void H1FETransformation<OutputShape>::map_phi( const unsigned int dim,
const Elem* const elem,
const std::vector<Point>& qp,
const FEGenericBase<OutputShape>& fe,
std::vector<std::vector<OutputShape> >& phi ) const
{
switch(dim)
{
case 0:
{
for (unsigned int i=0; i<phi.size(); i++)
{
libmesh_assert_equal_to ( qp.size(), phi[i].size() );
for (unsigned int p=0; p<phi[i].size(); p++)
FEInterface::shape<OutputShape>(0, fe.get_fe_type(), elem, i, qp[p], phi[i][p]);
}
break;
}
case 1:
{
for (unsigned int i=0; i<phi.size(); i++)
{
libmesh_assert_equal_to ( qp.size(), phi[i].size() );
for (unsigned int p=0; p<phi[i].size(); p++)
FEInterface::shape<OutputShape>(1, fe.get_fe_type(), elem, i, qp[p], phi[i][p]);
}
break;
}
case 2:
{
for (unsigned int i=0; i<phi.size(); i++)
{
libmesh_assert_equal_to ( qp.size(), phi[i].size() );
for (unsigned int p=0; p<phi[i].size(); p++)
FEInterface::shape<OutputShape>(2, fe.get_fe_type(), elem, i, qp[p], phi[i][p]);
}
break;
}
case 3:
{
for (unsigned int i=0; i<phi.size(); i++)
{
libmesh_assert_equal_to ( qp.size(), phi[i].size() );
for (unsigned int p=0; p<phi[i].size(); p++)
FEInterface::shape<OutputShape>(3, fe.get_fe_type(), elem, i, qp[p], phi[i][p]);
}
break;
}
default:
libmesh_error();
}
return;
}
void HCurlFETransformation<OutputShape>::map_phi( const unsigned int dim,
const Elem* const elem,
const std::vector<Point>& qp,
const FEGenericBase<OutputShape>& fe,
std::vector<std::vector<OutputShape> >& phi ) const
{
switch(dim)
{
// These element transformations only make sense in 2D and 3D
case 0:
case 1:
{
libmesh_error();
}
case 2:
{
const std::vector<Real>& dxidx_map = fe.get_fe_map().get_dxidx();
const std::vector<Real>& dxidy_map = fe.get_fe_map().get_dxidy();
const std::vector<Real>& detadx_map = fe.get_fe_map().get_detadx();
const std::vector<Real>& detady_map = fe.get_fe_map().get_detady();
// FIXME: Need to update for 2D elements in 3D space
/* phi = (dx/dxi)^-T * \hat{phi}
In 2D:
(dx/dxi)^{-1} = [ dxi/dx dxi/dy
deta/dx deta/dy ]
so: dxi/dx^{-T} * \hat{phi} = [ dxi/dx deta/dx [ \hat{phi}_xi
dxi/dy deta/dy ] \hat{phi}_eta ]
or in indicial notation: phi_j = xi_{i,j}*\hat{phi}_i */
for (unsigned int i=0; i<phi.size(); i++)
for (unsigned int p=0; p<phi[i].size(); p++)
{
// Need to temporarily cache reference shape functions
// TODO: PB: Might be worth trying to build phi_ref separately to see
// if we can get vectorization
OutputShape phi_ref;
FEInterface::shape<OutputShape>(2, fe.get_fe_type(), elem, i, qp[p], phi_ref);
phi[i][p](0) = dxidx_map[p]*phi_ref.slice(0) + detadx_map[p]*phi_ref.slice(1);
phi[i][p](1) = dxidy_map[p]*phi_ref.slice(0) + detady_map[p]*phi_ref.slice(1);
}
break;
}
case 3:
{
const std::vector<Real>& dxidx_map = fe.get_fe_map().get_dxidx();
const std::vector<Real>& dxidy_map = fe.get_fe_map().get_dxidy();
const std::vector<Real>& dxidz_map = fe.get_fe_map().get_dxidz();
const std::vector<Real>& detadx_map = fe.get_fe_map().get_detadx();
const std::vector<Real>& detady_map = fe.get_fe_map().get_detady();
const std::vector<Real>& detadz_map = fe.get_fe_map().get_detadz();
const std::vector<Real>& dzetadx_map = fe.get_fe_map().get_dzetadx();
const std::vector<Real>& dzetady_map = fe.get_fe_map().get_dzetady();
const std::vector<Real>& dzetadz_map = fe.get_fe_map().get_dzetadz();
/* phi = (dx/dxi)^-T * \hat{phi}
In 3D:
dx/dxi^-1 = [ dxi/dx dxi/dy dxi/dz
deta/dx deta/dy deta/dz
dzeta/dx dzeta/dy dzeta/dz]
so: dxi/dx^-T * \hat{phi} = [ dxi/dx deta/dx dzeta/dx [ \hat{phi}_xi
dxi/dy deta/dy dzeta/dy \hat{phi}_eta
dxi/dz deta/dz dzeta/dz ] \hat{phi}_zeta ]
or in indicial notation: phi_j = xi_{i,j}*\hat{phi}_i */
for (unsigned int i=0; i<phi.size(); i++)
for (unsigned int p=0; p<phi[i].size(); p++)
{
// Need to temporarily cache reference shape functions
// TODO: PB: Might be worth trying to build phi_ref separately to see
// if we can get vectorization
OutputShape phi_ref;
FEInterface::shape<OutputShape>(3, fe.get_fe_type(), elem, i, qp[p], phi_ref);
phi[i][p].slice(0) = dxidx_map[p]*phi_ref.slice(0) + detadx_map[p]*phi_ref.slice(1)
+ dzetadx_map[p]*phi_ref.slice(2);
phi[i][p].slice(1) = dxidy_map[p]*phi_ref.slice(0) + detady_map[p]*phi_ref.slice(1)
+ dzetady_map[p]*phi_ref.slice(2);
phi[i][p].slice(2) = dxidz_map[p]*phi_ref.slice(0) + detadz_map[p]*phi_ref.slice(1)
+ dzetadz_map[p]*phi_ref.slice(2);
}
break;
}
default:
libmesh_error();
} // switch(dim)
return;
}
