int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
int polyOrder = 3;
int pToAdd = 2; // for tests
// define our manufactured solution or problem bilinear form:
double epsilon = 1e-2;
bool useTriangles = false;
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 1.0;
quadPoints(1,1) = 0.0;
quadPoints(2,0) = 1.0;
quadPoints(2,1) = 1.0;
quadPoints(3,0) = 0.0;
quadPoints(3,1) = 1.0;
int H1Order = polyOrder + 1;
int horizontalCells = 1, verticalCells = 1;
double energyThreshold = 0.2; // for mesh refinements
double nonlinearStepSize = 0.5;
double nonlinearRelativeEnergyTolerance = 0.015; // used to determine convergence of the nonlinear solution
////////////////////////////////////////////////////////////////////
// SET UP PROBLEM
////////////////////////////////////////////////////////////////////
Teuchos::RCP<BurgersBilinearForm> oldBurgersBF = Teuchos::rcp(new BurgersBilinearForm(epsilon));
// new-style bilinear form definition
VarFactory varFactory;
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_hat = varFactory.fluxVar("\\widehat{\\beta_n u - \\sigma_n}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
VarPtr tau = varFactory.testVar("\\tau",HDIV);
VarPtr v = varFactory.testVar("v",HGRAD);
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(quadPoints, horizontalCells, verticalCells, bf, H1Order, H1Order+pToAdd, useTriangles);
mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));
Teuchos::RCP<Solution> backgroundFlow = Teuchos::rcp(new Solution(mesh, Teuchos::rcp((BC*)NULL) , Teuchos::rcp((RHS*)NULL), Teuchos::rcp((DPGInnerProduct*)NULL))); // create null solution
oldBurgersBF->setBackgroundFlow(backgroundFlow);
// tau parts:
// 1/eps (sigma, tau)_K + (u, div tau)_K - (u_hat, tau_n)_dK
bf->addTerm(sigma1 / epsilon, tau->x());
bf->addTerm(sigma2 / epsilon, tau->y());
bf->addTerm(u, tau->div());
bf->addTerm( - uhat, tau->dot_normal() );
vector<double> e1(2); // (1,0)
e1[0] = 1;
vector<double> e2(2); // (0,1)
e2[1] = 1;
FunctionPtr u_prev = Teuchos::rcp( new PreviousSolutionFunction(backgroundFlow, u) );
FunctionPtr beta = e1 * u_prev + Teuchos::rcp( new ConstantVectorFunction( e2 ) );
// v:
// (sigma, grad v)_K - (sigma_hat_n, v)_dK - (u, beta dot grad v) + (u_hat * n dot beta, v)_dK
bf->addTerm( sigma1, v->dx() );
bf->addTerm( sigma2, v->dy() );
bf->addTerm( -u, beta * v->grad());
bf->addTerm( beta_n_u_minus_sigma_hat, v);
// ==================== SET INITIAL GUESS ==========================
mesh->registerSolution(backgroundFlow);
map<int, Teuchos::RCP<AbstractFunction> > functionMap;
functionMap[BurgersBilinearForm::U] = Teuchos::rcp(new InitialGuess());
functionMap[BurgersBilinearForm::SIGMA_1] = Teuchos::rcp(new ZeroFunction());
functionMap[BurgersBilinearForm::SIGMA_2] = Teuchos::rcp(new ZeroFunction());
backgroundFlow->projectOntoMesh(functionMap);
// ==================== END SET INITIAL GUESS ==========================
// compare stiffness matrices for first linear step:
int trialOrder = 1;
pToAdd = 0;
int testOrder = trialOrder + pToAdd;
CellTopoPtr quadTopoPtr = Teuchos::rcp(new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ));
DofOrderingFactory dofOrderingFactory(bf);
DofOrderingPtr testOrdering = dofOrderingFactory.testOrdering(testOrder, *quadTopoPtr);
DofOrderingPtr trialOrdering = dofOrderingFactory.trialOrdering(trialOrder, *quadTopoPtr);
int numCells = 1;
// just use testOrdering for both trial and test spaces (we only use to define BasisCache)
ElementTypePtr elemType = Teuchos::rcp( new ElementType(trialOrdering, testOrdering, quadTopoPtr) );
BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(elemType) );
quadPoints.resize(1,quadPoints.dimension(0),quadPoints.dimension(1));
basisCache->setPhysicalCellNodes(quadPoints,vector<int>(1),true); // true: do create side cache
FieldContainer<double> cellSideParities(numCells,quadTopoPtr->getSideCount());
cellSideParities.initialize(1.0); // not worried here about neighbors actually having opposite parity -- just want the two BF implementations to agree...
FieldContainer<double> expectedValues(numCells, testOrdering->totalDofs(), trialOrdering->totalDofs() );
FieldContainer<double> actualValues(numCells, testOrdering->totalDofs(), trialOrdering->totalDofs() );
oldBurgersBF->stiffnessMatrix(expectedValues, elemType, cellSideParities, basisCache);
bf->stiffnessMatrix(actualValues, elemType, cellSideParities, basisCache);
// compare beta's as well
FieldContainer<double> expectedBeta = oldBurgersBF->getBeta(basisCache);
Teuchos::Array<int> dim;
expectedBeta.dimensions(dim);
FieldContainer<double> actualBeta(dim);
beta->values(actualBeta,basisCache);
double tol = 1e-14;
double maxDiff;
if (rank == 0)
{
if ( ! TestSuite::fcsAgree(expectedBeta,actualBeta,tol,maxDiff) )
{
cout << "Test failed: old Burgers beta differs from new; maxDiff " << maxDiff << ".\n";
cout << "Old beta: \n" << expectedBeta;
cout << "New beta: \n" << actualBeta;
}
else
{
cout << "Old and new Burgers beta agree!!\n";
}
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old Burgers stiffness differs from new; maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "TrialDofOrdering: \n" << *trialOrdering;
cout << "TestDofOrdering:\n" << *testOrdering;
}
else
{
cout << "Old and new Burgers stiffness agree!!\n";
}
}
// define our inner product:
// Teuchos::RCP<BurgersInnerProduct> ip = Teuchos::rcp( new BurgersInnerProduct( bf, mesh ) );
// function to scale the squared guy by epsilon/h
FunctionPtr epsilonOverHScaling = Teuchos::rcp( new EpsilonScaling(epsilon) );
IPPtr ip = Teuchos::rcp( new IP );
ip->addTerm(tau);
ip->addTerm(tau->div());
ip->addTerm( epsilonOverHScaling * v );
ip->addTerm( sqrt(sqrt(epsilon)) * v->grad() );
ip->addTerm( beta * v->grad() );
// use old IP instead, for now...
Teuchos::RCP<BurgersInnerProduct> oldIP = Teuchos::rcp( new BurgersInnerProduct( oldBurgersBF, mesh ) );
expectedValues.resize(numCells, testOrdering->totalDofs(), testOrdering->totalDofs() );
actualValues.resize (numCells, testOrdering->totalDofs(), testOrdering->totalDofs() );
BasisCachePtr ipBasisCache = Teuchos::rcp( new BasisCache(elemType, true) ); // true: test vs. test
ipBasisCache->setPhysicalCellNodes(quadPoints,vector<int>(1),false); // false: don't create side cache
oldIP->computeInnerProductMatrix(expectedValues,testOrdering,ipBasisCache);
ip->computeInnerProductMatrix(actualValues,testOrdering,ipBasisCache);
tol = 1e-14;
maxDiff = 0.0;
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old inner product differs from new IP; maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New IP: \n" << actualValues;
cout << "testOrdering: \n" << *testOrdering;
}
else
{
cout << "Old inner product and new IP agree!!\n";
}
}
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
// the RHS as implemented by BurgersProblem divides the first component of beta by 2.0
// so we follow that. I've not done the math; just imitating the code...
Teuchos::RCP<RHSEasy> otherRHS = Teuchos::rcp( new RHSEasy );
vector<double> e1_div2 = e1;
e1_div2[0] /= 2.0;
FunctionPtr rhsBeta = (e1_div2 * beta * e1 + Teuchos::rcp( new ConstantVectorFunction( e2 ) )) * u_prev;
otherRHS->addTerm( rhsBeta * v->grad() - u_prev * tau->div() );
Teuchos::RCP<BurgersProblem> problem = Teuchos::rcp( new BurgersProblem(oldBurgersBF) );
expectedValues.resize(numCells, testOrdering->totalDofs() );
actualValues.resize (numCells, testOrdering->totalDofs() );
problem->integrateAgainstStandardBasis(expectedValues,testOrdering,basisCache);
otherRHS->integrateAgainstStandardBasis(actualValues,testOrdering,basisCache);
tol = 1e-14;
maxDiff = 0.0;
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old RHS differs from new (\"otherRHS\"); maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "testOrdering: \n" << *testOrdering;
}
else
{
cout << "Old and new RHS (\"otherRHS\") agree!!\n";
}
}
FunctionPtr u_prev_squared_div2 = 0.5 * u_prev * u_prev;
rhs->addTerm( (e1 * u_prev_squared_div2 + e2 * u_prev) * v->grad() - u_prev * tau->div());
if (! functionsAgree(e2 * u_prev,
Teuchos::rcp( new ConstantVectorFunction( e2 ) ) * u_prev,
basisCache) )
{
cout << "two like functions differ...\n";
}
FunctionPtr e1_f = Teuchos::rcp( new ConstantVectorFunction( e1 ) );
FunctionPtr e2_f = Teuchos::rcp( new ConstantVectorFunction( e2 ) );
FunctionPtr one = Teuchos::rcp( new ConstantScalarFunction( 1.0 ) );
if (! functionsAgree( Teuchos::rcp( new ProductFunction(e1_f, (e1_f + e2_f)) ), // e1_f * (e1_f + e2_f)
one,
basisCache) )
{
cout << "two like functions differ...\n";
}
if (! functionsAgree(u_prev_squared_div2,
(e1_div2 * beta) * u_prev,
basisCache) )
{
cout << "two like functions differ...\n";
}
if (! functionsAgree(e1 * u_prev_squared_div2,
(e1_div2 * beta * e1) * u_prev,
basisCache) )
{
cout << "two like functions differ...\n";
}
if (! functionsAgree(e1 * u_prev_squared_div2 + e2 * u_prev,
(e1_div2 * beta * e1 + Teuchos::rcp( new ConstantVectorFunction( e2 ) )) * u_prev,
basisCache) )
{
cout << "two like functions differ...\n";
}
problem->integrateAgainstStandardBasis(expectedValues,testOrdering,basisCache);
rhs->integrateAgainstStandardBasis(actualValues,testOrdering,basisCache);
tol = 1e-14;
maxDiff = 0.0;
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old RHS differs from new (\"rhs\"); maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "testOrdering: \n" << *testOrdering;
}
else
{
cout << "Old and new RHS (\"rhs\") agree!!\n";
}
}
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new TopBoundary );
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new NegatedSpatialFilter(outflowBoundary) );
Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp(new PenaltyConstraints);
LinearTermPtr sigma_hat = beta * uhat->times_normal() - beta_n_u_minus_sigma_hat;
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
pc->addConstraint(sigma_hat==zero,outflowBoundary);
FunctionPtr u0 = Teuchos::rcp( new U0 );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
Teuchos::RCP<BCEasy> inflowBC = Teuchos::rcp( new BCEasy );
FunctionPtr u0_squared_div_2 = 0.5 * u0 * u0;
inflowBC->addDirichlet(beta_n_u_minus_sigma_hat,inflowBoundary, ( e1 * u0_squared_div_2 + e2 * u0) * n );
// create a solution object
Teuchos::RCP<Solution> solution = Teuchos::rcp(new Solution(mesh, inflowBC, rhs, ip));
mesh->registerSolution(solution);
solution->setFilter(pc);
// old penalty filter:
Teuchos::RCP<LocalStiffnessMatrixFilter> penaltyBC = Teuchos::rcp(new PenaltyMethodFilter(problem));
// solution->setFilter(penaltyBC);
// compare old and new filters
elemType = mesh->getElement(0)->elementType();
trialOrdering = elemType->trialOrderPtr;
testOrdering = elemType->testOrderPtr;
// stiffness
expectedValues.resize(numCells, trialOrdering->totalDofs(), trialOrdering->totalDofs() );
actualValues.resize (numCells, trialOrdering->totalDofs(), trialOrdering->totalDofs() );
expectedValues.initialize(0.0);
actualValues.initialize(0.0);
// load
FieldContainer<double> expectedLoad(numCells, trialOrdering->totalDofs() );
FieldContainer<double> actualLoad(numCells, trialOrdering->totalDofs() );
penaltyBC->filter(expectedValues,expectedLoad,basisCache,mesh,problem);
pc->filter(actualValues,actualLoad,basisCache,mesh,problem);
maxDiff = 0.0;
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedValues,actualValues,tol,maxDiff) )
{
cout << "Test failed: old penalty stiffness differs from new; maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "trialOrdering: \n" << *trialOrdering;
}
else
{
cout << "Old and new penalty stiffness agree!!\n";
}
}
if (rank==0)
{
if ( ! TestSuite::fcsAgree(expectedLoad,actualLoad,tol,maxDiff) )
{
cout << "Test failed: old penalty load differs from new; maxDiff " << maxDiff << ".\n";
cout << "Old: \n" << expectedValues;
cout << "New: \n" << actualValues;
cout << "trialOrdering: \n" << *trialOrdering;
}
else
{
cout << "Old and new penalty load agree!!\n";
}
}
// define refinement strategy:
Teuchos::RCP<RefinementStrategy> refinementStrategy = Teuchos::rcp(new RefinementStrategy(solution,energyThreshold));
// =================== END INITIALIZATION CODE ==========================
// refine the spectral mesh, for comparability with the original Burgers' driver
mesh->hRefine(vector<int>(1),RefinementPattern::regularRefinementPatternQuad());
int numRefs = 5;
Teuchos::RCP<NonlinearStepSize> stepSize = Teuchos::rcp(new NonlinearStepSize(nonlinearStepSize));
Teuchos::RCP<NonlinearSolveStrategy> solveStrategy = Teuchos::rcp(
new NonlinearSolveStrategy(backgroundFlow, solution, stepSize, nonlinearRelativeEnergyTolerance)
);
for (int refIndex=0; refIndex<numRefs; refIndex++)
{
solveStrategy->solve(rank==0);
refinementStrategy->refine(rank==0); // print to console on rank 0
}
// one more nonlinear solve on refined mesh
int numNRSteps = 5;
for (int i=0; i<numNRSteps; i++)
{
solution->solve(false);
backgroundFlow->addSolution(solution,1.0);
}
if (rank==0)
{
backgroundFlow->writeFieldsToFile(BurgersBilinearForm::U, "u_ref.m");
backgroundFlow->writeFieldsToFile(BurgersBilinearForm::SIGMA_1, "sigmax.m");
backgroundFlow->writeFieldsToFile(BurgersBilinearForm::SIGMA_2, "sigmay.m");
solution->writeFluxesToFile(BurgersBilinearForm::U_HAT, "du_hat_ref.dat");
}
return 0;
}
bool LobattoBasisTests::testSimpleStiffnessMatrix() {
bool success = true;
int rank = Teuchos::GlobalMPISession::getRank();
VarFactory varFactory;
VarPtr u = varFactory.fieldVar("u");
VarPtr un = varFactory.fluxVar("un_hat");
VarPtr v = varFactory.testVar("v", HGRAD);
BFPtr bf = Teuchos::rcp( new BF(varFactory) );
vector<double> beta;
beta.push_back(1);
beta.push_back(1);
bf->addTerm(beta * u, v->grad());
bf->addTerm(un, v);
DofOrderingPtr trialSpace = Teuchos::rcp( new DofOrdering );
DofOrderingPtr testSpace = Teuchos::rcp( new DofOrdering );
const int numSides = 4;
const int spaceDim = 2;
int fieldOrder = 3;
int testOrder = fieldOrder+2;
BasisPtr fieldBasis = Camellia::intrepidQuadHGRAD(fieldOrder);
BasisPtr fluxBasis = Camellia::intrepidLineHGRAD(fieldOrder);
trialSpace->addEntry(u->ID(), fieldBasis, fieldBasis->rangeRank());
for (int i=0; i<numSides; i++) {
trialSpace->addEntry(un->ID(), fluxBasis, fluxBasis->rangeRank(), i);
}
BasisPtr testBasis = Camellia::lobattoQuadHGRAD(testOrder+1,false); // +1 because it lives in HGRAD
testSpace->addEntry(v->ID(), testBasis, testBasis->rangeRank());
int numTrialDofs = trialSpace->totalDofs();
int numTestDofs = testSpace->totalDofs();
int numCells = 1;
FieldContainer<double> cellNodes(numCells,numSides,spaceDim);
cellNodes(0,0,0) = 0;
cellNodes(0,0,1) = 0;
cellNodes(0,1,0) = 1;
cellNodes(0,1,1) = 0;
cellNodes(0,2,0) = 1;
cellNodes(0,2,1) = 1;
cellNodes(0,3,0) = 0;
cellNodes(0,3,1) = 1;
FieldContainer<double> stiffness(numCells,numTestDofs,numTrialDofs);
FieldContainer<double> cellSideParities(numCells,numSides);
cellSideParities.initialize(1.0);
Teuchos::RCP<shards::CellTopology> quad_4 = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ) );
Teuchos::RCP<ElementType> elemType = Teuchos::rcp( new ElementType(trialSpace, testSpace, quad_4));
BasisCachePtr basisCache = Teuchos::rcp( new BasisCache(elemType) );
vector<GlobalIndexType> cellIDs;
cellIDs.push_back(0);
basisCache->setPhysicalCellNodes(cellNodes, cellIDs, true);
bf->stiffnessMatrix(stiffness, elemType, cellSideParities, basisCache);
// TODO: finish this test
// cout << stiffness;
if (rank==0)
cout << "Warning: testSimpleStiffnessMatrix() unfinished.\n";
return success;
}
