();
RieszRep rieszRep(problem->backgroundFlow()->mesh(), problem->backgroundFlow()->ip(), rhsLT);
rieszRep.computeRieszRep();
double costFunction = rieszRep.getNorm();
double incr_norm = sqrt(l2_incr->integrate(problem->mesh()));
if (rank==0)
{
cout << setprecision(6) << scientific;
cout << "\x1B[2K"; // Erase the entire current line.
cout << "\x1B[0E"; // Move to the beginning of the current line.
cout << "Iteration: " << problem->iterationCount() << "; L^2(incr) = " << incr_norm;
flush(cout);
// cout << setprecision(6) << scientific;
// cout << "Took " << weight << "-weighted step for " << numCells1D;
// cout << " x " << numCells1D << " mesh: " << problem->iterationCount();
// cout << setprecision(6) << fixed;
// cout << " iterations; cost function " << costFunction << endl;
}
}
while ((sqrt(l2_incr->integrate(problem->mesh())) > minL2Increment ) && (problem->iterationCount() < maxIters) && (weight != 0));
if (rank==0) cout << endl;
solutions.push_back( problem->backgroundFlow() );
// set the IP to the naive norm for clearer comparison with the best approximation energy error
// problem->backgroundFlow()->setIP(problem->bf()->naiveNorm());
// double energyError = problem->backgroundFlow()->energyErrorTotal();
// if (rank==0) {
// cout << setprecision(6) << fixed;
// cout << numCells1D << " x " << numCells1D << ": " << problem->iterationCount();
// cout << " iterations; actual energy error " << energyError << endl;
// }
numCells1D *= 2;
}
study.setSolutions(solutions);
for (int i=0; i<=maxLogElements-minLogElements; i++)
{
SolutionPtr bestApproximation = study.bestApproximations()[i];
VGPNavierStokesFormulation nsFormBest = VGPNavierStokesFormulation(Re, bestApproximation);
SpatialFilterPtr entireBoundary = Teuchos::rcp( new SpatialFilterUnfiltered ); // SpatialFilterUnfiltered returns true everywhere
Teuchos::RCP<ExactSolution<double>> exact = nsFormBest.exactSolution(u1_exact, u2_exact, p_exact, entireBoundary);
// bestApproximation->setIP( nsFormBest.bf()->naiveNorm() );
// bestApproximation->setRHS( exact->rhs() );
// use backgroundFlow's IP so that they're comparable
IPPtr ip = problems[i].backgroundFlow()->ip();
LinearTermPtr rhsLT = exact->rhs()->linearTerm();
RieszRep rieszRep(bestApproximation->mesh(), ip, rhsLT);
rieszRep.computeRieszRep();
double bestCostFunction = rieszRep.getNorm();
if (rank==0)
cout << "best energy error (measured according to the actual solution's test space IP): " << bestCostFunction << endl;
}
map< int, double > energyNormWeights;
if (useCompliantNorm)
{
energyNormWeights[u1_vgp->ID()] = 1.0; // should be 1/h
energyNormWeights[u2_vgp->ID()] = 1.0; // should be 1/h
energyNormWeights[sigma11_vgp->ID()] = Re; // 1/mu
energyNormWeights[sigma12_vgp->ID()] = Re; // 1/mu
energyNormWeights[sigma21_vgp->ID()] = Re; // 1/mu
energyNormWeights[sigma22_vgp->ID()] = Re; // 1/mu
if (Re < 1) // assuming we're using the experimental small Re thing
{
energyNormWeights[p_vgp->ID()] = Re;
}
else
{
energyNormWeights[p_vgp->ID()] = 1.0;
}
}
else
{
energyNormWeights[u1_vgp->ID()] = 1.0;
energyNormWeights[u2_vgp->ID()] = 1.0;
energyNormWeights[sigma11_vgp->ID()] = 1.0;
energyNormWeights[sigma12_vgp->ID()] = 1.0;
energyNormWeights[sigma21_vgp->ID()] = 1.0;
energyNormWeights[sigma22_vgp->ID()] = 1.0;
energyNormWeights[p_vgp->ID()] = 1.0;
}
vector<double> bestEnergy = study.weightedL2Error(energyNormWeights,true);
vector<double> solnEnergy = study.weightedL2Error(energyNormWeights,false);
map<int, double> velocityWeights;
velocityWeights[u1_vgp->ID()] = 1.0;
velocityWeights[u2_vgp->ID()] = 1.0;
vector<double> bestVelocityError = study.weightedL2Error(velocityWeights,true);
vector<double> solnVelocityError = study.weightedL2Error(velocityWeights,false);
map<int, double> pressureWeight;
pressureWeight[p_vgp->ID()] = 1.0;
vector<double> bestPressureError = study.weightedL2Error(pressureWeight,true);
vector<double> solnPressureError = study.weightedL2Error(pressureWeight,false);
if (rank==0)
{
cout << setw(25);
cout << "Solution Energy Error:" << setw(25) << "Best Energy Error:" << endl;
cout << scientific << setprecision(1);
for (int i=0; i<bestEnergy.size(); i++)
{
cout << setw(25) << solnEnergy[i] << setw(25) << bestEnergy[i] << endl;
}
cout << setw(25);
cout << "Solution Velocity Error:" << setw(25) << "Best Velocity Error:" << endl;
cout << scientific << setprecision(1);
for (int i=0; i<bestEnergy.size(); i++)
{
cout << setw(25) << solnVelocityError[i] << setw(25) << bestVelocityError[i] << endl;
}
cout << setw(25);
cout << "Solution Pressure Error:" << setw(25) << "Best Pressure Error:" << endl;
cout << scientific << setprecision(1);
for (int i=0; i<bestEnergy.size(); i++)
{
cout << setw(25) << solnPressureError[i] << setw(25) << bestPressureError[i] << endl;
}
vector< string > tableHeaders;
vector< vector<double> > dataTable;
vector< double > meshWidths;
for (int i=minLogElements; i<=maxLogElements; i++)
{
double width = pow(2.0,i);
meshWidths.push_back(width);
}
tableHeaders.push_back("mesh_width");
dataTable.push_back(meshWidths);
tableHeaders.push_back("soln_energy_error");
dataTable.push_back(solnEnergy);
tableHeaders.push_back("best_energy_error");
dataTable.push_back(bestEnergy);
tableHeaders.push_back("soln_velocity_error");
dataTable.push_back(solnVelocityError);
tableHeaders.push_back("best_velocity_error");
dataTable.push_back(bestVelocityError);
tableHeaders.push_back("soln_pressure_error");
dataTable.push_back(solnPressureError);
tableHeaders.push_back("best_pressure_error");
dataTable.push_back(bestPressureError);
ostringstream fileNameStream;
fileNameStream << "nsStudy_Re" << Re << "k" << polyOrder << "_results.dat";
DataIO::outputTableToFile(tableHeaders,dataTable,fileNameStream.str());
}
if (rank == 0)
{
cout << study.TeXErrorRateTable();
vector<int> primaryVariables;
stokesForm.primaryTrialIDs(primaryVariables);
vector<int> fieldIDs,traceIDs;
vector<string> fieldFileNames;
stokesForm.trialIDs(fieldIDs,traceIDs,fieldFileNames);
cout << "******** Best Approximation comparison: ********\n";
cout << study.TeXBestApproximationComparisonTable(primaryVariables);
ostringstream filePathPrefix;
filePathPrefix << "navierStokes/" << formulationTypeStr << "_p" << polyOrder << "_velpressure";
study.TeXBestApproximationComparisonTable(primaryVariables,filePathPrefix.str());
filePathPrefix.str("");
filePathPrefix << "navierStokes/" << formulationTypeStr << "_p" << polyOrder << "_all";
study.TeXBestApproximationComparisonTable(fieldIDs);
for (int i=0; i<fieldIDs.size(); i++)
{
int fieldID = fieldIDs[i];
int traceID = traceIDs[i];
string fieldName = fieldFileNames[i];
ostringstream filePathPrefix;
filePathPrefix << "navierStokes/" << fieldName << "_p" << polyOrder;
bool writeMATLABplotData = false;
study.writeToFiles(filePathPrefix.str(),fieldID,traceID, writeMATLABplotData);
}
for (int i=0; i<primaryVariables.size(); i++)
{
string convData = study.convergenceDataMATLAB(primaryVariables[i], minPolyOrder);
cout << convData;
convergenceDataForMATLAB[fieldFileNames[i]] += convData;
}
filePathPrefix.str("");
filePathPrefix << "navierStokes/" << formulationTypeStr << "_p" << polyOrder << "_numDofs";
cout << study.TeXNumGlobalDofsTable();
}
if (computeMaxConditionNumber)
{
for (int i=minLogElements; i<=maxLogElements; i++)
{
SolutionPtr soln = study.getSolution(i);
ostringstream fileNameStream;
fileNameStream << "nsStudy_maxConditionIPMatrix_" << i << ".dat";
IPPtr ip = Teuchos::rcp( dynamic_cast< IP* >(soln->ip().get()), false );
bool jacobiScalingTrue = true;
double maxConditionNumber = MeshUtilities::computeMaxLocalConditionNumber(ip, soln->mesh(), jacobiScalingTrue, fileNameStream.str());
if (rank==0)
{
cout << "max Gram matrix condition number estimate for logElements " << i << ": " << maxConditionNumber << endl;
cout << "putative worst-conditioned Gram matrix written to: " << fileNameStream.str() << "." << endl;
}
}
}
}
if (rank==0)
{
ostringstream filePathPrefix;
filePathPrefix << "navierStokes/" << formulationTypeStr << "_";
for (map<string,string>::iterator convIt = convergenceDataForMATLAB.begin(); convIt != convergenceDataForMATLAB.end(); convIt++)
{
string fileName = convIt->first + ".m";
string data = convIt->second;
fileName = filePathPrefix.str() + fileName;
ofstream fout(fileName.c_str());
fout << data;
fout.close();
}
}
}
void LinearTermTests::setup()
{
// 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;
sine_x = Teuchos::rcp( new Sine_x );
cos_y = Teuchos::rcp( new Cosine_y );
VarFactoryPtr varFactory = VarFactory::varFactory();
q1 = varFactory->testVar("q_1", HDIV);
q2 = varFactory->testVar("q_2", HDIV);
q3 = varFactory->testVar("q_3", HDIV);
v1 = varFactory->testVar("v_1", HGRAD);
v2 = varFactory->testVar("v_2", HGRAD);
v3 = varFactory->testVar("v_3", HGRAD);
u1 = varFactory->fieldVar("u_1", HGRAD);
u2 = varFactory->fieldVar("u_2", HGRAD);
u3 = varFactory->fieldVar("u_3", HGRAD);
u1_hat = varFactory->traceVar("\\widehat{u}_1");
u2_hat = varFactory->traceVar("\\widehat{u}_2");
u3_hat_n = varFactory->fluxVar("\\widehat{u}_3n");
bf = Teuchos::rcp(new BF(varFactory)); // made-up bf for Mesh + previous solution tests
bf->addTerm(u1_hat, q1->dot_normal());
bf->addTerm(u1, q1->x());
bf->addTerm(u2, q1->y());
bf->addTerm(u3_hat_n, v1);
bf->addTerm(u3, v1);
// DofOrderingFactory discreteSpaceFactory(bf);
int polyOrder = 3, testToAdd = 2;
Teuchos::RCP<shards::CellTopology> quadTopoPtr;
// quadTopoPtr = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ));
// define nodes for mesh
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = -1.0; // x1
quadPoints(0,1) = -1.0; // y1
quadPoints(1,0) = 1.0;
quadPoints(1,1) = -1.0;
quadPoints(2,0) = 1.0;
quadPoints(2,1) = 1.0;
quadPoints(3,0) = -1.0;
quadPoints(3,1) = 1.0;
int horizontalElements = 2, verticalElements = 2;
mesh = MeshFactory::buildQuadMesh(quadPoints, horizontalElements, verticalElements, bf, polyOrder+1, polyOrder+1+testToAdd);
ElementTypePtr elemType = mesh->getElement(0)->elementType();
trialOrder = elemType->trialOrderPtr;
testOrder = elemType->testOrderPtr;
basisCache = Teuchos::rcp(new BasisCache(elemType, mesh));
vector<GlobalIndexType> cellIDs;
cellIDs.push_back(0);
cellIDs.push_back(1);
cellIDs.push_back(2);
cellIDs.push_back(3);
bool createSideCacheToo = true;
basisCache->setPhysicalCellNodes(mesh->physicalCellNodesGlobal(elemType), cellIDs, createSideCacheToo);
}
PoissonFormulation::PoissonFormulation(int spaceDim, bool useConformingTraces, PoissonFormulationChoice formulationChoice)
{
_spaceDim = spaceDim;
if (formulationChoice == ULTRAWEAK)
{
Space tauSpace = (spaceDim > 1) ? HDIV : HGRAD;
Space phi_hat_space = useConformingTraces ? HGRAD : L2;
Space psiSpace = (spaceDim > 1) ? VECTOR_L2 : L2;
// fields
VarPtr phi;
VarPtr psi;
// traces
VarPtr phi_hat, psi_n_hat;
// tests
VarPtr q;
VarPtr tau;
VarFactoryPtr vf = VarFactory::varFactory();
phi = vf->fieldVar(S_PHI);
psi = vf->fieldVar(S_PSI, psiSpace);
TFunctionPtr<double> parity = TFunction<double>::sideParity();
if (spaceDim > 1)
phi_hat = vf->traceVar(S_PHI_HAT, phi, phi_hat_space);
else
phi_hat = vf->fluxVar(S_PHI_HAT, phi * (Function::normal_1D() * parity), phi_hat_space); // for spaceDim==1, the "normal" component is in the flux-ness of phi_hat (it's a plus or minus 1)
TFunctionPtr<double> n = TFunction<double>::normal();
if (spaceDim > 1)
psi_n_hat = vf->fluxVar(S_PSI_N_HAT, psi * (n * parity));
else
psi_n_hat = vf->fluxVar(S_PSI_N_HAT, psi * (Function::normal_1D() * parity));
q = vf->testVar(S_Q, HGRAD);
tau = vf->testVar(S_TAU, tauSpace);
_poissonBF = Teuchos::rcp( new BF(vf) );
if (spaceDim==1)
{
// for spaceDim==1, the "normal" component is in the flux-ness of phi_hat (it's a plus or minus 1)
_poissonBF->addTerm(phi, tau->dx());
_poissonBF->addTerm(psi, tau);
_poissonBF->addTerm(-phi_hat, tau);
_poissonBF->addTerm(-psi, q->dx());
_poissonBF->addTerm(psi_n_hat, q);
}
else
{
_poissonBF->addTerm(phi, tau->div());
_poissonBF->addTerm(psi, tau);
_poissonBF->addTerm(-phi_hat, tau->dot_normal());
_poissonBF->addTerm(-psi, q->grad());
_poissonBF->addTerm(psi_n_hat, q);
}
}
else if ((formulationChoice == PRIMAL) || (formulationChoice == CONTINUOUS_GALERKIN))
{
// field
VarPtr phi;
// flux
VarPtr psi_n_hat;
// tests
VarPtr q;
VarFactoryPtr vf = VarFactory::varFactory();
phi = vf->fieldVar(S_PHI, HGRAD);
TFunctionPtr<double> parity = TFunction<double>::sideParity();
TFunctionPtr<double> n = TFunction<double>::normal();
if (formulationChoice == PRIMAL)
{
if (spaceDim > 1)
psi_n_hat = vf->fluxVar(S_PSI_N_HAT, phi->grad() * (n * parity));
else
psi_n_hat = vf->fluxVar(S_PSI_N_HAT, phi->dx() * (Function::normal_1D() * parity));
}
q = vf->testVar(S_Q, HGRAD);
_poissonBF = BF::bf(vf);
_poissonBF->addTerm(-phi->grad(), q->grad());
if (formulationChoice == CONTINUOUS_GALERKIN)
{
FunctionPtr boundaryIndicator = Function::meshBoundaryCharacteristic();
_poissonBF->addTerm(phi->grad() * n, boundaryIndicator * q);
}
else // primal
{
_poissonBF->addTerm(psi_n_hat, q);
}
}
else
{
TEUCHOS_TEST_FOR_EXCEPTION(true, std::invalid_argument, "Unsupported PoissonFormulationChoice");
}
}
bool LinearTermTests::testMixedTermConsistency()
{
bool success = true;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr tau = varFactory->testVar("\\tau", HDIV);
VarPtr v = varFactory->testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory->traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory->fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory->fieldVar("u");
VarPtr sigma1 = varFactory->fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory->fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
double eps = .01;
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = 1;
int pToAdd = 1;
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 1.0;
quadPoints(1,1) = 0.0;
quadPoints(2,0) = 1.0;
quadPoints(2,1) = 1.0;
quadPoints(3,0) = 0.0;
quadPoints(3,1) = 1.0;
int nCells = 1;
int horizontalCells = nCells, verticalCells = nCells;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> myMesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
confusionBF, H1Order, H1Order+pToAdd);
ElementTypePtr elemType = myMesh->getElement(0)->elementType();
// DofOrderingPtr testOrder = elemType->testOrderPtr;
BasisCachePtr basisCache = Teuchos::rcp(new BasisCache(elemType, myMesh, true));
LinearTermPtr integrandIBP = Teuchos::rcp(new LinearTerm);// residual
vector<double> e1(2); // (1,0)
vector<double> e2(2); // (0,1)
e1[0] = 1;
e2[1] = 1;
FunctionPtr n = Function::normal();
FunctionPtr X = Function::xn(1);
FunctionPtr Y = Function::yn(1);
FunctionPtr testFxn1 = X;
FunctionPtr testFxn2 = Y;
FunctionPtr divTestFxn = testFxn1->dx() + testFxn2->dy();
FunctionPtr vectorTest = testFxn1*e1 + testFxn2*e2;
integrandIBP->addTerm(vectorTest*n*v + -vectorTest*v->grad()); // boundary term
// define dummy IP to initialize riesz rep class, but just integrate RHS
IPPtr dummyIP = Teuchos::rcp(new IP);
dummyIP->addTerm(v);
Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(myMesh, dummyIP, integrandIBP));
map<GlobalIndexType,FieldContainer<double> > rieszRHS = riesz->integrateFunctional();
set<GlobalIndexType> cellIDs = myMesh->cellIDsInPartition();
for (set<GlobalIndexType>::iterator cellIDIt=cellIDs.begin(); cellIDIt !=cellIDs.end(); cellIDIt++)
{
GlobalIndexType cellID = *cellIDIt;
ElementTypePtr elemTypePtr = myMesh->getElementType(cellID);
DofOrderingPtr testOrderingPtr = elemTypePtr->testOrderPtr;
int numTestDofs = testOrderingPtr->totalDofs();
BasisCachePtr basisCache = BasisCache::basisCacheForCell(myMesh, cellID, true);
FieldContainer<double> rhsIBPValues(1,numTestDofs);
integrandIBP->integrate(rhsIBPValues, testOrderingPtr, basisCache);
FieldContainer<double> rieszValues(1,numTestDofs);
(riesz->getFunctional())->integrate(rieszValues, testOrderingPtr, basisCache);
double maxDiff;
double tol = 1e-13;
FieldContainer<double> rhsIBPVals(numTestDofs);
for (int i = 0; i< numTestDofs; i++)
{
rhsIBPVals(i) = rhsIBPValues(0,i);
// cout << "riesz rhs values = " << rieszRHS[cellID](i) << ", rhsIBPValues = " << rhsIBPVals(i) << ", riesz returned values = " << rieszValues(0,i) << endl;
}
bool fcsAgree = TestSuite::fcsAgree(rieszRHS[cellID],rhsIBPVals,tol,maxDiff);
if (!fcsAgree)
{
success=false;
cout << "Failed mixed term consistency test with maxDiff = " << maxDiff << " on cellID " << cellID<< endl;
}
}
return allSuccess(success);
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
Epetra_MpiComm Comm(MPI_COMM_WORLD);
#else
Epetra_SerialComm Comm;
#endif
int commRank = Teuchos::GlobalMPISession::getRank();
Comm.Barrier(); // set breakpoint here to allow debugger attachment to other MPI processes than the one you automatically attached to.
Teuchos::CommandLineProcessor cmdp(false,true); // false: don't throw exceptions; true: do return errors for unrecognized options
// problem parameters:
double mu = 0.1;
double permCoef = 1e4;
int numRefs = 0;
int k = 2, delta_k = 2;
string norm = "Graph";
cmdp.setOption("polyOrder",&k,"polynomial order for field variable u");
cmdp.setOption("delta_k", &delta_k, "test space polynomial order enrichment");
cmdp.setOption("numRefs",&numRefs,"number of refinements");
cmdp.setOption("norm", &norm, "norm");
cmdp.setOption("mu", &mu, "mu");
cmdp.setOption("permCoef", &permCoef, "Permeability coefficient");
if (cmdp.parse(argc,argv) != Teuchos::CommandLineProcessor::PARSE_SUCCESSFUL)
{
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return -1;
}
FunctionPtr zero = TFunction<double>::zero();
FunctionPtr one = TFunction<double>::constant(1);
FunctionPtr sin2pix = Teuchos::rcp( new Sin_ax(2*pi) );
FunctionPtr cos2pix = Teuchos::rcp( new Cos_ax(2*pi) );
FunctionPtr sin2piy = Teuchos::rcp( new Sin_ay(2*pi) );
FunctionPtr cos2piy = Teuchos::rcp( new Cos_ay(2*pi) );
FunctionPtr u1_exact = sin2pix*cos2piy;
FunctionPtr u2_exact = -cos2pix*sin2piy;
FunctionPtr x2 = TFunction<double>::xn(2);
FunctionPtr y2 = TFunction<double>::yn(2);
FunctionPtr p_exact = x2*y2 - 1./9;
FunctionPtr permInv = permCoef*(sin2pix + 1.1);
VarFactoryPtr vf = VarFactory::varFactory();
//fields:
VarPtr sigma1 = vf->fieldVar("sigma1", VECTOR_L2);
VarPtr sigma2 = vf->fieldVar("sigma2", VECTOR_L2);
VarPtr u1 = vf->fieldVar("u1", L2);
VarPtr u2 = vf->fieldVar("u2", L2);
VarPtr p = vf->fieldVar("p", L2);
// traces:
VarPtr u1hat = vf->traceVar("u1hat");
VarPtr u2hat = vf->traceVar("u2hat");
VarPtr t1c = vf->fluxVar("t1c");
VarPtr t2c = vf->fluxVar("t2c");
// test:
VarPtr v1 = vf->testVar("v1", HGRAD);
VarPtr v2 = vf->testVar("v2", HGRAD);
VarPtr tau1 = vf->testVar("tau1", HDIV);
VarPtr tau2 = vf->testVar("tau2", HDIV);
VarPtr q = vf->testVar("q", HGRAD);
BFPtr bf = Teuchos::rcp( new BF(vf) );
bf->addTerm(1./mu*sigma1, tau1);
bf->addTerm(1./mu*sigma2, tau2);
bf->addTerm(u1, tau1->div());
bf->addTerm(u2, tau2->div());
bf->addTerm(-u1hat, tau1->dot_normal());
bf->addTerm(-u2hat, tau2->dot_normal());
bf->addTerm(sigma1, v1->grad());
bf->addTerm(sigma2, v2->grad());
bf->addTerm(-p, v1->dx());
bf->addTerm(-p, v2->dy());
bf->addTerm(t1c, v1);
bf->addTerm(t2c, v2);
bf->addTerm(mu*permInv*u1, v1);
bf->addTerm(mu*permInv*u2, v2);
bf->addTerm(-u1, q->dx());
bf->addTerm(-u2, q->dy());
bf->addTerm(u1hat, q->times_normal_x());
bf->addTerm(u2hat, q->times_normal_y());
RHSPtr rhs = RHS::rhs();
BCPtr bc = BC::bc();
SpatialFilterPtr y_equals_one = SpatialFilter::matchingY(1.0);
SpatialFilterPtr y_equals_zero = SpatialFilter::matchingY(0);
SpatialFilterPtr x_equals_one = SpatialFilter::matchingX(1.0);
SpatialFilterPtr x_equals_zero = SpatialFilter::matchingX(0.0);
bc->addDirichlet(u1hat, y_equals_zero, u1_exact);
bc->addDirichlet(u2hat, y_equals_zero, u2_exact);
bc->addDirichlet(u1hat, x_equals_zero, u1_exact);
bc->addDirichlet(u2hat, x_equals_zero, u2_exact);
bc->addDirichlet(u1hat, y_equals_one, u1_exact);
bc->addDirichlet(u2hat, y_equals_one, u2_exact);
bc->addDirichlet(u1hat, x_equals_one, u1_exact);
bc->addDirichlet(u2hat, x_equals_one, u2_exact);
bc->addZeroMeanConstraint(p);
MeshPtr mesh = MeshFactory::quadMesh(bf, k+1, delta_k, 1, 1, 4, 4);
map<string, IPPtr> brinkmanIPs;
brinkmanIPs["Graph"] = bf->graphNorm();
brinkmanIPs["Decoupled"] = Teuchos::rcp(new IP);
brinkmanIPs["Decoupled"]->addTerm(tau1);
brinkmanIPs["Decoupled"]->addTerm(tau2);
brinkmanIPs["Decoupled"]->addTerm(tau1->div());
brinkmanIPs["Decoupled"]->addTerm(tau2->div());
brinkmanIPs["Decoupled"]->addTerm(permInv*v1);
brinkmanIPs["Decoupled"]->addTerm(permInv*v2);
brinkmanIPs["Decoupled"]->addTerm(v1->grad());
brinkmanIPs["Decoupled"]->addTerm(v2->grad());
brinkmanIPs["Decoupled"]->addTerm(q);
brinkmanIPs["Decoupled"]->addTerm(q->grad());
// brinkmanIPs["CoupledRobust"] = Teuchos::rcp(new IP);
// brinkmanIPs["CoupledRobust"]->addTerm(tau->div()-beta*v->grad());
// brinkmanIPs["CoupledRobust"]->addTerm(Function<double>::min(one/Function<double>::h(),Function<double>::constant(1./sqrt(epsilon)))*tau);
// brinkmanIPs["CoupledRobust"]->addTerm(sqrt(epsilon)*v->grad());
// brinkmanIPs["CoupledRobust"]->addTerm(beta*v->grad());
// brinkmanIPs["CoupledRobust"]->addTerm(Function<double>::min(sqrt(epsilon)*one/Function<double>::h(),one)*v);
IPPtr ip = brinkmanIPs[norm];
SolutionPtr soln = TSolution<double>::solution(mesh, bc, rhs, ip);
double threshold = 0.20;
RefinementStrategy refStrategy(soln, threshold);
ostringstream refName;
refName << "brinkman";
HDF5Exporter exporter(mesh,refName.str());
for (int refIndex=0; refIndex <= numRefs; refIndex++)
{
soln->solve(false);
double energyError = soln->energyErrorTotal();
if (commRank == 0)
{
// if (refIndex > 0)
// refStrategy.printRefinementStatistics(refIndex-1);
cout << "Refinement:\t " << refIndex << " \tElements:\t " << mesh->numActiveElements()
<< " \tDOFs:\t " << mesh->numGlobalDofs() << " \tEnergy Error:\t " << energyError << endl;
}
exporter.exportSolution(soln, refIndex);
if (refIndex != numRefs)
refStrategy.refine();
}
return 0;
}
// test variables:
VarPtr PoissonFormulation::q()
{
VarFactoryPtr vf = _poissonBF->varFactory();
return vf->testVar(S_Q, HGRAD);
}
// tests whether a mixed type LT
bool ScratchPadTests::testIntegrateDiscontinuousFunction()
{
bool success = true;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr v = varFactory->testVar("v", HGRAD);
vector<double> beta;
beta.push_back(1.0);
beta.push_back(1.0);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// robust test norm
IPPtr ip = Teuchos::rcp(new IP);
ip->addTerm(v);
ip->addTerm(beta*v->grad());
// for projections
IPPtr ipL2 = Teuchos::rcp(new IP);
ipL2->addTerm(v);
// define trial variables
VarPtr beta_n_u = varFactory->fluxVar("\\widehat{\\beta \\cdot n }");
VarPtr u = varFactory->fieldVar("u");
//////////////////// BUILD MESH ///////////////////////
BFPtr convectionBF = Teuchos::rcp( new BF(varFactory) );
// v terms:
convectionBF->addTerm( -u, beta * v->grad() );
convectionBF->addTerm( beta_n_u, v);
// define nodes for mesh
int order = 1;
int H1Order = order+1;
int pToAdd = 1;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(2, 1, convectionBF, H1Order, H1Order+pToAdd);
//////////////////// integrate discontinuous function - cellIDFunction ///////////////////////
// FunctionPtr cellIDFxn = Teuchos::rcp(new CellIDFunction); // should be 0 on cellID 0, 1 on cellID 1
set<int> cellIDs;
cellIDs.insert(1); // 0 on cell 0, 1 on cell 1
FunctionPtr indicator = Teuchos::rcp(new IndicatorFunction(cellIDs)); // should be 0 on cellID 0, 1 on cellID 1
double jumpWeight = 13.3; // some random number
FunctionPtr edgeRestrictionFxn = Teuchos::rcp(new EdgeFunction);
FunctionPtr X = Function::xn(1);
LinearTermPtr integrandLT = Function::constant(1.0)*v + Function::constant(jumpWeight)*X*edgeRestrictionFxn*v;
// make riesz representation function to more closely emulate the error rep
LinearTermPtr indicatorLT = Teuchos::rcp(new LinearTerm);// residual
indicatorLT->addTerm(indicator*v);
Teuchos::RCP<RieszRep> riesz = Teuchos::rcp(new RieszRep(mesh, ipL2, indicatorLT));
riesz->computeRieszRep();
map<int,FunctionPtr> vmap;
vmap[v->ID()] = RieszRep::repFunction(v,riesz); // SHOULD BE L2 projection = same thing!!!
FunctionPtr volumeIntegrand = integrandLT->evaluate(vmap,false);
FunctionPtr edgeRestrictedIntegrand = integrandLT->evaluate(vmap,true);
double edgeRestrictedValue = volumeIntegrand->integrate(mesh,10) + edgeRestrictedIntegrand->integrate(mesh,10);
double expectedValue = .5 + .5*jumpWeight;
double diff = abs(expectedValue-edgeRestrictedValue);
if (abs(diff)>1e-11)
{
success = false;
cout << "Failed testIntegrateDiscontinuousFunction() with expectedValue = " << expectedValue << " and actual value = " << edgeRestrictedValue << endl;
}
return success;
}