MaximalQuadratureIntegral::MaximalQuadratureIntegral(
const CellType& cellType,
const QuadratureFamily& quad,
const ParametrizedCurve& globalCurve,
const Mesh& mesh,
int verb)
: ElementIntegral(dimension(cellType), cellType, dimension(cellType),
cellType, true, globalCurve, mesh, verb),
quad_(quad),
quadPts_(),
quadWeights_(),
W_(),
useSumFirstMethod_(true)
{
Tabs tab0(0);
SUNDANCE_MSG1(setupVerb(), tab0 << "MaximalQuadratureIntegral ctor for 0-form");
if (setupVerb()) describe(Out::os());
SUNDANCE_MSG1(setupVerb(), tab0 << "quadrature family=" << quad);
/* create the quad points and weights */
quad.getPoints(cellType, quadPts_, quadWeights_);
int nQuad = quadPts_.size();
W_.resize(nQuad);
for (int q=0; q<nQuad; q++)
{
W_[q] = quadWeights_[q];
}
}
void ElementIntegral::getQuad(const QuadratureFamily& quad,
int evalCase, Array<Point>& quadPts, Array<double>& quadWeights) const
{
Tabs tab(0);
SUNDANCE_MSG2(setupVerb(), tab << "getting quad points for rule "
<< quad);
if (nFacetCases()==1)
{
quad.getPoints(cellType(), quadPts, quadWeights);
}
else
{
int dim = dimension(cellType());
quad.getFacetPoints(maxCellType(), dim, evalCase,
quadPts, quadWeights);
}
if (setupVerb() >= 4)
{
Tabs tab1;
SUNDANCE_MSG4(setupVerb(),
tab1 << "quadrature points on ref cell are:");
printQuad(Out::os(), quadPts, quadWeights);
}
}
IQI_HdivLF_DivV_Cell::IQI_HdivLF_DivV_Cell( int spatialDim,
const CellType& maxCellType,
const BasisFamily& testBasis,
const QuadratureFamily& quad,
const ParameterList& verbParams):
ElementIntegralLinearFormCell( spatialDim ,
maxCellType ,
testBasis ,
quad ,
verbParams ),
DivV_( testBasis.nReferenceDOFs(maxCellType,maxCellType) , quad.getNumPoints(maxCellType) ),
QP_( quad.getNumPoints( maxCellType ) , spatialDim ),
QW_( quad.getNumPoints( maxCellType ) )
{
// bypass testBasis.refEval and use Intrepid to fill DivV
// warning: only works on tets right now.
Intrepid::Basis_HDIV_TET_I1_FEM<double,Intrepid::FieldContainer<double> > myBasis;
// move quadrature points into a field container
Array<Point> qpSundance;
Array<double> qwSundance;
quad.getPoints( maxCellType , qpSundance , qwSundance );
for (int i=0;i<(int)qpSundance.size();i++) {
for (int j=0;j<3;j++) {
QP_(i,j) = qpSundance[i][j];
}
QW_(i)=qwSundance[i];
}
// now tabulate the divergences
myBasis.getValues( DivV_ , QP_ , Intrepid::OPERATOR_DIV );
}
CurveEvalMediator::CurveEvalMediator(
const Mesh& mesh, const ParametrizedCurve& paramcurve ,
int cellDim, const QuadratureFamily& quad) : StdFwkEvalMediator(mesh, cellDim) ,
numEvaluationCases_(-1),
quad_(quad),
numQuadPtsForMaxCell_(0) ,
paramcurve_(paramcurve) {
// set the cell types
maxCellType_ = mesh.cellType(mesh.spatialDim() );
curveCellType_ = mesh.cellType(mesh.spatialDim()-1);
// detect the (constant) quadrature points (we must have the same nr quad points per cell!!!)
Array<Point> quadPoints;
Array<double> quadWeights;
quad.getPoints(curveCellType_ , quadPoints , quadWeights );
numQuadPtsForMaxCell_ = quadWeights.size();
}
RefIntegral::RefIntegral(int spatialDim,
const CellType& maxCellType,
int dim,
const CellType& cellType,
const QuadratureFamily& quad_in,
bool isInternalBdry,
const ParametrizedCurve& globalCurve,
const Mesh& mesh,
int verb)
: ElementIntegral(spatialDim, maxCellType, dim, cellType, isInternalBdry, globalCurve , mesh,
verb), W_()
{
Tabs tab0(0);
SUNDANCE_MSG1(setupVerb(),
tab0 << "************* creating reference 0-form integrals ********");
if (setupVerb()) describe(Out::os());
/* we need to sum the quadrature weights
to compute the volume of the reference cell */
QuadratureFamily quad = new GaussianQuadrature(2);
/* If we have a valid curve (in case of Adaptive Cell Integration)
* then we have to choose the quadrature which the user specified*/
if (globalCurve.isCurveValid()){
quad = quad_in;
Tabs tab1;
SUNDANCE_MSG1(setupVerb(),tab1 << "ACI change quadrature to Quadrature of order: "<<quad.order());
}
quad_ = quad;
Array<Point> quadPts;
Array<double> quadWeights;
W_.resize(1);
W_[0].resize(1);
quad.getPoints(cellType, quadPts, quadWeights);
quadWeights_ = quadWeights;
for (int q=0; q<quadWeights.size(); q++) {
W_[0][0] += quadWeights[q];
}
}
int main(int argc, char** argv)
{
try
{
GlobalMPISession session(&argc, &argv);
TimeMonitor t(totalTimer());
int pMax = 1;
int dim=2;
CellType cellType = TriangleCell;
Point a = Point(0.0, 0.0);
Point b = Point(1.0, 0.0);
Point c = Point(0.0, 1.0);
CellJacobianBatch JBatch;
JBatch.resize(1, 2, 2);
double* J = JBatch.jVals(0);
J[0] = b[0] - a[0];
J[1] = c[0] - a[0];
J[2] = b[1] - a[1];
J[3] = c[1] - a[1];
bool isInternalBdry=false;
/* ------ evaluate Lagrange and FIAT-Lagrange at the vertices */
Array<Point> verts = tuple(a,b,c);
BasisFamily lagrange = new Lagrange(1);
BasisFamily fiatLagrange = new Lagrange(1);
MultiIndex d0(0,0,0);
MultiIndex dx(1,0,0);
MultiIndex dy(0,1,0);
Array<Array<Array<double> > > result;
Array<int> dummy;
std::cerr << "------ Evaluating bases at vertices ----------" << std::endl
<< std::endl;
std::cerr << "Evaluating phi(vert) with FIAT-Lagrange" << std::endl;
fiatLagrange.ptr()->refEval(cellType, verts, d0, result);
std::cerr << "results = " << result << std::endl << std::endl;
std::cerr << "Evaluating phi(vert) with Lagrange" << std::endl;
lagrange.ptr()->refEval(cellType, verts, d0, result);
std::cerr << "results = " << result << std::endl << std::endl;
std::cerr << std::endl ;
std::cerr << "Evaluating Dx*phi(vert) with FIAT-Lagrange" << std::endl;
fiatLagrange.ptr()->refEval(cellType, verts, dx, result);
std::cerr << "results = " << result << std::endl << std::endl;
std::cerr << "Evaluating Dx*phi(vert) with Lagrange" << std::endl;
lagrange.ptr()->refEval(cellType, verts, dx, result);
std::cerr << "results = " << result << std::endl << std::endl;
std::cerr << std::endl ;
std::cerr << "Evaluating Dy*phi(vert) with FIAT-Lagrange" << std::endl;
fiatLagrange.ptr()->refEval(cellType, verts, dy, result);
std::cerr << "results = " << result << std::endl << std::endl;
std::cerr << "Evaluating Dy*phi(vert) with Lagrange" << std::endl;
lagrange.ptr()->refEval(cellType, verts, dy, result);
std::cerr << "results = " << result << std::endl << std::endl;
/* --------- evaluate integrals over elements ----------- */
RCP<Array<double> > A = rcp(new Array<double>());
QuadratureFamily quad = new GaussianQuadrature(4);
Array<double> quadWeights;
Array<Point> quadPts;
quad.getPoints(cellType, quadPts, quadWeights);
int nQuad = quadPts.size();
Array<double> coeff(nQuad);
for (int i=0; i<nQuad; i++)
{
double s = quadPts[i][0];
double t = quadPts[i][1];
double x = a[0] + J[0]*s + J[1]*t;
double y = a[1] + J[2]*s + J[3]*t;
coeff[i] = x*y;
}
const double* const f = &(coeff[0]);
std::cerr << std::endl << std::endl
<< "---------------- One-forms --------------------"
<< std::endl << std::endl;
for (int p=1; p<=pMax; p++)
{
BasisFamily P = new Lagrange(p);
for (int dp=0; dp<=1; dp++)
{
if (dp > p) continue;
Tabs tab0;
std::cerr << tab0 << "test function deriv order = " << dp << std::endl;
int numTestDir = 1;
if (dp==1) numTestDir = dim;
for (int t=0; t<numTestDir; t++)
{
int alpha = t;
Tabs tab;
QuadratureIntegral ref(dim, cellType, dim, cellType, P, alpha, dp, quad, isInternalBdry);
A->resize(ref.nNodesTest());
ref.transformOneForm(JBatch, JBatch, dummy, f, A);
std::cerr << tab << "test deriv direction =" << t << std::endl;
std::cerr << tab << "transformed local vector: " << std::endl;
std::cerr << tab << "{";
for (int r=0; r<ref.nNodesTest(); r++)
{
if (r!=0) std::cerr << ", ";
std::cerr << (*A)[r];
}
std::cerr << "}" << std::endl << std::endl;
}
}
}
std::cerr << std::endl << std::endl
<< "---------------- Two-forms --------------------"
<< std::endl << std::endl;
for (int p=1; p<=pMax; p++)
{
BasisFamily P = new Lagrange(p);
for (int q=1; q<=pMax; q++)
{
BasisFamily Q = new Lagrange(q);
for (int dp=0; dp<=1; dp++)
{
if (dp > p) continue;
Tabs tab0;
std::cerr << tab0 << "test function deriv order = " << dp << std::endl;
for (int dq=0; dq<=1; dq++)
{
if (dq > q) continue;
Tabs tab1;
std::cerr << tab1
<< "unk function deriv order = " << dq << std::endl;
int numTestDir = 1;
if (dp==1) numTestDir = dim;
for (int t=0; t<numTestDir; t++)
{
int alpha = t;
int numUnkDir = 1;
if (dq==1) numUnkDir = dim;
for (int u=0; u<numUnkDir; u++)
{
Tabs tab;
int beta = u;
QuadratureIntegral ref(dim, cellType, dim, cellType, P, alpha,
dp, Q, beta, dq, quadd, isInternalBdry);
A->resize(ref.nNodesTest()*ref.nNodesUnk());
ref.transformTwoForm(JBatch, JBatch, dummy, f, A);
std::cerr << tab << "test deriv direction =" <<
t << ", unk deriv direction =" << u << std::endl;
std::cerr << tab << "transformed local stiffness matrix" << std::endl;
std::cerr << tab << "{";
for (int r=0; r<ref.nNodesTest(); r++)
{
if (r!=0) std::cerr << ", ";
std::cerr << "{";
for (int c=0; c<ref.nNodesUnk(); c++)
{
if (c!=0) std::cerr << ", ";
std::cerr << chop((*A)[r + ref.nNodesTest()*c]);
}
std::cerr << "}";
}
std::cerr << "}" << std::endl << std::endl;
}
}
}
}
}
}
TimeMonitor::summarize();
}
catch(std::exception& e)
{
std::cerr << e.what() << std::endl;
}
}
void checkbasis( BasisFamily &b1 , BasisFamily &b2 )
{
int maxDim=3;
double tol = 1.0e-13;
int maxDiffOrder = 0;
int numErrors = 0;
QuadratureFamily quad = new GaussianQuadrature(4);
for (int spatialDim=1; spatialDim<=maxDim; spatialDim++) {
std::cerr << "\t" << "spatial dimension =" << spatialDim << std::endl;
for (int cellDim=0; cellDim<=spatialDim; cellDim++) {
std::cerr << "\t\t" << "cell dimension =" << cellDim << std::endl;
CellType cellType;
if (cellDim==0) cellType=PointCell;
if (cellDim==1) cellType=LineCell;
if (cellDim==2) cellType=TriangleCell;
if (cellDim==3) cellType=TetCell;
Array<Point> qPts;
Array<double> qWts;
quad.getPoints(cellType, qPts, qWts);
for (int d=0; d<=maxDiffOrder; d++) {
if (cellDim==0 && d>0) continue;
cerr << "\t\t\t" << "differentiation order = " << d << std::endl;
for (int dir=0; dir<iPow(cellDim, d); dir++) {
std::cerr << "\t\t\t\t" << "direction = " << dir << std::endl;
MultiIndex mi;
mi[dir]=d;
Array<Array<double> > values1;
Array<Array<double> > values2;
std::cerr << "\t\t\t\t" << "computing basis1...";
b1.ptr()->refEval(spatialDim, cellType, qPts, mi, values1);
std::cerr << "done" << std::endl << "\t\t\t\t" << "computing basis2...";
b2.ptr()->refEval(spatialDim, cellType, qPts, mi, values2);
std::cerr << "done" << std::endl;
int nNodes1 = b1.ptr()->nNodes(spatialDim, cellType);
int nNodes2 = b2.ptr()->nNodes(spatialDim, cellType);
std::cerr << "\t\t\t\t" << "num nodes: basis1=" << nNodes1
<< " basis2=" << nNodes2 << std::endl;
if (nNodes1 != nNodes2) {
std::cerr << "******** ERROR: node counts should be equal" << std::endl;
numErrors++;
continue;
}
if (values1.size() != values2.size()) {
std::cerr << "******** ERROR: value array outer sizes should be equal" << std::endl;
numErrors++;
continue;
}
if (values1.size() != qPts.size()) {
std::cerr << "******** ERROR: value array outer size should be equal to number of quad points" << std::endl;
numErrors++;
continue;
}
for (int q=0; q<qPts.length(); q++) {
if (values1[q].length() != nNodes1) {
std::cerr << "******** ERROR: value array inner size should be equal to number of nodes" << std::endl;
numErrors++;
continue;
}
std::cerr << "\t\t\t\t\t" << "quad point q=" << q << " pt=" << qPts[q]
<< std::endl;
for (int n=0; n<nNodes1; n++) {
std::cerr << "\t\t\t\t\t\t" << "node n=" << n << " phi1="
<< values1[q][n]
<< " phi2=" << values2[q][n]
<< " |phi1-phi2|=" << fabs(values1[q][n]-values2[q][n])
<< std::endl;
if (fabs(values1[q][n]-values2[q][n]) > tol) {
cout << "ERROR" << std::endl; numErrors++;
}
}
}
}
}
}
}
std::cerr << std::endl << std::endl << "Summary: detected " << numErrors << " errors " << std::endl;
}
MaximalQuadratureIntegral::MaximalQuadratureIntegral(
const CellType& cellType,
const BasisFamily& testBasis,
int alpha,
int testDerivOrder,
const BasisFamily& unkBasis,
int beta,
int unkDerivOrder,
const QuadratureFamily& quad,
const ParametrizedCurve& globalCurve,
const Mesh& mesh,
int verb)
: ElementIntegral(dimension(cellType), cellType, dimension(cellType),
cellType, testBasis,
alpha, testDerivOrder, unkBasis, beta, unkDerivOrder, true,
globalCurve, mesh,
verb),
quad_(quad),
quadPts_(),
quadWeights_(),
W_(),
useSumFirstMethod_(true)
{
Tabs tab0(0);
SUNDANCE_MSG1(setupVerb(), tab0 << "MaximalQuadratureIntegral ctor for 2-form");
if (setupVerb()) describe(Out::os());
assertBilinearForm();
// store the quadrature points and weights
quad.getPoints(cellType, quadPts_, quadWeights_);
int nQuad = quadPts_.size();
W_.resize(nQuad * nRefDerivTest() * nNodesTest()
* nRefDerivUnk() * nNodesUnk());
/* compute the basis functions */
Array<Array<Array<Array<double> > > > testBasisVals(nRefDerivTest());
Array<Array<Array<Array<double> > > > unkBasisVals(nRefDerivUnk());
for (int r=0; r<nRefDerivTest(); r++)
{
testBasisVals[r].resize(testBasis.dim());
MultiIndex mi;
if (testDerivOrder==1) mi[r] = 1;
SpatialDerivSpecifier deriv(mi);
testBasis.refEval(evalCellType(), quadPts_, deriv,
testBasisVals[r], setupVerb());
}
for (int r=0; r<nRefDerivUnk(); r++)
{
unkBasisVals[r].resize(unkBasis.dim());
MultiIndex mi;
if (unkDerivOrder==1) mi[r] = 1;
SpatialDerivSpecifier deriv(mi);
unkBasis.refEval(evalCellType(),
quadPts_, deriv, unkBasisVals[r], setupVerb());
}
int vecComp = 0;
/* form the products of basis functions at each quad pt */
W_ACI_F2_.resize(nQuad);
for (int q=0; q<nQuad; q++)
{
W_ACI_F2_[q].resize(nRefDerivTest());
for (int t=0; t<nRefDerivTest(); t++)
{
W_ACI_F2_[q][t].resize(nNodesTest());
for (int nt=0; nt<nNodesTest(); nt++)
{
W_ACI_F2_[q][t][nt].resize(nRefDerivUnk());
for (int u=0; u<nRefDerivUnk(); u++)
{
W_ACI_F2_[q][t][nt][u].resize(nNodesUnk());
for (int nu=0; nu<nNodesUnk(); nu++)
{
wValue(q, t, nt, u, nu)
= chop(quadWeights_[q] * testBasisVals[t][vecComp][q][nt]
* unkBasisVals[u][vecComp][q][nu]);
W_ACI_F2_[q][t][nt][u][nu] =
chop(testBasisVals[t][vecComp][q][nt] * unkBasisVals[u][vecComp][q][nu]);
}
}
}
}
}
addFlops(3*nQuad*nRefDerivTest()*nNodesTest()*nRefDerivUnk()*nNodesUnk()
+ W_.size());
for (int i=0; i<W_.size(); i++) W_[i] = chop(W_[i]);
}
MaximalQuadratureIntegral::MaximalQuadratureIntegral(
const CellType& cellType,
const BasisFamily& testBasis,
int alpha,
int testDerivOrder,
const QuadratureFamily& quad,
const ParametrizedCurve& globalCurve,
const Mesh& mesh,
int verb)
: ElementIntegral(dimension(cellType), cellType, dimension(cellType),
cellType, testBasis,
alpha, testDerivOrder, true, globalCurve, mesh, verb),
quad_(quad),
quadPts_(),
quadWeights_(),
W_(),
useSumFirstMethod_(true)
{
Tabs tab0(0);
SUNDANCE_MSG1(setupVerb(), tab0 << "MaximalQuadratureIntegral ctor for 1-form");
if (setupVerb()) describe(Out::os());
assertLinearForm();
SUNDANCE_MSG1(setupVerb(), tab0 << "quadrature family=" << quad);
quad.getPoints(cellType, quadPts_, quadWeights_);
int nQuad = quadPts_.size();
W_.resize(nQuad * nRefDerivTest() * nNodesTest());
SUNDANCE_MSG1(setupVerb(), tab0 << "num nodes for test function " << nNodesTest());
Array<Array<Array<Array<double> > > > testBasisVals(nRefDerivTest());
for (int r=0; r<nRefDerivTest(); r++)
{
Tabs tab3;
SUNDANCE_MSG1(setupVerb(), tab3
<< "evaluating basis functions for ref deriv direction " << r);
MultiIndex mi;
testBasisVals[r].resize(testBasis.dim());
if (testDerivOrder==1) mi[r] = 1;
SpatialDerivSpecifier deriv(mi);
testBasis.refEval(evalCellType(), quadPts_, deriv,
testBasisVals[r], setupVerb());
}
int vecComp = 0;
W_ACI_F1_.resize(nQuad);
for (int q=0; q<nQuad; q++)
{
W_ACI_F1_[q].resize(nRefDerivTest());
for (int t=0; t<nRefDerivTest(); t++)
{
W_ACI_F1_[q][t].resize(nNodesTest());
for (int nt=0; nt<nNodesTest(); nt++)
{
wValue(q, t, nt)
= chop(quadWeights_[q] * testBasisVals[t][vecComp][q][nt]) ;
W_ACI_F1_[q][t][nt] = chop(testBasisVals[t][vecComp][q][nt]);
}
}
}
addFlops(2*nQuad*nRefDerivTest()*nNodesTest());
}