void HCurlFETransformation<OutputShape>::map_curl( const unsigned int dim,
const Elem* const,
const std::vector<Point>&,
const FEGenericBase<OutputShape>& fe,
std::vector<std::vector<OutputShape> >& curl_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<std::vector<OutputShape> >& dphi_dxi = fe.get_dphidxi();
const std::vector<std::vector<OutputShape> >& dphi_deta = fe.get_dphideta();
const std::vector<Real>& J = fe.get_fe_map().get_jacobian();
// FIXME: I don't think this is valid for 2D elements in 3D space
/* In 2D: curl(phi) = J^{-1} * curl(\hat{phi}) */
for (unsigned int i=0; i<curl_phi.size(); i++)
for (unsigned int p=0; p<curl_phi[i].size(); p++)
{
curl_phi[i][p].slice(0) = curl_phi[i][p].slice(1) = 0.0;
curl_phi[i][p].slice(2) = ( dphi_dxi[i][p].slice(1) - dphi_deta[i][p].slice(0) )/J[p];
}
break;
}
case 3:
{
const std::vector<std::vector<OutputShape> >& dphi_dxi = fe.get_dphidxi();
const std::vector<std::vector<OutputShape> >& dphi_deta = fe.get_dphideta();
const std::vector<std::vector<OutputShape> >& dphi_dzeta = fe.get_dphidzeta();
const std::vector<RealGradient>& dxyz_dxi = fe.get_fe_map().get_dxyzdxi();
const std::vector<RealGradient>& dxyz_deta = fe.get_fe_map().get_dxyzdeta();
const std::vector<RealGradient>& dxyz_dzeta = fe.get_fe_map().get_dxyzdzeta();
const std::vector<Real>& J = fe.get_fe_map().get_jacobian();
for (unsigned int i=0; i<curl_phi.size(); i++)
for (unsigned int p=0; p<curl_phi[i].size(); p++)
{
Real dx_dxi = dxyz_dxi[p](0);
Real dx_deta = dxyz_deta[p](0);
Real dx_dzeta = dxyz_dzeta[p](0);
Real dy_dxi = dxyz_dxi[p](1);
Real dy_deta = dxyz_deta[p](1);
Real dy_dzeta = dxyz_dzeta[p](1);
Real dz_dxi = dxyz_dxi[p](2);
Real dz_deta = dxyz_deta[p](2);
Real dz_dzeta = dxyz_dzeta[p](2);
const Real inv_jac = 1.0/J[p];
/* In 3D: curl(phi) = J^{-1} dx/dxi * curl(\hat{phi})
dx/dxi = [ dx/dxi dx/deta dx/dzeta
dy/dxi dy/deta dy/dzeta
dz/dxi dz/deta dz/dzeta ]
curl(u) = [ du_z/deta - du_y/dzeta
du_x/dzeta - du_z/dxi
du_y/dxi - du_x/deta ]
*/
curl_phi[i][p].slice(0) = inv_jac*( dx_dxi*( dphi_deta[i][p].slice(2) -
dphi_dzeta[i][p].slice(1) ) +
dx_deta*( dphi_dzeta[i][p].slice(0) -
dphi_dxi[i][p].slice(2) ) +
dx_dzeta*( dphi_dxi[i][p].slice(1) -
dphi_deta[i][p].slice(0) ) );
curl_phi[i][p].slice(1) = inv_jac*( dy_dxi*( dphi_deta[i][p].slice(2) -
dphi_dzeta[i][p].slice(1) ) +
dy_deta*( dphi_dzeta[i][p].slice(0)-
dphi_dxi[i][p].slice(2) ) +
dy_dzeta*( dphi_dxi[i][p].slice(1) -
dphi_deta[i][p].slice(0) ) );
curl_phi[i][p].slice(2) = inv_jac*( dz_dxi*( dphi_deta[i][p].slice(2) -
dphi_dzeta[i][p].slice(1) ) +
dz_deta*( dphi_dzeta[i][p].slice(0) -
dphi_dxi[i][p].slice(2) ) +
dz_dzeta*( dphi_dxi[i][p].slice(1) -
dphi_deta[i][p].slice(0) ) );
}
break;
}
default:
libmesh_error();
} // switch(dim)
return;
}
void H1FETransformation<OutputShape>::map_dphi( const unsigned int dim,
const Elem* const,
const std::vector<Point>&,
const FEGenericBase<OutputShape>& fe,
std::vector<std::vector<typename FEGenericBase<OutputShape>::OutputGradient> >& dphi,
std::vector<std::vector<OutputShape> >& dphidx,
std::vector<std::vector<OutputShape> >& dphidy,
std::vector<std::vector<OutputShape> >& dphidz ) const
{
switch(dim)
{
case 0: // No derivatives in 0D
{
for (unsigned int i=0; i<dphi.size(); i++)
for (unsigned int p=0; p<dphi[i].size(); p++)
{
dphi[i][p] = 0.;
}
break;
}
case 1:
{
const std::vector<std::vector<OutputShape> >& dphidxi = fe.get_dphidxi();
const std::vector<Real>& dxidx_map = fe.get_fe_map().get_dxidx();
#if LIBMESH_DIM>1
const std::vector<Real>& dxidy_map = fe.get_fe_map().get_dxidy();
#endif
#if LIBMESH_DIM>2
const std::vector<Real>& dxidz_map = fe.get_fe_map().get_dxidz();
#endif
for (unsigned int i=0; i<dphi.size(); i++)
for (unsigned int p=0; p<dphi[i].size(); p++)
{
// dphi/dx = (dphi/dxi)*(dxi/dx)
dphi[i][p].slice(0) = dphidx[i][p] = dphidxi[i][p]*dxidx_map[p];
#if LIBMESH_DIM>1
dphi[i][p].slice(1) = dphidy[i][p] = dphidxi[i][p]*dxidy_map[p];
#endif
#if LIBMESH_DIM>2
dphi[i][p].slice(2) = dphidz[i][p] = dphidxi[i][p]*dxidz_map[p];
#endif
}
break;
}
case 2:
{
const std::vector<std::vector<OutputShape> >& dphidxi = fe.get_dphidxi();
const std::vector<std::vector<OutputShape> >& dphideta = fe.get_dphideta();
const std::vector<Real>& dxidx_map = fe.get_fe_map().get_dxidx();
const std::vector<Real>& dxidy_map = fe.get_fe_map().get_dxidy();
#if LIBMESH_DIM > 2
const std::vector<Real>& dxidz_map = fe.get_fe_map().get_dxidz();
#endif
const std::vector<Real>& detadx_map = fe.get_fe_map().get_detadx();
const std::vector<Real>& detady_map = fe.get_fe_map().get_detady();
#if LIBMESH_DIM > 2
const std::vector<Real>& detadz_map = fe.get_fe_map().get_detadz();
#endif
for (unsigned int i=0; i<dphi.size(); i++)
for (unsigned int p=0; p<dphi[i].size(); p++)
{
// dphi/dx = (dphi/dxi)*(dxi/dx) + (dphi/deta)*(deta/dx)
dphi[i][p].slice(0) = dphidx[i][p] = (dphidxi[i][p]*dxidx_map[p] +
dphideta[i][p]*detadx_map[p]);
// dphi/dy = (dphi/dxi)*(dxi/dy) + (dphi/deta)*(deta/dy)
dphi[i][p].slice(1) = dphidy[i][p] = (dphidxi[i][p]*dxidy_map[p] +
dphideta[i][p]*detady_map[p]);
#if LIBMESH_DIM > 2
// dphi/dz = (dphi/dxi)*(dxi/dz) + (dphi/deta)*(deta/dz)
dphi[i][p].slice(2) = dphidz[i][p] = (dphidxi[i][p]*dxidz_map[p] +
dphideta[i][p]*detadz_map[p]);
#endif
}
break;
}
case 3:
{
const std::vector<std::vector<OutputShape> >& dphidxi = fe.get_dphidxi();
const std::vector<std::vector<OutputShape> >& dphideta = fe.get_dphideta();
const std::vector<std::vector<OutputShape> >& dphidzeta = fe.get_dphidzeta();
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();
for (unsigned int i=0; i<dphi.size(); i++)
for (unsigned int p=0; p<dphi[i].size(); p++)
{
// dphi/dx = (dphi/dxi)*(dxi/dx) + (dphi/deta)*(deta/dx) + (dphi/dzeta)*(dzeta/dx);
dphi[i][p].slice(0) = dphidx[i][p] = (dphidxi[i][p]*dxidx_map[p] +
dphideta[i][p]*detadx_map[p] +
dphidzeta[i][p]*dzetadx_map[p]);
// dphi/dy = (dphi/dxi)*(dxi/dy) + (dphi/deta)*(deta/dy) + (dphi/dzeta)*(dzeta/dy);
dphi[i][p].slice(1) = dphidy[i][p] = (dphidxi[i][p]*dxidy_map[p] +
dphideta[i][p]*detady_map[p] +
dphidzeta[i][p]*dzetady_map[p]);
// dphi/dz = (dphi/dxi)*(dxi/dz) + (dphi/deta)*(deta/dz) + (dphi/dzeta)*(dzeta/dz);
dphi[i][p].slice(2) = dphidz[i][p] = (dphidxi[i][p]*dxidz_map[p] +
dphideta[i][p]*detadz_map[p] +
dphidzeta[i][p]*dzetadz_map[p]);
}
break;
}
default:
libmesh_error();
} // switch(dim)
return;
}
