void ScalarFiniteElement<D> ::
CalcMappedDShape (const MappedIntegrationPoint<D,D> & mip,
SliceMatrix<> dshape) const
{
CalcDShape (mip.IP(), dshape);
for (int i = 0; i < dshape.Height(); i++)
{
Vec<D> hv = dshape.Row(i);
FlatVec<D> (&dshape(i,0)) = Trans (mip.GetJacobianInverse ()) * hv;
}
}
void ScalarFiniteElement<D> :: CalcMappedDDShape (const MappedIntegrationPoint<D,D> & mip,
FlatMatrix<> ddshape) const
{
int nd = GetNDof();
double eps = 1e-7;
MatrixFixWidth<D> dshape1(nd), dshape2(nd);
const ElementTransformation & eltrans = mip.GetTransformation();
for (int i = 0; i < D; i++)
{
IntegrationPoint ip1 = mip.IP();
IntegrationPoint ip2 = mip.IP();
ip1(i) -= eps;
ip2(i) += eps;
MappedIntegrationPoint<D,D> mip1(ip1, eltrans);
MappedIntegrationPoint<D,D> mip2(ip2, eltrans);
CalcMappedDShape (mip1, dshape1);
CalcMappedDShape (mip2, dshape2);
ddshape.Cols(D*i,D*(i+1)) = (0.5/eps) * (dshape2-dshape1);
}
for (int j = 0; j < D; j++)
{
for (int k = 0; k < nd; k++)
for (int l = 0; l < D; l++)
dshape1(k,l) = ddshape(k, l*D+j);
dshape2 = dshape1 * mip.GetJacobianInverse();
for (int k = 0; k < nd; k++)
for (int l = 0; l < D; l++)
ddshape(k, l*D+j) = dshape2(k,l);
}
}