void FluxTrace<D>::T_CalcElementMatrix (const FiniteElement & base_fel,
const ElementTransformation & eltrans,
FlatMatrix<SCAL> elmat,
LocalHeap & lh) const {
const CompoundFiniteElement & cfel // product space
= dynamic_cast<const CompoundFiniteElement&> (base_fel);
const HDivFiniteElement<D> & fel_q = // q space
dynamic_cast<const HDivFiniteElement<D>& > (cfel[GetInd1()]);
const ScalarFiniteElement<D> & fel_e = // e space
dynamic_cast<const ScalarFiniteElement<D>&> (cfel[GetInd2()]);
elmat = SCAL(0.0);
IntRange rq = cfel.GetRange(GetInd1());
IntRange re = cfel.GetRange(GetInd2());
int ndofq = rq.Size();
int ndofe = re.Size();
FlatMatrix<SCAL> submat(ndofe,ndofq,lh);
FlatMatrixFixWidth<D> shapeq(ndofq,lh); // q-basis (vec) values
FlatVector<> shapee(ndofe,lh); // e-basis basis
ELEMENT_TYPE eltype // get the type of element:
= fel_q.ElementType(); // ET_TRIG in 2d, ET_TET in 3d.
// transform facet integration points to volume integration points
Facet2ElementTrafo transform(eltype);
int nfa = ElementTopology::GetNFacets(eltype); /* nfa = number of facets
of an element */
submat = 0.0;
for(int k = 0; k<nfa; k++) {
// type of geometry of k-th facet
ELEMENT_TYPE eltype_facet = ElementTopology::GetFacetType(eltype, k);
const IntegrationRule & facet_ir =
SelectIntegrationRule (eltype_facet, fel_q.Order()+fel_e.Order());
// reference element normal vector
FlatVec<D> normal_ref = ElementTopology::GetNormals(eltype) [k];
for (int l = 0; l < facet_ir.GetNIP(); l++) {
// map 1D facet points to volume integration points
IntegrationPoint volume_ip = transform(k, facet_ir[l]);
MappedIntegrationPoint<D,D> mip (volume_ip, eltrans);
// compute normal on physcial element
Mat<D> inv_jac = mip.GetJacobianInverse();
double det = mip.GetJacobiDet();
Vec<D> normal = fabs(det) * Trans(inv_jac) * normal_ref;
double len = L2Norm(normal);
normal /= len;
double weight = facet_ir[l].Weight()*len;
// mapped H(div) basis fn values and DG fn (no need to map) values
fel_q.CalcMappedShape(mip,shapeq);
fel_e.CalcShape(volume_ip,shapee);
// evaluate coefficient
SCAL dd = coeff_d -> T_Evaluate<SCAL>(mip);
// [ndofe x 1] [ndofq x D] * [D x 1]
submat += (dd*weight) * shapee * Trans( shapeq * normal ) ;
}
}
elmat.Rows(re).Cols(rq) += submat;
elmat.Rows(rq).Cols(re) += Conj(Trans(submat));
}
void TraceTrace<D>::T_CalcElementMatrix (const FiniteElement & base_fel,
const ElementTransformation & eltrans,
FlatMatrix<SCAL> elmat,
LocalHeap & lh) const {
const CompoundFiniteElement & cfel // product space
= dynamic_cast<const CompoundFiniteElement&> (base_fel);
const ScalarFiniteElement<D> & fel_u = // u space
dynamic_cast<const ScalarFiniteElement<D>&> (cfel[GetInd1()]);
const ScalarFiniteElement<D> & fel_e = // e space
dynamic_cast<const ScalarFiniteElement<D>&> (cfel[GetInd2()]);
elmat = SCAL(0.0);
IntRange ru = cfel.GetRange(GetInd1());
IntRange re = cfel.GetRange(GetInd2());
int ndofe = re.Size();
int ndofu = ru.Size();
FlatVector<> shapee(ndofe,lh);
FlatVector<> shapeu(ndofu,lh);
FlatMatrix<SCAL> submat(ndofe,ndofu, lh);
submat = SCAL(0.0);
ELEMENT_TYPE eltype = fel_u.ElementType();
Facet2ElementTrafo transform(eltype);
int nfa = ElementTopology :: GetNFacets(eltype);
for(int k = 0; k<nfa; k++) {
// type of geometry of k-th facet
ELEMENT_TYPE eltype_facet = ElementTopology::GetFacetType(eltype, k);
const IntegrationRule & facet_ir =
SelectIntegrationRule (eltype_facet, fel_u.Order()+fel_e.Order());
// reference element normal vector
FlatVec<D> normal_ref = ElementTopology::GetNormals(eltype) [k];
for (int l = 0; l < facet_ir.GetNIP(); l++) {
// map 1D facet points to volume integration points
IntegrationPoint volume_ip = transform(k, facet_ir[l]);
MappedIntegrationPoint<D,D> mip (volume_ip, eltrans);
// compute normal on physcial element
Mat<D> inv_jac = mip.GetJacobianInverse();
double det = mip.GetJacobiDet();
Vec<D> normal = fabs(det) * Trans(inv_jac) * normal_ref;
double len = L2Norm(normal);
normal /= len;
double weight = facet_ir[l].Weight()*len;
fel_e.CalcShape(volume_ip,shapee);
fel_u.CalcShape(volume_ip,shapeu);
SCAL cc = coeff_c -> T_Evaluate<SCAL>(mip);
// [ndofe x 1] [1 x ndofu]
submat += (cc*weight) * shapee * Trans(shapeu);
}
}
elmat.Rows(re).Cols(ru) += submat;
if (GetInd1() != GetInd2())
elmat.Rows(ru).Cols(re) += Conj(Trans(submat));
}