// builds a [0,1]x[0,1] square mesh with evenly spaced horizontal/vertical cells
MeshPtr MeshUtilities::buildUnitQuadMesh(int horizontalCells, int verticalCells, Teuchos::RCP< BilinearForm > bilinearForm, int H1Order, int pTest){
FieldContainer<double> quadPoints(4,2);
double squareSize = 1.0;
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = squareSize;
quadPoints(1,1) = 0.0;
quadPoints(2,0) = squareSize;
quadPoints(2,1) = squareSize;
quadPoints(3,0) = 0.0;
quadPoints(3,1) = squareSize;
// create a pointer to a new mesh:
return MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells, bilinearForm, H1Order, pTest);
}
MeshTopologyPtr MeshTopologyTests::makeRectMesh(double x0, double y0, double width, double height,
unsigned horizontalCells, unsigned verticalCells)
{
unsigned spaceDim = 2;
Teuchos::RCP<MeshTopology> mesh = Teuchos::rcp( new MeshTopology(spaceDim) );
double dx = width / horizontalCells;
double dy = height / verticalCells;
CellTopoPtrLegacy quadTopo = Teuchos::rcp( new shards::CellTopology(shards::getCellTopologyData<shards::Quadrilateral<4> >() ) );
for (unsigned i=0; i<horizontalCells; i++)
{
double x = x0 + dx * i;
for (unsigned j=0; j<verticalCells; j++)
{
double y = y0 + dy * j;
vector< vector<double> > vertices = quadPoints(x, y, dx, dy);
mesh->addCell(quadTopo, vertices);
}
}
return mesh;
}
// 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::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);
}
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);
}
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);
}
void ElementTests::setup()
{
/**********************************
_________________________________
| | |
| | |
| | |
| 1 | 3 |
| | |
| | |
| | |
---------------------------------
| | | |
| 7 | 6 | |
| | | |
|-------0-------| 2 |
| | 11| 10| |
| 4 |---5---| |
| | 8 | 9 | |
---------------------------------
in the code:
_sw: 0
_nw: 1
_se: 2
_ne: 3
_sw_se: 5
_sw_ne: 6
_sw_se_se: 9
_sw_se_ne: 10
*********************************/
// first, build a simple mesh
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 = 2;
int testOrder = H1Order;
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);
_mesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells, confusionBF, H1Order, testOrder);
// the right way to determine the southwest element, etc. is as follows:
FieldContainer<double> points(4,2);
// southwest center:
points(0,0) = 0.25;
points(0,1) = 0.25;
// southeast center:
points(1,0) = 0.75;
points(1,1) = 0.25;
// northwest center:
points(2,0) = 0.25;
points(2,1) = 0.75;
// northeast center:
points(3,0) = 0.75;
points(3,1) = 0.75;
vector<ElementPtr> elements = _mesh->elementsForPoints(points, false);
_sw = elements[0]; // as presently implemented, cellID = 0
_se = elements[1]; // as presently implemented, cellID = 2
_nw = elements[2]; // as presently implemented, cellID = 1
_ne = elements[3]; // as presently implemented, cellID = 3
vector<GlobalIndexType> cellIDsToRefine;
cellIDsToRefine.push_back(_sw->cellID());
_mesh->hRefine(cellIDsToRefine,RefinementPattern::regularRefinementPatternQuad());
// get the new elements; these are all within the original SW quadrant
// southwest center:
points(0,0) = 0.125;
points(0,1) = 0.125;
// southeast center:
points(1,0) = 0.375;
points(1,1) = 0.125;
// northwest center:
points(2,0) = 0.125;
points(2,1) = 0.375;
// northeast center:
points(3,0) = 0.375;
points(3,1) = 0.375;
elements = _mesh->elementsForPoints(points, false);
_sw_se = elements[1]; // as presently implemented, cellID = 5
_sw_ne = elements[3]; // as presently implemented, cellID = 6
cellIDsToRefine.clear();
cellIDsToRefine.push_back(_sw_se->cellID());
_mesh->hRefine(cellIDsToRefine,RefinementPattern::regularRefinementPatternQuad());
// get the new elements; these are all within the SE of the original SW quadrant
// southwest center:
points(0,0) = 0.31125;
points(0,1) = 0.31125;
// southeast center:
points(1,0) = 0.4375;
points(1,1) = 0.31125;
// northwest center:
points(2,0) = 0.31125;
points(2,1) = 0.4375;
// northeast center:
points(3,0) = 0.4375;
points(3,1) = 0.4375;
elements = _mesh->elementsForPoints(points, false);
_sw_se_se = elements[1]; // as presently implemented, cellID = 9
_sw_se_ne = elements[3]; // as presently implemented, cellID = 10
// setup test points:
static const int NUM_POINTS_1D = 3;
double x[NUM_POINTS_1D] = {-0.5,0.25,0.75};
_testPoints1D = FieldContainer<double>(NUM_POINTS_1D,1);
for (int i=0; i<NUM_POINTS_1D; i++)
{
_testPoints1D(i, 0) = x[i];
}
}
bool FunctionTests::testJumpIntegral()
{
bool success = true;
double tol = 1e-14;
// define nodes for mesh
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 = 1, pToAdd = 0;
int horizontalCells = 2, verticalCells = 2;
int numSides = 4;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
_confusionBF, H1Order, H1Order+pToAdd);
FieldContainer<double> points(1,2);
// southwest center:
points(0,0) = 0.25;
points(0,1) = 0.25;
vector< Teuchos::RCP<Element> > elements = mesh->elementsForPoints(points, false);
int swCellID = elements[0]->cellID();
double val = 1.0;
FunctionPtr valFxn = Function::constant(val);
FunctionPtr valOnSWCell = Teuchos::rcp( new CellIDFilteredFunction(valFxn,swCellID) );
// the jump for this should be 1 along the two interior edges, each of length 0.5
double sideLength = 0.5;
int cubEnrichment = 0;
for (int sideIndex=0; sideIndex<numSides; sideIndex++)
{
double actualValue = valOnSWCell->integralOfJump(mesh, swCellID, sideIndex, cubEnrichment);
double expectedValue;
if (mesh->getTopology()->getCell(swCellID)->isBoundary(sideIndex))
{
expectedValue = 0;
}
else
{
double sideParity = mesh->parityForSide(swCellID, sideIndex);
expectedValue = sideParity * val * sideLength;
}
double diff = abs(actualValue-expectedValue);
if (diff > tol)
{
cout << "testJumpFunction(): expected " << expectedValue << " but actualValue was " << actualValue << endl;
success = false;
}
}
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 );
}
bool FunctionTests::testBasisSumFunction()
{
bool success = true;
// on a single-element mesh, the BasisSumFunction should be identical to
// the Solution with those coefficients
// define a new mesh: more interesting if we're not on the ref cell
int spaceDim = 2;
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 2.0;
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 = 1, pToAdd = 0;
int horizontalCells = 1, verticalCells = 1;
// create a pointer to a new mesh:
MeshPtr spectralConfusionMesh = MeshFactory::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
_confusionBF, H1Order, H1Order+pToAdd);
BCPtr bc = BC::bc();
SolutionPtr soln = Teuchos::rcp( new Solution(spectralConfusionMesh, bc) );
soln->initializeLHSVector();
int cellID = 0;
double tol = 1e-16; // overly restrictive, just for now.
DofOrderingPtr trialSpace = spectralConfusionMesh->getElementType(cellID)->trialOrderPtr;
set<int> trialIDs = trialSpace->getVarIDs();
BasisCachePtr volumeCache = BasisCache::basisCacheForCell(spectralConfusionMesh, cellID);
for (set<int>::iterator trialIt=trialIDs.begin(); trialIt != trialIDs.end(); trialIt++)
{
int trialID = *trialIt;
const vector<int>* sidesForVar = &trialSpace->getSidesForVarID(trialID);
bool boundaryValued = sidesForVar->size() != 1;
// note that for volume trialIDs, sideIndex = 0, and numSides = 1…
for (vector<int>::const_iterator sideIt = sidesForVar->begin(); sideIt != sidesForVar->end(); sideIt++)
{
int sideIndex = *sideIt;
BasisCachePtr sideCache = volumeCache->getSideBasisCache(sideIndex);
BasisPtr basis = trialSpace->getBasis(trialID, sideIndex);
int basisCardinality = basis->getCardinality();
for (int basisOrdinal = 0; basisOrdinal<basisCardinality; basisOrdinal++)
{
FieldContainer<double> basisCoefficients(basisCardinality);
basisCoefficients(basisOrdinal) = 1.0;
soln->setSolnCoeffsForCellID(basisCoefficients, cellID, trialID, sideIndex);
VarPtr v = Var::varForTrialID(trialID, spectralConfusionMesh->bilinearForm());
FunctionPtr solnFxn = Function::solution(v, soln, false);
FunctionPtr basisSumFxn = Teuchos::rcp( new BasisSumFunction(basis, basisCoefficients, Teuchos::rcp((BasisCache*)NULL), OP_VALUE, boundaryValued) );
if (!boundaryValued)
{
double l2diff = (solnFxn - basisSumFxn)->l2norm(spectralConfusionMesh);
// cout << "l2diff = " << l2diff << endl;
if (l2diff > tol)
{
success = false;
cout << "testBasisSumFunction: l2diff of " << l2diff << " exceeds tol of " << tol << endl;
cout << "l2norm of basisSumFxn: " << basisSumFxn->l2norm(spectralConfusionMesh) << endl;
cout << "l2norm of solnFxn: " << solnFxn->l2norm(spectralConfusionMesh) << endl;
}
l2diff = (solnFxn->dx() - basisSumFxn->dx())->l2norm(spectralConfusionMesh);
// cout << "l2diff = " << l2diff << endl;
if (l2diff > tol)
{
success = false;
cout << "testBasisSumFunction: l2diff of dx() " << l2diff << " exceeds tol of " << tol << endl;
cout << "l2norm of basisSumFxn->dx(): " << basisSumFxn->dx()->l2norm(spectralConfusionMesh) << endl;
cout << "l2norm of solnFxn->dx(): " << solnFxn->dx()->l2norm(spectralConfusionMesh) << endl;
}
// test that the restriction to a side works
int numSides = volumeCache->cellTopology()->getSideCount();
for (int i=0; i<numSides; i++)
{
BasisCachePtr mySideCache = volumeCache->getSideBasisCache(i);
if (! solnFxn->equals(basisSumFxn, mySideCache, tol))
{
success = false;
cout << "testBasisSumFunction: on side 0, l2diff of " << l2diff << " exceeds tol of " << tol << endl;
reportFunctionValueDifferences(solnFxn, basisSumFxn, mySideCache, tol);
}
if (! solnFxn->grad(spaceDim)->equals(basisSumFxn->grad(spaceDim), mySideCache, tol))
{
success = false;
cout << "testBasisSumFunction: on side 0, l2diff of dx() " << l2diff << " exceeds tol of " << tol << endl;
reportFunctionValueDifferences(solnFxn->grad(spaceDim), basisSumFxn->grad(spaceDim), mySideCache, tol);
}
}
}
else
{
FieldContainer<double> cellIntegral(1);
// compute l2 diff of integral along the one side where we can legitimately assert equality:
FunctionPtr diffFxn = solnFxn - basisSumFxn;
(diffFxn*diffFxn)->integrate(cellIntegral, sideCache);
double l2diff = sqrt(cellIntegral(0));
if (l2diff > tol)
{
success = false;
cout << "testBasisSumFunction: on side " << sideIndex << ", l2diff of " << l2diff << " exceeds tol of " << tol << endl;
int numCubPoints = sideCache->getPhysicalCubaturePoints().dimension(1);
FieldContainer<double> solnFxnValues(1,numCubPoints);
FieldContainer<double> basisFxnValues(1,numCubPoints);
solnFxn->values(solnFxnValues, sideCache);
basisSumFxn->values(basisFxnValues, sideCache);
cout << "solnFxnValues:\n" << solnFxnValues;
cout << "basisFxnValues:\n" << basisFxnValues;
}
else
{
// cout << "testBasisSumFunction: on side " << sideIndex << ", l2diff of " << l2diff << " is within tol of " << tol << endl;
}
}
}
}
}
return success;
}
int main(int argc, char *argv[])
{
#ifdef HAVE_MPI
Teuchos::GlobalMPISession mpiSession(&argc, &argv,0);
int rank=mpiSession.getRank();
int numProcs=mpiSession.getNProc();
#else
int rank = 0;
int numProcs = 1;
#endif
//////////////////// DECLARE VARIABLES ///////////////////////
// define test variables
VarFactory varFactory;
VarPtr tau = varFactory.testVar("\\tau", HDIV);
VarPtr v = varFactory.testVar("v", HGRAD);
// define trial variables
VarPtr uhat = varFactory.traceVar("\\widehat{u}");
VarPtr beta_n_u_minus_sigma_n = varFactory.fluxVar("\\widehat{\\beta \\cdot n u - \\sigma_{n}}");
VarPtr u = varFactory.fieldVar("u");
VarPtr sigma1 = varFactory.fieldVar("\\sigma_1");
VarPtr sigma2 = varFactory.fieldVar("\\sigma_2");
vector<double> beta_const;
double c = sqrt(1.25);
beta_const.push_back(1.0/c);
beta_const.push_back(.5/c);
// FunctionPtr beta = Teuchos::rcp(new Beta());
double eps = 1e-3;
//////////////////// DEFINE BILINEAR FORM ///////////////////////
BFPtr confusionBF = Teuchos::rcp( new BF(varFactory) );
// tau terms:
confusionBF->addTerm(sigma1 / eps, tau->x());
confusionBF->addTerm(sigma2 / eps, tau->y());
confusionBF->addTerm(u, tau->div());
confusionBF->addTerm(-uhat, tau->dot_normal());
// v terms:
confusionBF->addTerm( sigma1, v->dx() );
confusionBF->addTerm( sigma2, v->dy() );
confusionBF->addTerm( beta_const * u, - v->grad() );
confusionBF->addTerm( beta_n_u_minus_sigma_n, v);
//////////////////// DEFINE INNER PRODUCT(S) ///////////////////////
// quasi-optimal norm
IPPtr qoptIP = Teuchos::rcp(new IP);
qoptIP->addTerm( v );
qoptIP->addTerm( tau / eps + v->grad() );
qoptIP->addTerm( beta_const * v->grad() - tau->div() );
// robust test norm
IPPtr robIP = Teuchos::rcp(new IP);
FunctionPtr ip_scaling = Teuchos::rcp( new EpsilonScaling(eps) );
if (enforceLocalConservation)
{
robIP->addZeroMeanTerm( v );
}
else
{
robIP->addTerm( ip_scaling * v );
}
robIP->addTerm( sqrt(eps) * v->grad() );
bool useNewBC = false;
FunctionPtr weight = Teuchos::rcp( new SqrtWeight(eps) );
if (useNewBC)
{
robIP->addTerm( beta_const * v->grad() );
robIP->addTerm( tau->div() );
robIP->addTerm( ip_scaling/sqrt(eps) * tau );
}
else
{
robIP->addTerm( weight * beta_const * v->grad() );
robIP->addTerm( weight * tau->div() );
robIP->addTerm( weight * ip_scaling/sqrt(eps) * tau );
}
//////////////////// SPECIFY RHS ///////////////////////
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
Teuchos::RCP<RHSEasy> rhs = Teuchos::rcp( new RHSEasy );
FunctionPtr f = zero;
rhs->addTerm( f * v ); // obviously, with f = 0 adding this term is not necessary!
//////////////////// CREATE BCs ///////////////////////
Teuchos::RCP<BCEasy> bc = Teuchos::rcp( new BCEasy );
SpatialFilterPtr inflowBoundary = Teuchos::rcp( new InflowSquareBoundary );
SpatialFilterPtr outflowBoundary = Teuchos::rcp( new OutflowSquareBoundary );
FunctionPtr u0 = Teuchos::rcp( new U0 );
FunctionPtr n = Teuchos::rcp( new UnitNormalFunction );
bc->addDirichlet(uhat, outflowBoundary, zero);
if (useNewBC)
{
bc->addDirichlet(beta_n_u_minus_sigma_n, inflowBoundary, beta_const*n*u0);
}
else
{
SpatialFilterPtr inflowBot = Teuchos::rcp( new InflowSquareBot );
SpatialFilterPtr inflowLeft = Teuchos::rcp( new InflowSquareLeft );
bc->addDirichlet(beta_n_u_minus_sigma_n, inflowLeft, beta_const*n*u0);
bc->addDirichlet(uhat, inflowBot, u0);
}
// Teuchos::RCP<PenaltyConstraints> pc = Teuchos::rcp(new PenaltyConstraints);
// pc->addConstraint(uhat==u0,inflowBoundary);
//////////////////// BUILD MESH ///////////////////////
// define nodes for mesh
int H1Order = 2, pToAdd = 2;
FieldContainer<double> quadPoints(4,2);
quadPoints(0,0) = 0.0; // x1
quadPoints(0,1) = 0.0; // y1
quadPoints(1,0) = 1.0;
quadPoints(1,1) = 0.0;
quadPoints(2,0) = 1.0;
quadPoints(2,1) = 1.0;
quadPoints(3,0) = 0.0;
quadPoints(3,1) = 1.0;
int nCells = 2;
int horizontalCells = nCells, verticalCells = nCells;
// create a pointer to a new mesh:
Teuchos::RCP<Mesh> mesh = Mesh::buildQuadMesh(quadPoints, horizontalCells, verticalCells,
confusionBF, H1Order, H1Order+pToAdd);
//////////////////// SOLVE & REFINE ///////////////////////
Teuchos::RCP<Solution> solution = Teuchos::rcp( new Solution(mesh, bc, rhs, robIP) );
// solution->setFilter(pc);
if (enforceLocalConservation)
{
FunctionPtr zero = Teuchos::rcp( new ConstantScalarFunction(0.0) );
solution->lagrangeConstraints()->addConstraint(beta_n_u_minus_sigma_n == zero);
}
double energyThreshold = 0.2; // for mesh refinements
RefinementStrategy refinementStrategy( solution, energyThreshold );
int numRefs = 9;
for (int refIndex=0; refIndex<numRefs; refIndex++)
{
solution->solve(false);
refinementStrategy.refine(rank==0); // print to console on rank 0
}
// one more solve on the final refined mesh:
solution->solve(false);
if (rank==0)
{
solution->writeToVTK("Hughes.vtu",min(H1Order+1,4));
solution->writeFluxesToFile(uhat->ID(), "uhat.dat");
cout << "wrote files: u.m, uhat.dat\n";
}
return 0;
}
