double integralOverMesh(LinearTermPtr testTerm, VarPtr testVar, FunctionPtr fxnToSubstitute) {
map<int, FunctionPtr > varAsFunction;
varAsFunction[testVar->ID()] = fxnToSubstitute;
FunctionPtr substituteOnBoundary = testTerm->evaluate(varAsFunction, true);
FunctionPtr substituteOnInterior = testTerm->evaluate(varAsFunction, false);
double integral = substituteOnBoundary->integrate(mesh);
integral += substituteOnInterior->integrate(mesh);
return integral;
}
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;
}
bool LinearTermTests::testBoundaryPlusVolumeTerms()
{
bool success = true;
// notion is integration by parts:
// (div f, v) = < f * n, v > - (f, grad v)
// We perform two subtests for each test: first we try with a particular
// function substituted for the variable. Second, we integrate over the
// basis for the mesh (i.e. we test a whole bunch of functions, whose
// precise definition is a bit complicated).
// A third test is against the two-term LinearTerm::integrate() method.
// This doesn't do integration by parts, but rather tests that
// (u + u->dot_normal(), v) = (u,v) + (u->dot_normal(), v)
///////////// FIRST TEST ////////////////
// start simply: define f to be (x, 0)
// (div f, v) = (1, v)
// < f * n, v > - (f, grad v) = < x n1, v > - ( x, v->dx() )
FunctionPtr x = Function::xn(1);
FunctionPtr y = Function::yn(1);
FunctionPtr x2 = Function::xn(2);
FunctionPtr y2 = Function::yn(2);
FunctionPtr x3 = Function::xn(3);
FunctionPtr y3 = Function::yn(3);
vector< FunctionPtr > f_fxns;
f_fxns.push_back( Function::vectorize( x, Function::zero() ) ); // div of this = 1
f_fxns.push_back( Function::vectorize( x2 / 6.0, x2 * y / 2.0 ) ); // div of this = x / 3 + x^2 / 2
for ( vector< FunctionPtr >::iterator fIt = f_fxns.begin(); fIt != f_fxns.end(); fIt++)
{
FunctionPtr vector_fxn = *fIt;
LinearTermPtr lt_v = vector_fxn->div()*v1;
// part a: substitute v1 = x*y^2
FunctionPtr v1_value = x*y2;
map< int, FunctionPtr > var_values;
var_values[v1->ID()] = v1_value;
double expectedValue = lt_v->evaluate(var_values, false)->integrate(mesh);
FunctionPtr n = Function::normal();
LinearTermPtr ibp = vector_fxn * n * v1 - vector_fxn * v1->grad();
int numCells = basisCache->getPhysicalCubaturePoints().dimension(0);
int numPoints = basisCache->getPhysicalCubaturePoints().dimension(1);
int spaceDim = basisCache->getSpaceDim();
FieldContainer<double> vector_fxn_values(numCells,numPoints,spaceDim);
vector_fxn->values(vector_fxn_values,basisCache);
// cout << "vector_fxn values: \n" << vector_fxn_values;
double boundaryIntegralSum = ibp->evaluate(var_values,true)->integrate(mesh);
double volumeIntegralSum = ibp->evaluate(var_values,false)->integrate(mesh);
double actualValue = boundaryIntegralSum + volumeIntegralSum;
double tol = 1e-14;
if (abs(expectedValue - actualValue)>tol)
{
success = false;
}
// part b: integrate the bases over each of the cells:
int num_dofs = testOrder->totalDofs();
FieldContainer<double> integrals_expected( mesh->numActiveElements(), num_dofs );
FieldContainer<double> integrals_actual( mesh->numActiveElements(), num_dofs );
lt_v->integrate(integrals_expected,testOrder,basisCache);
ibp->integrate(integrals_actual,testOrder,basisCache);
double maxDiff = 0;
if (! fcsAgree(integrals_actual, integrals_expected, tol, maxDiff) )
{
cout << "LT integrated by parts does not agree with the original; maxDiff: " << maxDiff << endl;
success = false;
}
// just on the odd chance that ordering makes a difference, repeat this test with the opposite order in ibp:
ibp = - vector_fxn * v1->grad() + vector_fxn * n * v1;
ibp->integrate(integrals_actual,testOrder,basisCache, false, false);
maxDiff = 0;
if (! fcsAgree(integrals_actual, integrals_expected, tol, maxDiff) )
{
cout << "LT integrated by parts does not agree with the original; maxDiff: " << maxDiff << endl;
success = false;
}
// part c: two-term integrals
FieldContainer<double> integrals_expected_two_term( mesh->numActiveElements(), num_dofs, num_dofs);
FieldContainer<double> integrals_actual_two_term( mesh->numActiveElements(), num_dofs, num_dofs );
LinearTermPtr ibp1 = vector_fxn * n * v1;
LinearTermPtr ibp2 = - vector_fxn * v1->grad();
lt_v->integrate(integrals_expected_two_term, testOrder, ibp1 + ibp2, testOrder, basisCache, false, false);
lt_v->integrate(integrals_actual_two_term, testOrder, ibp1, testOrder, basisCache, false, false); // don't forceBoundary, don't sumInto
lt_v->integrate(integrals_actual_two_term, testOrder, ibp2, testOrder, basisCache, false, true); // DO sumInto
maxDiff = 0;
if (! fcsAgree(integrals_actual_two_term, integrals_expected_two_term, tol, maxDiff) )
{
cout << "two-term integration is not bilinear; maxDiff: " << maxDiff << endl;
success = false;
}
// now, same thing but with the roles of ibp{1|2} and lt_v reversed:
(ibp1 + ibp2)->integrate(integrals_expected_two_term, testOrder, lt_v, testOrder, basisCache, false, false);
ibp1->integrate(integrals_actual_two_term, testOrder, lt_v, testOrder, basisCache, false, false); // don't forceBoundary, don't sumInto
ibp2->integrate(integrals_actual_two_term, testOrder, lt_v, testOrder, basisCache, false, true); // DO sumInto
maxDiff = 0;
if (! fcsAgree(integrals_actual_two_term, integrals_expected_two_term, tol, maxDiff) )
{
cout << "two-term integration is not bilinear; maxDiff: " << maxDiff << endl;
success = false;
}
// now, test that two-term integration commutes in the two terms:
ibp1->integrate(integrals_expected_two_term, testOrder, lt_v, testOrder, basisCache, false, false);
lt_v->integrate(integrals_actual_two_term, testOrder, ibp1, testOrder, basisCache, false, false);
// we expect the integrals to commute up to a transpose, so let's transpose one of the containers:
transposeFieldContainer(integrals_expected_two_term);
maxDiff = 0;
if (! fcsAgree(integrals_actual_two_term, integrals_expected_two_term, tol, maxDiff) )
{
cout << "two-term integration does not commute for boundary value (ibp1); maxDiff: " << maxDiff << endl;
success = false;
}
ibp2->integrate(integrals_expected_two_term, testOrder, lt_v, testOrder, basisCache, false, false);
lt_v->integrate(integrals_actual_two_term, testOrder, ibp2, testOrder, basisCache, false, false);
// we expect the integrals to commute up to a transpose, so let's transpose one of the containers:
transposeFieldContainer(integrals_expected_two_term);
maxDiff = 0;
if (! fcsAgree(integrals_actual_two_term, integrals_expected_two_term, tol, maxDiff) )
{
cout << "two-term integration does not commute for volume value (ibp2); maxDiff: " << maxDiff << endl;
success = false;
}
// part d: to suss out where the integration failure happens in the non-commuting case:
// 1. Substitute v1 = 1 in ibp2; get a function ibp2_at_v1_equals_one back.
// 2. Substitute v1 = 1 in lt_v; get a function lt_v_at_v1_equals_one back.
// 3. Integrate ibp2_at_v1_equals_one * lt_v_at_v1_equals_one over the mesh. Get a double result.
// 4. Because basis is nodal, the representation for v1 = 1 is just all 1s for coefficients.
// Therefore, the sum of the entries in the integrals_*_two_term matrices will should match
// the function integral. Whichever doesn't match is wrong.
// first, let's confirm that the v1 basis *is* nodal:
BasisPtr v1Basis = testOrder->getBasis(v1->ID());
if (! v1Basis->isNodal())
{
cout << "testBoundaryPlusVolumeTerms: final part of test relies on a nodal basis, but the basis is not nodal.";
cout << " Exiting test early (with whatever success value we have thus far).\n";
return success;
}
map< int, FunctionPtr > v1_equals_one;
v1_equals_one[v1->ID()] = Function::constant(1.0);
FunctionPtr ibp1_at_v1_equals_one = ibp1->evaluate(v1_equals_one,true); // ibp1 has only a boundary term, so we just ask for this
FunctionPtr ibp2_at_v1_equals_one = ibp2->evaluate(v1_equals_one,false); // ibp2 has no boundary terms, so we don't ask for these
FunctionPtr lt_v_at_v1_equals_one = lt_v->evaluate(v1_equals_one,false); // lt_v also has no boundary terms
if (ibp1_at_v1_equals_one->isZero())
{
cout << "ibp1_at_v1_equals_one->isZero() = true.\n";
}
if (lt_v_at_v1_equals_one->isZero())
{
cout << "lt_v_at_v1_equals_one->isZero() = true.\n";
}
FieldContainer<double> integrals_lt_v_first( mesh->numActiveElements(), num_dofs, num_dofs );
FieldContainer<double> integrals_ibp1_first( mesh->numActiveElements(), num_dofs, num_dofs );
FieldContainer<double> integrals_ibp2_first( mesh->numActiveElements(), num_dofs, num_dofs );
double lt_v_first_integral = 0.0, ibp1_first_integral = 0.0, ibp2_first_integral = 0.0;
double integral = (ibp1_at_v1_equals_one * lt_v_at_v1_equals_one)->integrate(mesh);
ibp1->integrate(integrals_ibp1_first, testOrder, lt_v, testOrder, basisCache, false, false);
lt_v->integrate(integrals_lt_v_first, testOrder, ibp1, testOrder, basisCache, false, false);
for (int i=0; i<integrals_lt_v_first.size(); i++)
{
lt_v_first_integral += integrals_lt_v_first[i];
ibp1_first_integral += integrals_ibp1_first[i];
}
if (abs(lt_v_first_integral - integral) > tol)
{
double diff = abs(lt_v_first_integral - integral);
success = false;
cout << "Integral with v1=1 substituted does not match two-term integration of (lt_v,ibp1) with lt_v as this. diff = " << diff << "\n";
cout << "lt_v_first_integral = " << lt_v_first_integral << endl;
cout << " (true) integral = " << integral << endl;
}
if (abs(ibp1_first_integral - integral) > tol)
{
double diff = abs(ibp1_first_integral - integral);
success = false;
cout << "Integral with v1=1 substituted does not match two-term integration of (lt_v,ibp1) with ibp1 as this. diff = " << diff << "\n";
cout << "ibp1_first_integral = " << ibp1_first_integral << endl;
cout << " (true) integral = " << integral << endl;
}
// now, do the same but for ibp2
integral = (ibp2_at_v1_equals_one * lt_v_at_v1_equals_one)->integrate(mesh);
ibp2->integrate(integrals_ibp2_first, testOrder, lt_v, testOrder, basisCache, false, false);
lt_v->integrate(integrals_lt_v_first, testOrder, ibp2, testOrder, basisCache, false, false);
// reset the sums:
lt_v_first_integral = 0.0;
ibp1_first_integral = 0.0;
ibp2_first_integral = 0.0;
for (int i=0; i<integrals_lt_v_first.size(); i++)
{
lt_v_first_integral += integrals_lt_v_first[i];
ibp2_first_integral += integrals_ibp2_first[i];
}
if (abs(lt_v_first_integral - integral) > tol)
{
double diff = abs(lt_v_first_integral - integral);
success = false;
cout << "Integral with v1=1 substituted does not match two-term integration of (lt_v,ibp2) with lt_v as this. diff = " << diff << "\n";
cout << "lt_v_first_integral = " << lt_v_first_integral << endl;
cout << " (true) integral = " << integral << endl;
}
if (abs(ibp2_first_integral - integral) > tol)
{
double diff = abs(ibp2_first_integral - integral);
success = false;
cout << "Integral with v1=1 substituted does not match two-term integration of (lt_v,ibp2) with ibp2 as this. diff = " << diff << "\n";
cout << "ibp1_first_integral = " << ibp1_first_integral << endl;
cout << " (true) integral = " << integral << endl;
}
}
return success;
}
int main(int argc, char *argv[]) {
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int rank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
int nCells = args.Input<int>("--nCells", "num cells",2);
int numRefs = args.Input<int>("--numRefs","num adaptive refinements",0);
int numPreRefs = args.Input<int>("--numPreRefs","num preemptive adaptive refinements",0);
int order = args.Input<int>("--order","order of approximation",2);
double eps = args.Input<double>("--epsilon","diffusion parameter",1e-2);
double energyThreshold = args.Input<double>("-energyThreshold","energy thresh for adaptivity", .5);
double rampHeight = args.Input<double>("--rampHeight","ramp height at x = 2", 0.0);
double ipSwitch = args.Input<double>("--ipSwitch","point at which to switch to graph norm", 0.0); // default to 0 to remain on robust norm
bool useAnisotropy = args.Input<bool>("--useAnisotropy","aniso flag ", false);
int H1Order = order+1;
int pToAdd = args.Input<int>("--pToAdd","test space enrichment", 2);
FunctionPtr zero = Function::constant(0.0);
FunctionPtr one = Function::constant(1.0);
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
vector<double> e1,e2;
e1.push_back(1.0);e1.push_back(0.0);
e2.push_back(0.0);e2.push_back(1.0);
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
// first order term with magnitude alpha
double alpha = 0.0;
// confusionBF->addTerm(alpha * u, v);
//////////////////// BUILD MESH ///////////////////////
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);
mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));
MeshInfo meshInfo(mesh); // gets info like cell measure, etc
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
IPPtr ip = Teuchos::rcp(new IP);
/*
// robust test norm
FunctionPtr C_h = Teuchos::rcp( new EpsilonScaling(eps) );
FunctionPtr invH = Teuchos::rcp(new InvHScaling);
FunctionPtr invSqrtH = Teuchos::rcp(new InvSqrtHScaling);
FunctionPtr sqrtH = Teuchos::rcp(new SqrtHScaling);
FunctionPtr hSwitch = Teuchos::rcp(new HSwitch(ipSwitch,mesh));
ip->addTerm(hSwitch*sqrt(eps) * v->grad() );
ip->addTerm(hSwitch*beta * v->grad() );
ip->addTerm(hSwitch*tau->div() );
// graph norm
ip->addTerm( (one-hSwitch)*((1.0/eps) * tau + v->grad()));
ip->addTerm( (one-hSwitch)*(beta * v->grad() - tau->div()));
// regularizing terms
ip->addTerm(C_h/sqrt(eps) * tau );
ip->addTerm(invSqrtH*v);
*/
// robust test norm
IPPtr robIP = Teuchos::rcp(new IP);
FunctionPtr C_h = Teuchos::rcp( new EpsilonScaling(eps) );
FunctionPtr invH = Teuchos::rcp(new InvHScaling);
FunctionPtr invSqrtH = Teuchos::rcp(new InvSqrtHScaling);
FunctionPtr sqrtH = Teuchos::rcp(new SqrtHScaling);
FunctionPtr hSwitch = Teuchos::rcp(new HSwitch(ipSwitch,mesh));
robIP->addTerm(sqrt(eps) * v->grad() );
robIP->addTerm(beta * v->grad() );
robIP->addTerm(tau->div() );
// regularizing terms
robIP->addTerm(C_h/sqrt(eps) * tau );
robIP->addTerm(invSqrtH*v);
IPPtr graphIP = confusionBF->graphNorm();
graphIP->addTerm(invSqrtH*v);
// graphIP->addTerm(C_h/sqrt(eps) * tau );
IPPtr switchIP = Teuchos::rcp(new IPSwitcher(robIP,graphIP,ipSwitch)); // rob IP for h>ipSwitch mesh size, graph norm o/w
ip = switchIP;
LinearTermPtr vVecLT = Teuchos::rcp(new LinearTerm);
LinearTermPtr tauVecLT = Teuchos::rcp(new LinearTerm);
vVecLT->addTerm(sqrt(eps)*v->grad());
tauVecLT->addTerm(C_h/sqrt(eps)*tau);
LinearTermPtr restLT = Teuchos::rcp(new LinearTerm);
restLT->addTerm(alpha*v);
restLT->addTerm(invSqrtH*v);
restLT = restLT + beta * v->grad();
restLT = restLT + tau->div();
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = zero;
// f = one;
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr Inflow = Teuchos::rcp(new LeftInflow);
SpatialFilterPtr wallBoundary = Teuchos::rcp(new WallBoundary);//MeshUtilities::rampBoundary(rampHeight);
SpatialFilterPtr freeStream = Teuchos::rcp(new FreeStreamBoundary);
bc->addDirichlet(uhat, wallBoundary, one);
// bc->addDirichlet(uhat, wallBoundary, Teuchos::rcp(new WallSmoothBC(eps)));
bc->addDirichlet(beta_n_u_minus_sigma_n, Inflow, zero);
bc->addDirichlet(beta_n_u_minus_sigma_n, freeStream, zero);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution;
solution = Teuchos::rcp( new Solution(mesh, bc, rhs, ip) );
BCPtr nullBC = Teuchos::rcp((BC*)NULL); RHSPtr nullRHS = Teuchos::rcp((RHS*)NULL); IPPtr nullIP = Teuchos::rcp((IP*)NULL);
SolutionPtr backgroundFlow = Teuchos::rcp(new Solution(mesh, nullBC, nullRHS, nullIP) );
mesh->registerSolution(backgroundFlow); // to trigger issue with p-refinements
map<int, Teuchos::RCP<Function> > functionMap; functionMap[u->ID()] = Function::constant(3.14);
backgroundFlow->projectOntoMesh(functionMap);
// lower p to p = 1 at SINGULARITY only
vector<int> ids;
/*
for (int i = 0;i<mesh->numActiveElements();i++){
bool cellIDset = false;
int cellID = mesh->activeElements()[i]->cellID();
int elemOrder = mesh->cellPolyOrder(cellID)-1;
FieldContainer<double> vv(4,2); mesh->verticesForCell(vv, cellID);
bool vertexOnWall = false; bool vertexAtSingularity = false;
for (int j = 0;j<4;j++){
if ((abs(vv(j,0)-.5) + abs(vv(j,1)))<1e-10){
vertexAtSingularity = true;
cellIDset = true;
}
}
if (!vertexAtSingularity && elemOrder<2 && !cellIDset ){
ids.push_back(cellID);
cout << "celliD = " << cellID << endl;
}
}
*/
ids.push_back(1);
ids.push_back(3);
mesh->pRefine(ids); // to put order = 1
return 0;
LinearTermPtr residual = rhs->linearTermCopy();
residual->addTerm(-confusionBF->testFunctional(solution));
RieszRepPtr rieszResidual = Teuchos::rcp(new RieszRep(mesh, ip, residual));
rieszResidual->computeRieszRep();
FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,rieszResidual));
FunctionPtr e_tau = Teuchos::rcp(new RepFunction(tau,rieszResidual));
map<int,FunctionPtr> errRepMap;
errRepMap[v->ID()] = e_v;
errRepMap[tau->ID()] = e_tau;
FunctionPtr errTau = tauVecLT->evaluate(errRepMap,false);
FunctionPtr errV = vVecLT->evaluate(errRepMap,false);
FunctionPtr errRest = restLT->evaluate(errRepMap,false);
FunctionPtr xErr = (errTau->x())*(errTau->x()) + (errV->dx())*(errV->dx());
FunctionPtr yErr = (errTau->y())*(errTau->y()) + (errV->dy())*(errV->dy());
FunctionPtr restErr = errRest*errRest;
RefinementStrategy refinementStrategy( solution, energyThreshold );
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// PRE REFINEMENTS
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
if (rank==0){
cout << "Number of pre-refinements = " << numPreRefs << endl;
}
for (int i =0;i<=numPreRefs;i++){
vector<ElementPtr> elems = mesh->activeElements();
vector<ElementPtr>::iterator elemIt;
vector<int> wallCells;
for (elemIt=elems.begin();elemIt != elems.end();elemIt++){
int cellID = (*elemIt)->cellID();
int numSides = mesh->getElement(cellID)->numSides();
FieldContainer<double> vertices(numSides,2); //for quads
mesh->verticesForCell(vertices, cellID);
bool cellIDset = false;
for (int j = 0;j<numSides;j++){
if ((abs(vertices(j,0)-.5)<1e-7) && (abs(vertices(j,1))<1e-7) && !cellIDset){ // if at singularity, i.e. if a vertex is (1,0)
wallCells.push_back(cellID);
cellIDset = true;
}
}
}
if (i<numPreRefs){
refinementStrategy.refineCells(wallCells);
}
}
double minSideLength = meshInfo.getMinCellSideLength() ;
double minCellMeasure = meshInfo.getMinCellMeasure() ;
if (rank==0){
cout << "after prerefs, sqrt min cell measure = " << sqrt(minCellMeasure) << ", min side length = " << minSideLength << endl;
}
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
VTKExporter exporter(solution, mesh, varFactory);
for (int refIndex=0;refIndex<numRefs;refIndex++){
if (rank==0){
cout << "on ref index " << refIndex << endl;
}
rieszResidual->computeRieszRep(); // in preparation to get anisotropy
vector<int> cellIDs;
refinementStrategy.getCellsAboveErrorThreshhold(cellIDs);
map<int,double> energyError = solution->energyError();
map<int,double> xErrMap = xErr->cellIntegrals(cellIDs,mesh,5,true);
map<int,double> yErrMap = yErr->cellIntegrals(cellIDs,mesh,5,true);
map<int,double> restErrMap = restErr->cellIntegrals(cellIDs,mesh,5,true);
for (vector<ElementPtr>::iterator elemIt = mesh->activeElements().begin();elemIt!=mesh->activeElements().end();elemIt++){
int cellID = (*elemIt)->cellID();
double err = xErrMap[cellID]+ yErrMap[cellID] + restErrMap[cellID];
// if (rank==0)
// cout << "err thru LT = " << sqrt(err) << ", while energy err = " << energyError[cellID] << endl;
}
/*
map<int,double> ratio,xErr,yErr;
vector<ElementPtr> elems = mesh->activeElements();
for (vector<ElementPtr>::iterator elemIt = elems.begin();elemIt!=elems.end();elemIt++){
int cellID = (*elemIt)->cellID();
ratio[cellID] = 0.0;
xErr[cellID] = 0.0;
yErr[cellID] = 0.0;
if (std::find(cellIDs.begin(),cellIDs.end(),cellID)!=cellIDs.end()){ // if this cell is above energy thresh
ratio[cellID] = yErrMap[cellID]/xErrMap[cellID];
xErr[cellID] = xErrMap[cellID];
yErr[cellID] = yErrMap[cellID];
}
}
FunctionPtr ratioFxn = Teuchos::rcp(new EnergyErrorFunction(ratio));
FunctionPtr xErrFxn = Teuchos::rcp(new EnergyErrorFunction(xErr));
FunctionPtr yErrFxn = Teuchos::rcp(new EnergyErrorFunction(yErr));
exporter.exportFunction(ratioFxn, string("ratio")+oss.str());
exporter.exportFunction(xErrFxn, string("xErr")+oss.str());
exporter.exportFunction(yErrFxn, string("yErr")+oss.str());
*/
if (useAnisotropy){
refinementStrategy.refine(rank==0,xErrMap,yErrMap); //anisotropic refinements
}else{
refinementStrategy.refine(rank==0); // no anisotropy
}
// lower p to p = 1 at SINGULARITY only
vector<int> ids;
for (int i = 0;i<mesh->numActiveElements();i++){
int cellID = mesh->activeElements()[i]->cellID();
int elemOrder = mesh->cellPolyOrder(cellID)-1;
FieldContainer<double> vv(4,2); mesh->verticesForCell(vv, cellID);
bool vertexOnWall = false; bool vertexAtSingularity = false;
for (int j = 0;j<4;j++){
if ((abs(vv(j,0)-.5) + abs(vv(j,1)))<1e-10)
vertexAtSingularity = true;
}
if (!vertexAtSingularity && elemOrder<2){
ids.push_back(cellID);
}
}
mesh->pRefine(ids); // to put order = 1
/*
if (elemOrder>1){
if (vertexAtSingularity){
vector<int> ids;
ids.push_back(cellID);
mesh->pRefine(ids,1-(elemOrder-1)); // to put order = 1
// mesh->pRefine(ids); // to put order = 1
if (rank==0)
cout << "p unrefining elem with elemOrder = " << elemOrder << endl;
}
}else{
if (!vertexAtSingularity){
vector<int> ids;
ids.push_back(cellID);
mesh->pRefine(ids,2-elemOrder);
}
}
*/
double minSideLength = meshInfo.getMinCellSideLength() ;
if (rank==0)
cout << "minSideLength is " << minSideLength << endl;
solution->condensedSolve();
std::ostringstream oss;
oss << refIndex;
}
// final solve on final mesh
solution->setWriteMatrixToFile(true,"K.mat");
solution->condensedSolve();
////////////////////////////////////////////////////////////////////////////////////////////////////////////
// CHECK CONDITIONING
////////////////////////////////////////////////////////////////////////////////////////////////////////////
bool checkConditioning = true;
if (checkConditioning){
double minSideLength = meshInfo.getMinCellSideLength() ;
StandardAssembler assembler(solution);
double maxCond = 0.0;
int maxCellID = 0;
for (int i = 0;i<mesh->numActiveElements();i++){
int cellID = mesh->getActiveElement(i)->cellID();
FieldContainer<double> ipMat = assembler.getIPMatrix(mesh->getElement(cellID));
double cond = SerialDenseWrapper::getMatrixConditionNumber(ipMat);
if (cond>maxCond){
maxCond = cond;
maxCellID = cellID;
}
}
if (rank==0){
cout << "cell ID " << maxCellID << " has minCellLength " << minSideLength << " and condition estimate " << maxCond << endl;
}
string ipMatName = string("ipMat.mat");
ElementPtr maxCondElem = mesh->getElement(maxCellID);
FieldContainer<double> ipMat = assembler.getIPMatrix(maxCondElem);
SerialDenseWrapper::writeMatrixToMatlabFile(ipMatName,ipMat);
}
//////////////////// print to file ///////////////////////
if (rank==0){
exporter.exportSolution(string("robustIP"));
cout << endl;
}
return 0;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
choice::MpiArgs args( argc, argv );
#else
choice::Args args( argc, argv );
#endif
int rank = Teuchos::GlobalMPISession::getRank();
int numProcs = Teuchos::GlobalMPISession::getNProc();
int nCells = args.Input<int>("--nCells", "num cells",2);
int numRefs = args.Input<int>("--numRefs","num adaptive refinements",0);
int numPreRefs = args.Input<int>("--numPreRefs","num preemptive adaptive refinements",0);
int order = args.Input<int>("--order","order of approximation",2);
double eps = args.Input<double>("--epsilon","diffusion parameter",1e-2);
double energyThreshold = args.Input<double>("-energyThreshold","energy thresh for adaptivity", .5);
double rampHeight = args.Input<double>("--rampHeight","ramp height at x = 2", 0.0);
bool useAnisotropy = args.Input<bool>("--useAnisotropy","aniso flag ", false);
FunctionPtr zero = Function::constant(0.0);
FunctionPtr one = Function::constant(1.0);
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
vector<double> e1,e2;
e1.push_back(1.0);
e1.push_back(0.0);
e2.push_back(0.0);
e2.push_back(1.0);
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
vector<double> beta;
beta.push_back(1.0);
beta.push_back(0.0);
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(uhat, -tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( -u, beta * v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
// first order term with magnitude alpha
double alpha = 0.0;
confusionBF->addTerm(alpha * u, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// robust test norm
IPPtr robIP = Teuchos::rcp(new IP);
FunctionPtr C_h = Teuchos::rcp( new EpsilonScaling(eps) );
FunctionPtr invH = Teuchos::rcp(new InvHScaling);
FunctionPtr invSqrtH = Teuchos::rcp(new InvSqrtHScaling);
FunctionPtr sqrtH = Teuchos::rcp(new SqrtHScaling);
robIP->addTerm(v*alpha);
robIP->addTerm(invSqrtH*v);
// robIP->addTerm(v);
robIP->addTerm(sqrt(eps) * v->grad() );
robIP->addTerm(beta * v->grad() );
robIP->addTerm(tau->div() );
robIP->addTerm(C_h/sqrt(eps) * tau );
LinearTermPtr vVecLT = Teuchos::rcp(new LinearTerm);
LinearTermPtr tauVecLT = Teuchos::rcp(new LinearTerm);
vVecLT->addTerm(sqrt(eps)*v->grad());
tauVecLT->addTerm(C_h/sqrt(eps)*tau);
LinearTermPtr restLT = Teuchos::rcp(new LinearTerm);
restLT->addTerm(alpha*v);
restLT->addTerm(invSqrtH*v);
restLT = restLT + beta * v->grad();
restLT = restLT + tau->div();
//////////////////// SPECIFY RHS ///////////////////////
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = zero;
// f = one;
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
// SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
// SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary);
// bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, zero);
// bc->addDirichlet(uhat, outflowBoundary, zero);
SpatialFilterPtr rampInflow = Teuchos::rcp(new LeftInflow);
SpatialFilterPtr rampBoundary = MeshUtilities::rampBoundary(rampHeight);
SpatialFilterPtr freeStream = Teuchos::rcp(new FreeStreamBoundary);
SpatialFilterPtr outflowBoundary = Teuchos::rcp(new OutflowBoundary);
bc->addDirichlet(uhat, rampBoundary, one);
// bc->addDirichlet(uhat, outflowBoundary, one);
bc->addDirichlet(beta_n_u_minus_sigma_n, rampInflow, zero);
bc->addDirichlet(beta_n_u_minus_sigma_n, freeStream, zero);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = order+1;
int pToAdd = 2;
// create a pointer to a new mesh:
// Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(nCells,confusionBF, H1Order, H1Order+pToAdd);
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildRampMesh(rampHeight,confusionBF, H1Order, H1Order+pToAdd);
mesh->setPartitionPolicy(Teuchos::rcp(new ZoltanMeshPartitionPolicy("HSFC")));
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution;
solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) );
// solution->solve(false);
solution->condensedSolve();
LinearTermPtr residual = rhs->linearTermCopy();
residual->addTerm(-confusionBF->testFunctional(solution));
RieszRepPtr rieszResidual = Teuchos::rcp(new RieszRep(mesh, robIP, residual));
rieszResidual->computeRieszRep();
FunctionPtr e_v = Teuchos::rcp(new RepFunction(v,rieszResidual));
FunctionPtr e_tau = Teuchos::rcp(new RepFunction(tau,rieszResidual));
map<int,FunctionPtr> errRepMap;
errRepMap[v->ID()] = e_v;
errRepMap[tau->ID()] = e_tau;
FunctionPtr errTau = tauVecLT->evaluate(errRepMap,false);
FunctionPtr errV = vVecLT->evaluate(errRepMap,false);
FunctionPtr errRest = restLT->evaluate(errRepMap,false);
FunctionPtr xErr = (errTau->x())*(errTau->x()) + (errV->dx())*(errV->dx());
FunctionPtr yErr = (errTau->y())*(errTau->y()) + (errV->dy())*(errV->dy());
FunctionPtr restErr = errRest*errRest;
RefinementStrategy refinementStrategy( solution, energyThreshold );
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// PRE REFINEMENTS
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
if (rank==0)
{
cout << "Number of pre-refinements = " << numPreRefs << endl;
}
for (int i =0; i<=numPreRefs; i++)
{
vector<ElementPtr> elems = mesh->activeElements();
vector<ElementPtr>::iterator elemIt;
vector<int> wallCells;
for (elemIt=elems.begin(); elemIt != elems.end(); elemIt++)
{
int cellID = (*elemIt)->cellID();
int numSides = mesh->getElement(cellID)->numSides();
FieldContainer<double> vertices(numSides,2); //for quads
mesh->verticesForCell(vertices, cellID);
bool cellIDset = false;
for (int j = 0; j<numSides; j++)
{
if ((abs(vertices(j,0)-1.0)<1e-7) && (abs(vertices(j,1))<1e-7) && !cellIDset) // if at singularity, i.e. if a vertex is (1,0)
{
wallCells.push_back(cellID);
cellIDset = true;
}
}
}
if (i<numPreRefs)
{
refinementStrategy.refineCells(wallCells);
}
}
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
VTKExporter exporter(solution, mesh, varFactory);
for (int refIndex=0; refIndex<numRefs; refIndex++)
{
if (rank==0)
{
cout << "on ref index " << refIndex << endl;
}
rieszResidual->computeRieszRep(); // in preparation to get anisotropy
vector<int> cellIDs;
refinementStrategy.getCellsAboveErrorThreshhold(cellIDs);
map<int,double> energyError = solution->energyError();
map<int,double> xErrMap = xErr->cellIntegrals(cellIDs,mesh,5,true);
map<int,double> yErrMap = yErr->cellIntegrals(cellIDs,mesh,5,true);
map<int,double> restErrMap = restErr->cellIntegrals(cellIDs,mesh,5,true);
for (vector<ElementPtr>::iterator elemIt = mesh->activeElements().begin(); elemIt!=mesh->activeElements().end(); elemIt++)
{
int cellID = (*elemIt)->cellID();
double err = xErrMap[cellID]+ yErrMap[cellID] + restErrMap[cellID];
if (rank==0)
cout << "err thru LT = " << sqrt(err) << ", while energy err = " << energyError[cellID] << endl;
}
map<int,double> ratio,xErr,yErr;
vector<ElementPtr> elems = mesh->activeElements();
for (vector<ElementPtr>::iterator elemIt = elems.begin(); elemIt!=elems.end(); elemIt++)
{
int cellID = (*elemIt)->cellID();
ratio[cellID] = 0.0;
xErr[cellID] = 0.0;
yErr[cellID] = 0.0;
if (std::find(cellIDs.begin(),cellIDs.end(),cellID)!=cellIDs.end()) // if this cell is above energy thresh
{
ratio[cellID] = yErrMap[cellID]/xErrMap[cellID];
xErr[cellID] = xErrMap[cellID];
yErr[cellID] = yErrMap[cellID];
}
}
FunctionPtr ratioFxn = Teuchos::rcp(new EnergyErrorFunction(ratio));
FunctionPtr xErrFxn = Teuchos::rcp(new EnergyErrorFunction(xErr));
FunctionPtr yErrFxn = Teuchos::rcp(new EnergyErrorFunction(yErr));
std::ostringstream oss;
oss << refIndex;
exporter.exportFunction(ratioFxn, string("ratio")+oss.str());
exporter.exportFunction(xErrFxn, string("xErr")+oss.str());
exporter.exportFunction(yErrFxn, string("yErr")+oss.str());
if (useAnisotropy)
{
refinementStrategy.refine(rank==0,xErrMap,yErrMap); //anisotropic refinements
}
else
{
refinementStrategy.refine(rank==0); // no anisotropy
}
solution->condensedSolve();
}
// final solve on final mesh
solution->condensedSolve();
//////////////////// print to file ///////////////////////
FunctionPtr orderFxn = Teuchos::rcp(new MeshPolyOrderFunction(mesh));
std::ostringstream oss;
oss << nCells;
if (rank==0)
{
exporter.exportSolution(string("robustIP")+oss.str());
exporter.exportFunction(orderFxn, "meshOrder");
cout << endl;
}
return 0;
}
// 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;
}
// 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;
}
// tests whether a mixed type LT
bool ScratchPadTests::testLinearTermEvaluationConsistency()
{
bool success = true;
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactoryPtr varFactory = VarFactory::varFactory();
VarPtr v = varFactory->testVar("v", HGRAD);
vector<double> beta;
beta.push_back(1.0);
beta.push_back(1.0);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// robust test norm
IPPtr ip = Teuchos::rcp(new IP);
ip->addTerm(v);
ip->addTerm(beta*v->grad());
// define trial variables
VarPtr beta_n_u = varFactory->fluxVar("\\widehat{\\beta \\cdot n }");
VarPtr u = varFactory->fieldVar("u");
//////////////////// BUILD MESH ///////////////////////
BFPtr convectionBF = Teuchos::rcp( new BF(varFactory) );
// v terms:
convectionBF->addTerm( -u, beta * v->grad() );
convectionBF->addTerm( beta_n_u, v);
// define nodes for mesh
int order = 1;
int H1Order = order+1;
int pToAdd = 1;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshUtilities::buildUnitQuadMesh(1, convectionBF, H1Order, H1Order+pToAdd);
//////////////////// get fake residual ///////////////////////
LinearTermPtr lt = Teuchos::rcp(new LinearTerm);
FunctionPtr edgeFxn = Teuchos::rcp(new EdgeFunction);
FunctionPtr Xsq = Function::xn(2);
FunctionPtr Ysq = Function::yn(2);
FunctionPtr XYsq = Xsq*Ysq;
lt->addTerm(edgeFxn*v + (beta*XYsq)*v->grad());
Teuchos::RCP<RieszRep> ltRiesz = Teuchos::rcp(new RieszRep(mesh, ip, lt));
ltRiesz->computeRieszRep();
FunctionPtr repFxn = RieszRep::repFunction(v,ltRiesz);
map<int,FunctionPtr> rep_map;
rep_map[v->ID()] = repFxn;
FunctionPtr edgeLt = lt->evaluate(rep_map, true) ;
FunctionPtr elemLt = lt->evaluate(rep_map, false);
double edgeVal = edgeLt->integrate(mesh,10);
double elemVal = elemLt->integrate(mesh,10);
LinearTermPtr edgeOnlyLt = Teuchos::rcp(new LinearTerm);// residual
edgeOnlyLt->addTerm(edgeFxn*v);
FunctionPtr edgeOnly = edgeOnlyLt->evaluate(rep_map,true);
double edgeOnlyVal = edgeOnly->integrate(mesh,10);
double diff = edgeOnlyVal-edgeVal;
if (abs(diff)>1e-11)
{
success = false;
cout << "Failed testLinearTermEvaluationConsistency() with diff = " << diff << endl;
}
return success;
}
