Real FE<3,HERMITE>::shape(const Elem* elem,
const Order order,
const unsigned int i,
const Point& p)
{
libmesh_assert(elem);
std::vector<std::vector<Real> > dxdxi(3, std::vector<Real>(2, 0));
#ifdef DEBUG
std::vector<Real> dydxi(2), dzdeta(2), dxdzeta(2);
std::vector<Real> dzdxi(2), dxdeta(2), dydzeta(2);
#endif //DEBUG
hermite_compute_coefs(elem, dxdxi
#ifdef DEBUG
, dydxi, dzdeta, dxdzeta, dzdxi, dxdeta, dydzeta
#endif
);
const ElemType type = elem->type();
const Order totalorder = static_cast<Order>(order + elem->p_level());
switch (totalorder)
{
// 3rd-order tricubic Hermite functions
case THIRD:
{
switch (type)
{
case HEX8:
case HEX20:
case HEX27:
{
libmesh_assert_less (i, 64);
std::vector<unsigned int> bases1D;
Real coef = hermite_bases_3D(bases1D, dxdxi, totalorder, i);
return coef *
FEHermite<1>::hermite_raw_shape(bases1D[0],p(0)) *
FEHermite<1>::hermite_raw_shape(bases1D[1],p(1)) *
FEHermite<1>::hermite_raw_shape(bases1D[2],p(2));
}
default:
libMesh::err << "ERROR: Unsupported element type!" << std::endl;
libmesh_error();
}
}
// by default throw an error
default:
libMesh::err << "ERROR: Unsupported polynomial order!" << std::endl;
libmesh_error();
}
libmesh_error();
return 0.;
}
Real FE<2,HERMITE>::shape_second_deriv(const Elem* elem,
const Order order,
const unsigned int i,
const unsigned int j,
const Point& p)
{
libmesh_assert(elem);
libmesh_assert (j == 0 || j == 1 || j == 2);
hermite_compute_coefs(elem);
#ifdef LIBMESH_HAVE_TBB_API
std::vector<std::vector<Real> > & dxdxi = dxdxi_tls.local();
#endif // LIBMESH_HAVE_TBB_API
const ElemType type = elem->type();
const Order totalorder = static_cast<Order>(order + elem->p_level());
switch (type)
{
case QUAD4:
libmesh_assert_less (totalorder, 4);
case QUAD8:
case QUAD9:
{
libmesh_assert_less (i, (totalorder+1u)*(totalorder+1u));
std::vector<unsigned int> bases1D;
Real coef = hermite_bases_2D(bases1D, dxdxi, totalorder, i);
switch (j)
{
case 0:
return coef *
FEHermite<1>::hermite_raw_shape_second_deriv(bases1D[0],p(0)) *
FEHermite<1>::hermite_raw_shape(bases1D[1],p(1));
case 1:
return coef *
FEHermite<1>::hermite_raw_shape_deriv(bases1D[0],p(0)) *
FEHermite<1>::hermite_raw_shape_deriv(bases1D[1],p(1));
case 2:
return coef *
FEHermite<1>::hermite_raw_shape(bases1D[0],p(0)) *
FEHermite<1>::hermite_raw_shape_second_deriv(bases1D[1],p(1));
default:
libmesh_error();
}
}
default:
libMesh::err << "ERROR: Unsupported element type!" << std::endl;
libmesh_error();
}
libmesh_error();
return 0.;
}
Real FE<3,HERMITE>::shape_second_deriv(const Elem* elem,
const Order order,
const unsigned int i,
const unsigned int j,
const Point& p)
{
libmesh_assert(elem);
hermite_compute_coefs(elem);
#ifdef LIBMESH_HAVE_TBB_API
std::vector<std::vector<Real> > & dxdxi = dxdxi_tls.local();
#endif
const ElemType type = elem->type();
const Order totalorder = static_cast<Order>(order + elem->p_level());
switch (totalorder)
{
// 3rd-order tricubic Hermite functions
case THIRD:
{
switch (type)
{
case HEX8:
case HEX20:
case HEX27:
{
libmesh_assert_less (i, 64);
std::vector<unsigned int> bases1D;
Real coef = hermite_bases_3D(bases1D, dxdxi, totalorder, i);
switch (j) // Derivative type
{
case 0:
return coef *
FEHermite<1>::hermite_raw_shape_second_deriv(bases1D[0],p(0)) *
FEHermite<1>::hermite_raw_shape(bases1D[1],p(1)) *
FEHermite<1>::hermite_raw_shape(bases1D[2],p(2));
break;
case 1:
return coef *
FEHermite<1>::hermite_raw_shape_deriv(bases1D[0],p(0)) *
FEHermite<1>::hermite_raw_shape_deriv(bases1D[1],p(1)) *
FEHermite<1>::hermite_raw_shape(bases1D[2],p(2));
break;
case 2:
return coef *
FEHermite<1>::hermite_raw_shape(bases1D[0],p(0)) *
FEHermite<1>::hermite_raw_shape_second_deriv(bases1D[1],p(1)) *
FEHermite<1>::hermite_raw_shape(bases1D[2],p(2));
break;
case 3:
return coef *
FEHermite<1>::hermite_raw_shape_deriv(bases1D[0],p(0)) *
FEHermite<1>::hermite_raw_shape(bases1D[1],p(1)) *
FEHermite<1>::hermite_raw_shape_deriv(bases1D[2],p(2));
break;
case 4:
return coef *
FEHermite<1>::hermite_raw_shape(bases1D[0],p(0)) *
FEHermite<1>::hermite_raw_shape_deriv(bases1D[1],p(1)) *
FEHermite<1>::hermite_raw_shape_deriv(bases1D[2],p(2));
break;
case 5:
return coef *
FEHermite<1>::hermite_raw_shape(bases1D[0],p(0)) *
FEHermite<1>::hermite_raw_shape(bases1D[1],p(1)) *
FEHermite<1>::hermite_raw_shape_second_deriv(bases1D[2],p(2));
break;
}
}
default:
libMesh::err << "ERROR: Unsupported element type!" << std::endl;
libmesh_error();
}
}
// by default throw an error
default:
libMesh::err << "ERROR: Unsupported polynomial order!" << std::endl;
libmesh_error();
}
libmesh_error();
return 0.;
}
