void GradGrad<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);
// u dofs [ru.First() : ru.Next()-1], e dofs [re.First() : re.Next()-1]
IntRange ru = cfel.GetRange(GetInd1());
IntRange re = cfel.GetRange(GetInd2());
int ndofe = re.Size();
int ndofu = ru.Size();
FlatMatrixFixWidth<D> dum(ndofu,lh); // to store grad(u-basis)
FlatMatrixFixWidth<D> dem(ndofe,lh); // to store grad(e-basis)
ELEMENT_TYPE eltype // get the type of element:
= fel_u.ElementType(); // ET_TRIG in 2d, ET_TET in 3d.
const IntegrationRule & // Note: p = fel_u.Order()-1
ir = SelectIntegrationRule(eltype, fel_u.Order()+fel_e.Order()-2);
FlatMatrix<SCAL> submat(ndofe,ndofu,lh);
submat = 0.0;
for(int k=0; k<ir.GetNIP(); k++) {
MappedIntegrationPoint<D,D> mip (ir[k],eltrans);
// set grad(u-basis) and grad(e-basis) at mapped pts in dum and dem.
fel_u.CalcMappedDShape( mip, dum );
fel_e.CalcMappedDShape( mip, dem );
// evaluate coefficient
SCAL fac = coeff_a -> T_Evaluate<SCAL>(mip);
fac *= mip.GetWeight() ;
// [ndofe x D] * [D x ndofu]
submat += fac * dem * Trans(dum) ;
}
elmat.Rows(re).Cols(ru) += submat;
if (GetInd1() != GetInd2())
elmat.Rows(ru).Cols(re) += Conj(Trans(submat));
}
void FluxFluxBoundary<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);
// This FE is already multiplied by normal:
const HDivNormalFiniteElement<D-1> & fel_q = // q.n space
dynamic_cast<const HDivNormalFiniteElement<D-1>&> (cfel[GetInd1()]);
const HDivNormalFiniteElement<D-1> & fel_r = // r.n space
dynamic_cast<const HDivNormalFiniteElement<D-1>&> (cfel[GetInd2()]);
elmat = SCAL(0.0);
IntRange rq = cfel.GetRange(GetInd1());
IntRange rr = cfel.GetRange(GetInd2());
int ndofq = rq.Size();
int ndofr = rr.Size();
FlatMatrix<SCAL> submat(ndofr, ndofq, lh);
submat = SCAL(0.0);
FlatVector<> qshape(fel_q.GetNDof(), lh);
FlatVector<> rshape(fel_r.GetNDof(), lh);
const IntegrationRule ir(fel_q.ElementType(),
fel_q.Order() + fel_r.Order());
for (int i = 0 ; i < ir.GetNIP(); i++) {
MappedIntegrationPoint<D-1,D> mip(ir[i], eltrans);
SCAL cc = coeff_c -> T_Evaluate<SCAL>(mip);
fel_r.CalcShape (ir[i], rshape);
fel_q.CalcShape (ir[i], qshape);
// mapped q.n-shape is simply reference q.n-shape / measure
qshape *= 1.0/mip.GetMeasure();
rshape *= 1.0/mip.GetMeasure();
// [ndofr x 1] [1 x ndofq]
submat += (cc*mip.GetWeight()) * rshape * Trans(qshape);
}
elmat.Rows(rr).Cols(rq) += submat;
if (GetInd1() != GetInd2())
elmat.Rows(rq).Cols(rr) += Conj(Trans(submat));
}
void DGFiniteElement<D>::
CalcGradientMatrix (FlatMatrix<> gmat) const
{
IntegrationRule ir (this->ElementType(), 2*order);
Vector<> shape(ndof);
MatrixFixWidth<D> dshape(ndof);
Vector<> norms(ndof);
gmat = 0.0;
norms = 0.0;
for (int i = 0; i < ir.Size(); i++)
{
this -> CalcShape (ir[i], shape);
this -> CalcDShape (ir[i], dshape);
for (int j = 0; j < ndof; j++)
for (int k = 0; k < ndof; k++)
for (int l = 0; l < D; l++)
gmat(k*D+l, j) += ir[i].Weight() * dshape(j,l) * shape(k);
for (int j = 0; j < norms.Size(); j++)
norms(j) += ir[i].Weight() * sqr (shape(j));
}
for (int j = 0; j < ndof; j++)
gmat.Rows(D*j, D*(j+1)) /= norms(j);
}
void TraceTraceBoundary<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);
// get surface elements
const ScalarFiniteElement<D-1> & fel_u = // u space
dynamic_cast<const ScalarFiniteElement<D-1>&> (cfel[GetInd1()]);
const ScalarFiniteElement<D-1> & fel_e = // u space
dynamic_cast<const ScalarFiniteElement<D-1>&> (cfel[GetInd2()]);
elmat = SCAL(0.0);
IntRange ru = cfel.GetRange(GetInd1());
IntRange re = cfel.GetRange(GetInd2());
int ndofu = ru.Size();
int ndofe = re.Size();
FlatMatrix<SCAL> submat(ndofe, ndofu, lh);
submat = SCAL(0.0);
FlatVector<> ushape(fel_u.GetNDof(), lh);
FlatVector<> eshape(fel_e.GetNDof(), lh);
const IntegrationRule ir(fel_u.ElementType(),
fel_u.Order() + fel_e.Order());
for (int i = 0 ; i < ir.GetNIP(); i++) {
MappedIntegrationPoint<D-1,D> mip(ir[i], eltrans);
SCAL cc = coeff_c -> T_Evaluate<SCAL>(mip);
fel_u.CalcShape (ir[i], ushape);
fel_e.CalcShape (ir[i], eshape);
// [ndofe x 1] [1 x ndofu]
submat += (cc*mip.GetWeight()) * eshape * Trans(ushape);
}
elmat.Rows(re).Cols(ru) += submat;
if (GetInd1() != GetInd2())
elmat.Rows(ru).Cols(re) += Conj(Trans(submat));
}
void EyeEye<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();
Vector<> ushape(ndofu);
Vector<> eshape(ndofe);
ELEMENT_TYPE eltype = fel_u.ElementType();
const IntegrationRule &
ir = SelectIntegrationRule(eltype, fel_u.Order()+fel_e.Order());
FlatMatrix<SCAL> submat(ndofe,ndofu,lh);
submat = SCAL(0.0);
for(int k=0; k<ir.GetNIP(); k++) {
MappedIntegrationPoint<D,D> mip (ir[k],eltrans);
fel_u.CalcShape( ir[k], ushape );
fel_e.CalcShape( ir[k], eshape );
SCAL fac = (coeff_a -> T_Evaluate<SCAL>(mip))* mip.GetWeight() ;
// [ndofe x D] * [D x ndofu]
submat += fac * eshape * Trans(ushape) ;
}
elmat.Rows(re).Cols(ru) += submat;
if (GetInd1() != GetInd2())
elmat.Rows(ru).Cols(re) += Conj(Trans(submat));
}
void CalcSchurComplement (const FlatMatrix<double> a,
FlatMatrix<double> s,
const BitArray & used,
LocalHeap & lh)
{
if (s.Height() == 0) return;
if (s.Height() == a.Height())
{
s = a;
return;
}
HeapReset hr(lh);
int n = a.Height();
Array<int> used_dofs(n, lh);
Array<int> unused_dofs(n, lh);
used_dofs.SetSize(0);
unused_dofs.SetSize(0);
for (int i = 0; i < n; i++)
if (used[i])
used_dofs.Append(i);
else
unused_dofs.Append(i);
s = a.Rows(used_dofs).Cols(used_dofs);
FlatMatrix<> b1 = a.Rows(unused_dofs).Cols(used_dofs) | lh;
FlatMatrix<> b2 = a.Rows(used_dofs).Cols(unused_dofs) | lh;
FlatMatrix<> c = a.Rows(unused_dofs).Cols(unused_dofs) | lh;
FlatMatrix<> hb1 (b1.Height(), b1.Width(), lh);
if (n > 10)
{
LapackInverse (c);
hb1 = c * b1 | Lapack;
s -= b2 * hb1 | Lapack;
}
else
{
CalcInverse (c);
hb1 = c * b1;
s -= b2 * hb1;
}
}
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 RobinVolume<D> ::
T_CalcElementMatrix (const FiniteElement & base_fel,
const ElementTransformation & eltrans,
FlatMatrix<SCAL> elmat,
LocalHeap & lh) const {
ELEMENT_TYPE eltype
= base_fel.ElementType();
const CompoundFiniteElement & cfel // product space
= dynamic_cast<const CompoundFiniteElement&> (base_fel);
// note how we do NOT refer to D-1 elements here:
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);
IntRange ru = cfel.GetRange(GetInd1());
IntRange re = cfel.GetRange(GetInd2());
int ndofe = re.Size();
int ndofu = ru.Size();
FlatVector<> ushape(fel_u.GetNDof(), lh);
FlatVector<> eshape(fel_e.GetNDof(), lh);
FlatMatrix<SCAL> submat(ndofe,ndofu,lh);
submat = SCAL(0);
int nfacet = ElementTopology::GetNFacets(eltype);
Facet2ElementTrafo transform(eltype);
FlatVector< Vec<D> > normals = ElementTopology::GetNormals<D>(eltype);
const MeshAccess & ma = *(const MeshAccess*)eltrans.GetMesh();
Array<int> fnums, sels;
ma.GetElFacets (eltrans.GetElementNr(), fnums);
for (int k = 0; k < nfacet; k++) {
ma.GetFacetSurfaceElements (fnums[k], sels);
// if interior element, then do nothing:
if (sels.Size() == 0) continue;
// else:
Vec<D> normal_ref = normals[k];
ELEMENT_TYPE etfacet=ElementTopology::GetFacetType(eltype, k);
IntegrationRule ir_facet(etfacet, fel_e.Order()+fel_u.Order());
// map the facet integration points to volume reference elt ipts
IntegrationRule & ir_facet_vol = transform(k, ir_facet, lh);
// ... and further to the physical element
MappedIntegrationRule<D,D> mir(ir_facet_vol, eltrans, lh);
for (int i = 0 ; i < ir_facet_vol.GetNIP(); i++) {
SCAL val = coeff_c->T_Evaluate<SCAL> (mir[i]);
// this is contrived to get the surface measure in "len"
Mat<D> inv_jac = mir[i].GetJacobianInverse();
double det = mir[i].GetMeasure();
Vec<D> normal = det * Trans (inv_jac) * normal_ref;
double len = L2Norm (normal);
val *= len * ir_facet[i].Weight();
fel_u.CalcShape (ir_facet_vol[i], ushape);
fel_e.CalcShape (ir_facet_vol[i], eshape);
submat += val * eshape * Trans(ushape);
}
}
elmat.Rows(re).Cols(ru) += submat;
if (GetInd1() != GetInd2())
elmat.Rows(ru).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));
}
