libMesh::FE< Dim, T > Class Template Reference

Template class which generates the different FE families and orders. More...

#include <fe.h>

Inheritance diagram for libMesh::FE< Dim, T >:

Public Types
typedef FEGenericBase< typename FEOutputType< T >::type >::OutputShape	OutputShape
typedef TensorTools::IncrementRank< OutputShape >::type	OutputGradient
typedef TensorTools::IncrementRank< OutputGradient >::type	OutputTensor
typedef TensorTools::DecrementRank< OutputShape >::type	OutputDivergence
typedef TensorTools::MakeNumber< OutputShape >::type	OutputNumber
typedef TensorTools::IncrementRank< OutputNumber >::type	OutputNumberGradient
typedef TensorTools::IncrementRank< OutputNumberGradient >::type	OutputNumberTensor
typedef TensorTools::DecrementRank< OutputNumber >::type	OutputNumberDivergence

Public Member Functions
	FE (const FEType &fet)
virtual unsigned int	n_shape_functions () const override
virtual FEContinuity	get_continuity () const override
virtual bool	is_hierarchic () const override
virtual void	reinit (const Elem *elem, const std::vector< Point > *const pts=nullptr, const std::vector< Real > *const weights=nullptr) override
virtual void	reinit (const Elem *elem, const unsigned int side, const Real tolerance=TOLERANCE, const std::vector< Point > *const pts=nullptr, const std::vector< Real > *const weights=nullptr) override
virtual void	edge_reinit (const Elem *elem, const unsigned int edge, const Real tolerance=TOLERANCE, const std::vector< Point > *const pts=nullptr, const std::vector< Real > *const weights=nullptr) override
virtual void	side_map (const Elem *elem, const Elem *side, const unsigned int s, const std::vector< Point > &reference_side_points, std::vector< Point > &reference_points) override
virtual void	attach_quadrature_rule (QBase *q) override
virtual unsigned int	n_quadrature_points () const override
virtual bool	shapes_need_reinit () const override
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
Real	shape (const ElemType, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order order, const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
Real	shape (const ElemType, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *libmesh_dbg_var(elem), const Order, const unsigned int, const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *libmesh_dbg_var(elem), const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *libmesh_dbg_var(elem), const Order, const unsigned int, const unsigned int, const Point &)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
Real	shape (const ElemType, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int, const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int, const Point &p)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
Real	shape (const ElemType, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const Point &p)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
template<>
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
Real	shape (const ElemType, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const Point &p)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
template<>
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
template<>
Real	shape (const ElemType, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order order, const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order order, const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
Real	shape (const ElemType, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order order, const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order order, const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
template<>
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
template<>
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
template<>
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
template<>
RealGradient	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
template<>
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
Real	shape (const ElemType, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const Point &p)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const Point &p)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const Point &p)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
void	nodal_soln (const Elem *, const Order, const std::vector< Number > &, std::vector< Number > &)
template<>
void	nodal_soln (const Elem *, const Order, const std::vector< Number > &, std::vector< Number > &)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
unsigned int	n_dofs (const ElemType, const Order)
template<>
unsigned int	n_dofs (const ElemType, const Order)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
template<>
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
RealGradient	shape (const Elem *, const Order, const unsigned int, const Point &)
template<>
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
RealGradient	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
RealGradient	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
RealGradient	shape (const Elem *, const Order, const unsigned int, const Point &)
template<>
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
RealGradient	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
RealGradient	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &)
template<>
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int libmesh_dbg_var(i), const unsigned int libmesh_dbg_var(j), const Point &)
template<>
RealGradient	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
RealGradient	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
RealGradient	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
RealGradient	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
RealGradient	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
RealGradient	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &libmesh_dbg_var(p))
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
unsigned int	n_dofs (const ElemType, const Order o)
template<>
unsigned int	n_dofs (const ElemType, const Order o)
template<>
unsigned int	n_dofs (const ElemType, const Order o)
template<>
unsigned int	n_dofs (const ElemType, const Order o)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
template<>
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int, const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int, const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int, const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int, const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType type, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType type, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
void	nodal_soln (const Elem *elem, const Order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	side_map (const Elem *, const Elem *, const unsigned int, const std::vector< Point > &, std::vector< Point > &)
template<>
void	edge_reinit (Elem const *, unsigned int, Real, const std::vector< Point > *const, const std::vector< Real > *const)
template<>
Point	inverse_map (const Elem *, const Point &, const Real, const bool)
template<>
void	inverse_map (const Elem *, const std::vector< Point > &, std::vector< Point > &, Real, bool)
template<>
unsigned int	n_dofs (const ElemType, const Order)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_per_elem (const ElemType, const Order)
template<>
void	dofs_on_side (const Elem *const, const Order, unsigned int, std::vector< unsigned int > &di)
template<>
void	dofs_on_edge (const Elem *const, const Order, unsigned int, std::vector< unsigned int > &di)
template<>
FEContinuity	get_continuity () const
template<>
bool	is_hierarchic () const
template<>
bool	shapes_need_reinit () const
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
Real	shape (const ElemType, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const Point &p)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int, const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
void	nodal_soln (const Elem *elem, const Order order, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_at_node (const ElemType, const Order, const unsigned int)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
FEContinuity	get_continuity () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
bool	is_hierarchic () const
template<>
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
template<>
void	compute_constraints (DofConstraints &, DofMap &, const unsigned int, const Elem *)
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
bool	shapes_need_reinit () const
template<>
Real	shape (const ElemType, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape (const Elem *, const Order, const unsigned int libmesh_dbg_var(i), const Point &)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const Point &point_in)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &point_in)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int libmesh_dbg_var(j), const Point &point_in)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const Point &point_in)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &point_in)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &point_in)
template<>
Real	shape (const ElemType, const Order, const unsigned int, const Point &)
template<>
Real	shape (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const Point &point_in)
template<>
Real	shape_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &point_in)
template<>
Real	shape_second_deriv (const ElemType, const Order, const unsigned int, const unsigned int, const Point &)
template<>
Real	shape_second_deriv (const Elem *elem, const Order libmesh_dbg_var(order), const unsigned int i, const unsigned int j, const Point &point_in)
template<>
Real	shape (const Elem *elem, const Order order, const unsigned int i, const Point &p)
template<>
Real	shape_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
template<>
Real	shape_second_deriv (const Elem *elem, const Order order, const unsigned int i, const unsigned int j, const Point &p)
std::unique_ptr< FEGenericBase< Real > >	build (const unsigned int dim, const FEType &fet)
std::unique_ptr< FEGenericBase< RealGradient > >	build (const unsigned int dim, const FEType &fet)
std::unique_ptr< FEGenericBase< Real > >	build_InfFE (const unsigned int dim, const FEType &fet)
std::unique_ptr< FEGenericBase< RealGradient > >	build_InfFE (const unsigned int, const FEType &)
const std::vector< std::vector< OutputShape > > &	get_phi () const
const std::vector< std::vector< OutputGradient > > &	get_dphi () const
const std::vector< std::vector< OutputShape > > &	get_curl_phi () const
const std::vector< std::vector< OutputDivergence > > &	get_div_phi () const
const std::vector< std::vector< OutputShape > > &	get_dphidx () const
const std::vector< std::vector< OutputShape > > &	get_dphidy () const
const std::vector< std::vector< OutputShape > > &	get_dphidz () const
const std::vector< std::vector< OutputShape > > &	get_dphidxi () const
const std::vector< std::vector< OutputShape > > &	get_dphideta () const
const std::vector< std::vector< OutputShape > > &	get_dphidzeta () const
const std::vector< std::vector< OutputTensor > > &	get_d2phi () const
const std::vector< std::vector< OutputShape > > &	get_d2phidx2 () const
const std::vector< std::vector< OutputShape > > &	get_d2phidxdy () const
const std::vector< std::vector< OutputShape > > &	get_d2phidxdz () const
const std::vector< std::vector< OutputShape > > &	get_d2phidy2 () const
const std::vector< std::vector< OutputShape > > &	get_d2phidydz () const
const std::vector< std::vector< OutputShape > > &	get_d2phidz2 () const
const std::vector< std::vector< OutputShape > > &	get_d2phidxi2 () const
const std::vector< std::vector< OutputShape > > &	get_d2phidxideta () const
const std::vector< std::vector< OutputShape > > &	get_d2phidxidzeta () const
const std::vector< std::vector< OutputShape > > &	get_d2phideta2 () const
const std::vector< std::vector< OutputShape > > &	get_d2phidetadzeta () const
const std::vector< std::vector< OutputShape > > &	get_d2phidzeta2 () const
const std::vector< OutputGradient > &	get_dphase () const
const std::vector< Real > &	get_Sobolev_weight () const
const std::vector< RealGradient > &	get_Sobolev_dweight () const
void	print_phi (std::ostream &os) const
void	print_dphi (std::ostream &os) const
void	print_d2phi (std::ostream &os) const
unsigned int	get_dim () const
const std::vector< Point > &	get_xyz () const
const std::vector< Real > &	get_JxW () const
const std::vector< RealGradient > &	get_dxyzdxi () const
const std::vector< RealGradient > &	get_dxyzdeta () const
const std::vector< RealGradient > &	get_dxyzdzeta () const
const std::vector< RealGradient > &	get_d2xyzdxi2 () const
const std::vector< RealGradient > &	get_d2xyzdeta2 () const
const std::vector< RealGradient > &	get_d2xyzdzeta2 () const
const std::vector< RealGradient > &	get_d2xyzdxideta () const
const std::vector< RealGradient > &	get_d2xyzdxidzeta () const
const std::vector< RealGradient > &	get_d2xyzdetadzeta () const
const std::vector< Real > &	get_dxidx () const
const std::vector< Real > &	get_dxidy () const
const std::vector< Real > &	get_dxidz () const
const std::vector< Real > &	get_detadx () const
const std::vector< Real > &	get_detady () const
const std::vector< Real > &	get_detadz () const
const std::vector< Real > &	get_dzetadx () const
const std::vector< Real > &	get_dzetady () const
const std::vector< Real > &	get_dzetadz () const
const std::vector< std::vector< Point > > &	get_tangents () const
const std::vector< Point > &	get_normals () const
const std::vector< Real > &	get_curvatures () const
ElemType	get_type () const
unsigned int	get_p_level () const
FEType	get_fe_type () const
Order	get_order () const
void	set_fe_order (int new_order)
FEFamily	get_family () const
const FEMap &	get_fe_map () const
void	print_JxW (std::ostream &os) const
void	print_xyz (std::ostream &os) const
void	print_info (std::ostream &os) const

Static Public Member Functions
static OutputShape	shape (const ElemType t, const Order o, const unsigned int i, const Point &p)
static OutputShape	shape (const Elem *elem, const Order o, const unsigned int i, const Point &p)
static OutputShape	shape_deriv (const ElemType t, const Order o, const unsigned int i, const unsigned int j, const Point &p)
static OutputShape	shape_deriv (const Elem *elem, const Order o, const unsigned int i, const unsigned int j, const Point &p)
static OutputShape	shape_second_deriv (const ElemType t, const Order o, const unsigned int i, const unsigned int j, const Point &p)
static OutputShape	shape_second_deriv (const Elem *elem, const Order o, const unsigned int i, const unsigned int j, const Point &p)
static void	nodal_soln (const Elem *elem, const Order o, const std::vector< Number > &elem_soln, std::vector< Number > &nodal_soln)
static unsigned int	n_shape_functions (const ElemType t, const Order o)
static unsigned int	n_dofs (const ElemType t, const Order o)
static unsigned int	n_dofs_at_node (const ElemType t, const Order o, const unsigned int n)
static unsigned int	n_dofs_per_elem (const ElemType t, const Order o)
static void	dofs_on_side (const Elem *const elem, const Order o, unsigned int s, std::vector< unsigned int > &di)
static void	dofs_on_edge (const Elem *const elem, const Order o, unsigned int e, std::vector< unsigned int > &di)
static Point	inverse_map (const Elem *elem, const Point &p, const Real tolerance=TOLERANCE, const bool secure=true)
static void	inverse_map (const Elem *elem, const std::vector< Point > &physical_points, std::vector< Point > &reference_points, const Real tolerance=TOLERANCE, const bool secure=true)
static void	compute_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
static Point	map (const Elem *elem, const Point &reference_point)
static Point	map_xi (const Elem *elem, const Point &reference_point)
static Point	map_eta (const Elem *elem, const Point &reference_point)
static Point	map_zeta (const Elem *elem, const Point &reference_point)
static std::unique_ptr< FEGenericBase >	build (const unsigned int dim, const FEType &type)
static std::unique_ptr< FEGenericBase >	build_InfFE (const unsigned int dim, const FEType &type)
static void	compute_proj_constraints (DofConstraints &constraints, DofMap &dof_map, const unsigned int variable_number, const Elem *elem)
static void	coarsened_dof_values (const NumericVector< Number > &global_vector, const DofMap &dof_map, const Elem *coarse_elem, DenseVector< Number > &coarse_dofs, const unsigned int var, const bool use_old_dof_indices=false)
static void	coarsened_dof_values (const NumericVector< Number > &global_vector, const DofMap &dof_map, const Elem *coarse_elem, DenseVector< Number > &coarse_dofs, const bool use_old_dof_indices=false)
static void	compute_periodic_constraints (DofConstraints &constraints, DofMap &dof_map, const PeriodicBoundaries &boundaries, const MeshBase &mesh, const PointLocatorBase *point_locator, const unsigned int variable_number, const Elem *elem)
static bool	on_reference_element (const Point &p, const ElemType t, const Real eps=TOLERANCE)
static void	get_refspace_nodes (const ElemType t, std::vector< Point > &nodes)
static void	compute_node_constraints (NodeConstraints &constraints, const Elem *elem)
static void	compute_periodic_node_constraints (NodeConstraints &constraints, const PeriodicBoundaries &boundaries, const MeshBase &mesh, const PointLocatorBase *point_locator, const Elem *elem)
static void	print_info (std::ostream &out=libMesh::out)
static std::string	get_info ()
static unsigned int	n_objects ()
static void	enable_print_counter_info ()
static void	disable_print_counter_info ()

Protected Types
typedef std::map< std::string, std::pair< unsigned int, unsigned int > >	Counts

Protected Member Functions
virtual void	init_shape_functions (const std::vector< Point > &qp, const Elem *e)
virtual void	init_base_shape_functions (const std::vector< Point > &qp, const Elem *e) override
void	determine_calculations ()
virtual void	compute_shape_functions (const Elem *elem, const std::vector< Point > &qp)
void	increment_constructor_count (const std::string &name)
void	increment_destructor_count (const std::string &name)

Protected Attributes
std::vector< Point >	cached_nodes
ElemType	last_side
unsigned int	last_edge
std::unique_ptr< FETransformationBase< FEOutputType< T >::type > >	_fe_trans
std::vector< std::vector< OutputShape > >	phi
std::vector< std::vector< OutputGradient > >	dphi
std::vector< std::vector< OutputShape > >	curl_phi
std::vector< std::vector< OutputDivergence > >	div_phi
std::vector< std::vector< OutputShape > >	dphidxi
std::vector< std::vector< OutputShape > >	dphideta
std::vector< std::vector< OutputShape > >	dphidzeta
std::vector< std::vector< OutputShape > >	dphidx
std::vector< std::vector< OutputShape > >	dphidy
std::vector< std::vector< OutputShape > >	dphidz
std::vector< std::vector< OutputTensor > >	d2phi
std::vector< std::vector< OutputShape > >	d2phidxi2
std::vector< std::vector< OutputShape > >	d2phidxideta
std::vector< std::vector< OutputShape > >	d2phidxidzeta
std::vector< std::vector< OutputShape > >	d2phideta2
std::vector< std::vector< OutputShape > >	d2phidetadzeta
std::vector< std::vector< OutputShape > >	d2phidzeta2
std::vector< std::vector< OutputShape > >	d2phidx2
std::vector< std::vector< OutputShape > >	d2phidxdy
std::vector< std::vector< OutputShape > >	d2phidxdz
std::vector< std::vector< OutputShape > >	d2phidy2
std::vector< std::vector< OutputShape > >	d2phidydz
std::vector< std::vector< OutputShape > >	d2phidz2
std::vector< OutputGradient >	dphase
std::vector< RealGradient >	dweight
std::vector< Real >	weight
std::unique_ptr< FEMap >	_fe_map
const unsigned int	dim
bool	calculations_started
bool	calculate_phi
bool	calculate_dphi
bool	calculate_d2phi
bool	calculate_curl_phi
bool	calculate_div_phi
bool	calculate_dphiref
FEType	fe_type
ElemType	elem_type
unsigned int	_p_level
QBase *	qrule
bool	shapes_on_quadrature

Static Protected Attributes
static Counts	_counts
static Threads::atomic< unsigned int >	_n_objects
static Threads::spin_mutex	_mutex
static bool	_enable_print_counter = true

Friends
template<unsigned int friend_Dim, FEFamily friend_T_radial, InfMapType friend_T_map>
class	InfFE

Detailed Description

template<unsigned int Dim, FEFamily T>
class libMesh::FE< Dim, T >

Template class which generates the different FE families and orders.

A specific instantiation of the FEBase class. This class is templated, and specific template instantiations will result in different Finite Element families. Full specialization of the template for specific dimensions(Dim) and families (T) provide support for specific finite element types. The use of templates allows for compile-time optimization, however it requires that the specific finite element family and dimension is also known at compile time. If this is too restricting for your application you can use the FEBase::build() member to create abstract (but still optimized) finite elements.

Author

Benjamin S. Kirk

Date

2002-2007

Definition at line 89 of file fe.h.

Member Typedef Documentation

Counts

typedef std::map<std::string, std::pair<unsigned int, unsigned int> > libMesh::ReferenceCounter::Counts

protectedinherited

Data structure to log the information. The log is identified by the class name.

Definition at line 117 of file reference_counter.h.

OutputDivergence

typedef TensorTools::DecrementRank<OutputShape>::type libMesh::FEGenericBase< FEOutputType< T >::type >::OutputDivergence

inherited

Definition at line 122 of file fe_base.h.

OutputGradient

typedef TensorTools::IncrementRank<OutputShape>::type libMesh::FEGenericBase< FEOutputType< T >::type >::OutputGradient

inherited

Definition at line 120 of file fe_base.h.

OutputNumber

typedef TensorTools::MakeNumber<OutputShape>::type libMesh::FEGenericBase< FEOutputType< T >::type >::OutputNumber

inherited

Definition at line 123 of file fe_base.h.

OutputNumberDivergence

typedef TensorTools::DecrementRank<OutputNumber>::type libMesh::FEGenericBase< FEOutputType< T >::type >::OutputNumberDivergence

inherited

Definition at line 126 of file fe_base.h.

OutputNumberGradient

typedef TensorTools::IncrementRank<OutputNumber>::type libMesh::FEGenericBase< FEOutputType< T >::type >::OutputNumberGradient

inherited

Definition at line 124 of file fe_base.h.

OutputNumberTensor

typedef TensorTools::IncrementRank<OutputNumberGradient>::type libMesh::FEGenericBase< FEOutputType< T >::type >::OutputNumberTensor

inherited

Definition at line 125 of file fe_base.h.

OutputShape

template<unsigned int Dim, FEFamily T>

typedef FEGenericBase<typename FEOutputType<T>::type>::OutputShape libMesh::FE< Dim, T >::OutputShape

Definition at line 101 of file fe.h.

OutputTensor

typedef TensorTools::IncrementRank<OutputGradient>::type libMesh::FEGenericBase< FEOutputType< T >::type >::OutputTensor

inherited

Definition at line 121 of file fe_base.h.

Constructor & Destructor Documentation

FE()

template<unsigned int Dim, FEFamily T>

libMesh::FE< Dim, T >::FE ( const FEType &  fet )

explicit

Constructor.

Definition at line 37 of file fe.C.

                                 :
  FEGenericBase<typename FEOutputType<T>::type> (Dim,fet),
  last_side(INVALID_ELEM),
  last_edge(libMesh::invalid_uint)
{
  // Sanity check.  Make sure the
  // Family specified in the template instantiation
  // matches the one in the FEType object
  libmesh_assert_equal_to (T, this->get_family());
}

Member Function Documentation

attach_quadrature_rule()

template<unsigned int Dim, FEFamily T>

void libMesh::FE< Dim, T >::attach_quadrature_rule ( QBase *  q )

overridevirtual

Provides the class with the quadrature rule, which provides the locations (on a reference element) where the shape functions are to be calculated.

Implements libMesh::FEAbstract.

Reimplemented in libMesh::FESubdivision.

Definition at line 58 of file fe.C.

{
  libmesh_assert(q);
  this->qrule = q;
  // make sure we don't cache results from a previous quadrature rule
  this->elem_type = INVALID_ELEM;
  return;
}

build() [1/3]

static std::unique_ptr<FEGenericBase> libMesh::FEGenericBase< FEOutputType< T >::type >::build ( const unsigned int  dim, const FEType &  type  )

staticinherited

Builds a specific finite element type. A std::unique_ptr<FEGenericBase> is returned to prevent a memory leak. This way the user need not remember to delete the object.

The build call will fail if the OutputType of this class is not compatible with the output required for the requested type

build() [2/3]

std::unique_ptr< FEGenericBase< Real > > libMesh::FEGenericBase< Real >::build ( const unsigned int  dim, const FEType &  fet  )

inherited

Definition at line 182 of file fe_base.C.

References libMesh::BERNSTEIN, libMesh::CLOUGH, libMesh::FEType::family, libMesh::HERMITE, libMesh::HIERARCHIC, libMesh::L2_HIERARCHIC, libMesh::L2_LAGRANGE, libMesh::LAGRANGE, libMesh::MONOMIAL, libMesh::SCALAR, libMesh::SUBDIVISION, libMesh::SZABAB, and libMesh::XYZ.

{
  switch (dim)
    {
      // 0D
    case 0:
      {
        switch (fet.family)
          {
          case CLOUGH:
            return libmesh_make_unique<FE<0,CLOUGH>>(fet);

          case HERMITE:
            return libmesh_make_unique<FE<0,HERMITE>>(fet);

          case LAGRANGE:
            return libmesh_make_unique<FE<0,LAGRANGE>>(fet);

          case L2_LAGRANGE:
            return libmesh_make_unique<FE<0,L2_LAGRANGE>>(fet);

          case HIERARCHIC:
            return libmesh_make_unique<FE<0,HIERARCHIC>>(fet);

          case L2_HIERARCHIC:
            return libmesh_make_unique<FE<0,L2_HIERARCHIC>>(fet);

          case MONOMIAL:
            return libmesh_make_unique<FE<0,MONOMIAL>>(fet);

#ifdef LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
          case SZABAB:
            return libmesh_make_unique<FE<0,SZABAB>>(fet);

          case BERNSTEIN:
            return libmesh_make_unique<FE<0,BERNSTEIN>>(fet);
#endif

          case XYZ:
            return libmesh_make_unique<FEXYZ<0>>(fet);

          case SCALAR:
            return libmesh_make_unique<FEScalar<0>>(fet);

          default:
            libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
          }
      }
      // 1D
    case 1:
      {
        switch (fet.family)
          {
          case CLOUGH:
            return libmesh_make_unique<FE<1,CLOUGH>>(fet);

          case HERMITE:
            return libmesh_make_unique<FE<1,HERMITE>>(fet);

          case LAGRANGE:
            return libmesh_make_unique<FE<1,LAGRANGE>>(fet);

          case L2_LAGRANGE:
            return libmesh_make_unique<FE<1,L2_LAGRANGE>>(fet);

          case HIERARCHIC:
            return libmesh_make_unique<FE<1,HIERARCHIC>>(fet);

          case L2_HIERARCHIC:
            return libmesh_make_unique<FE<1,L2_HIERARCHIC>>(fet);

          case MONOMIAL:
            return libmesh_make_unique<FE<1,MONOMIAL>>(fet);

#ifdef LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
          case SZABAB:
            return libmesh_make_unique<FE<1,SZABAB>>(fet);

          case BERNSTEIN:
            return libmesh_make_unique<FE<1,BERNSTEIN>>(fet);
#endif

          case XYZ:
            return libmesh_make_unique<FEXYZ<1>>(fet);

          case SCALAR:
            return libmesh_make_unique<FEScalar<1>>(fet);

          default:
            libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
          }
      }


      // 2D
    case 2:
      {
        switch (fet.family)
          {
          case CLOUGH:
            return libmesh_make_unique<FE<2,CLOUGH>>(fet);

          case HERMITE:
            return libmesh_make_unique<FE<2,HERMITE>>(fet);

          case LAGRANGE:
            return libmesh_make_unique<FE<2,LAGRANGE>>(fet);

          case L2_LAGRANGE:
            return libmesh_make_unique<FE<2,L2_LAGRANGE>>(fet);

          case HIERARCHIC:
            return libmesh_make_unique<FE<2,HIERARCHIC>>(fet);

          case L2_HIERARCHIC:
            return libmesh_make_unique<FE<2,L2_HIERARCHIC>>(fet);

          case MONOMIAL:
            return libmesh_make_unique<FE<2,MONOMIAL>>(fet);

#ifdef LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
          case SZABAB:
            return libmesh_make_unique<FE<2,SZABAB>>(fet);

          case BERNSTEIN:
            return libmesh_make_unique<FE<2,BERNSTEIN>>(fet);
#endif

          case XYZ:
            return libmesh_make_unique<FEXYZ<2>>(fet);

          case SCALAR:
            return libmesh_make_unique<FEScalar<2>>(fet);

          case SUBDIVISION:
            return libmesh_make_unique<FESubdivision>(fet);

          default:
            libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
          }
      }


      // 3D
    case 3:
      {
        switch (fet.family)
          {
          case CLOUGH:
            libmesh_error_msg("ERROR: Clough-Tocher elements currently only support 1D and 2D");

          case HERMITE:
            return libmesh_make_unique<FE<3,HERMITE>>(fet);

          case LAGRANGE:
            return libmesh_make_unique<FE<3,LAGRANGE>>(fet);

          case L2_LAGRANGE:
            return libmesh_make_unique<FE<3,L2_LAGRANGE>>(fet);

          case HIERARCHIC:
            return libmesh_make_unique<FE<3,HIERARCHIC>>(fet);

          case L2_HIERARCHIC:
            return libmesh_make_unique<FE<3,L2_HIERARCHIC>>(fet);

          case MONOMIAL:
            return libmesh_make_unique<FE<3,MONOMIAL>>(fet);

#ifdef LIBMESH_ENABLE_HIGHER_ORDER_SHAPES
          case SZABAB:
            return libmesh_make_unique<FE<3,SZABAB>>(fet);

          case BERNSTEIN:
            return libmesh_make_unique<FE<3,BERNSTEIN>>(fet);
#endif

          case XYZ:
            return libmesh_make_unique<FEXYZ<3>>(fet);

          case SCALAR:
            return libmesh_make_unique<FEScalar<3>>(fet);

          default:
            libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
          }
      }

    default:
      libmesh_error_msg("Invalid dimension dim = " << dim);
    }
}

build() [3/3]

std::unique_ptr< FEGenericBase< RealGradient > > libMesh::FEGenericBase< RealGradient >::build ( const unsigned int  dim, const FEType &  fet  )

inherited

Definition at line 380 of file fe_base.C.

References libMesh::FEType::family, libMesh::LAGRANGE_VEC, and libMesh::NEDELEC_ONE.

{
  switch (dim)
    {
      // 0D
    case 0:
      {
        switch (fet.family)
          {
          case LAGRANGE_VEC:
            return libmesh_make_unique<FELagrangeVec<0>>(fet);

          default:
            libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
          }
      }
    case 1:
      {
        switch (fet.family)
          {
          case LAGRANGE_VEC:
            return libmesh_make_unique<FELagrangeVec<1>>(fet);

          default:
            libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
          }
      }
    case 2:
      {
        switch (fet.family)
          {
          case LAGRANGE_VEC:
            return libmesh_make_unique<FELagrangeVec<2>>(fet);

          case NEDELEC_ONE:
            return libmesh_make_unique<FENedelecOne<2>>(fet);

          default:
            libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
          }
      }
    case 3:
      {
        switch (fet.family)
          {
          case LAGRANGE_VEC:
            return libmesh_make_unique<FELagrangeVec<3>>(fet);

          case NEDELEC_ONE:
            return libmesh_make_unique<FENedelecOne<3>>(fet);

          default:
            libmesh_error_msg("ERROR: Bad FEType.family= " << fet.family);
          }
      }

    default:
      libmesh_error_msg("Invalid dimension dim = " << dim);
    } // switch(dim)
}

build_InfFE() [1/3]

static std::unique_ptr<FEGenericBase> libMesh::FEGenericBase< FEOutputType< T >::type >::build_InfFE ( const unsigned int  dim, const FEType &  type  )

staticinherited

Builds a specific infinite element type. A std::unique_ptr<FEGenericBase> is returned to prevent a memory leak. This way the user need not remember to delete the object.

The build call will fail if the OutputShape of this class is not compatible with the output required for the requested type

build_InfFE() [2/3]

std::unique_ptr< FEGenericBase< Real > > libMesh::FEGenericBase< Real >::build_InfFE ( const unsigned int  dim, const FEType &  fet  )

inherited

Definition at line 453 of file fe_base.C.

References libMesh::CARTESIAN, libMesh::FEType::inf_map, libMesh::INFINITE_MAP, libMesh::JACOBI_20_00, libMesh::JACOBI_30_00, libMesh::LAGRANGE, libMesh::LEGENDRE, and libMesh::FEType::radial_family.

{
  switch (dim)
    {

      // 1D
    case 1:
      {
        switch (fet.radial_family)
          {
          case INFINITE_MAP:
            libmesh_error_msg("ERROR: Can't build an infinite element with FEFamily = " << fet.radial_family);

          case JACOBI_20_00:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return libmesh_make_unique<InfFE<1,JACOBI_20_00,CARTESIAN>>(fet);

                default:
                  libmesh_error_msg("ERROR: Can't build an infinite element with InfMapType = " << fet.inf_map);
                }
            }

          case JACOBI_30_00:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return libmesh_make_unique<InfFE<1,JACOBI_30_00,CARTESIAN>>(fet);

                default:
                  libmesh_error_msg("ERROR: Can't build an infinite element with InfMapType = " << fet.inf_map);
                }
            }

          case LEGENDRE:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return libmesh_make_unique<InfFE<1,LEGENDRE,CARTESIAN>>(fet);

                default:
                  libmesh_error_msg("ERROR: Can't build an infinite element with InfMapType = " << fet.inf_map);
                }
            }

          case LAGRANGE:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return libmesh_make_unique<InfFE<1,LAGRANGE,CARTESIAN>>(fet);

                default:
                  libmesh_error_msg("ERROR: Can't build an infinite element with InfMapType = " << fet.inf_map);
                }
            }

          default:
            libmesh_error_msg("ERROR: Bad FEType.radial_family= " << fet.radial_family);
          }
      }




      // 2D
    case 2:
      {
        switch (fet.radial_family)
          {
          case INFINITE_MAP:
            libmesh_error_msg("ERROR: Can't build an infinite element with FEFamily = " << fet.radial_family);

          case JACOBI_20_00:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return libmesh_make_unique<InfFE<2,JACOBI_20_00,CARTESIAN>>(fet);

                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
                }
            }

          case JACOBI_30_00:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return libmesh_make_unique<InfFE<2,JACOBI_30_00,CARTESIAN>>(fet);

                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
                }
            }

          case LEGENDRE:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return libmesh_make_unique<InfFE<2,LEGENDRE,CARTESIAN>>(fet);

                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
                }
            }

          case LAGRANGE:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return libmesh_make_unique<InfFE<2,LAGRANGE,CARTESIAN>>(fet);

                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
                }
            }

          default:
            libmesh_error_msg("ERROR: Bad FEType.radial_family= " << fet.radial_family);
          }
      }




      // 3D
    case 3:
      {
        switch (fet.radial_family)
          {
          case INFINITE_MAP:
            libmesh_error_msg("ERROR: Don't build an infinite element with FEFamily = " << fet.radial_family);

          case JACOBI_20_00:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return libmesh_make_unique<InfFE<3,JACOBI_20_00,CARTESIAN>>(fet);

                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
                }
            }

          case JACOBI_30_00:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return libmesh_make_unique<InfFE<3,JACOBI_30_00,CARTESIAN>>(fet);

                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
                }
            }

          case LEGENDRE:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return libmesh_make_unique<InfFE<3,LEGENDRE,CARTESIAN>>(fet);

                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
                }
            }

          case LAGRANGE:
            {
              switch (fet.inf_map)
                {
                case CARTESIAN:
                  return libmesh_make_unique<InfFE<3,LAGRANGE,CARTESIAN>>(fet);

                default:
                  libmesh_error_msg("ERROR: Don't build an infinite element with InfMapType = " << fet.inf_map);
                }
            }

          default:
            libmesh_error_msg("ERROR: Bad FEType.radial_family= " << fet.radial_family);
          }
      }

    default:
      libmesh_error_msg("Invalid dimension dim = " << dim);
    }
}

build_InfFE() [3/3]

std::unique_ptr< FEGenericBase< RealGradient > > libMesh::FEGenericBase< RealGradient >::build_InfFE ( const unsigned  int, const FEType &    )

inherited

Definition at line 657 of file fe_base.C.

{
  // No vector types defined... YET.
  libmesh_not_implemented();
  return std::unique_ptr<FEVectorBase>();
}

coarsened_dof_values() [1/2]

void libMesh::FEGenericBase< FEOutputType< T >::type >::coarsened_dof_values ( const NumericVector< Number > &  global_vector, const DofMap &  dof_map, const Elem *  coarse_elem, DenseVector< Number > &  coarse_dofs, const unsigned int  var, const bool  use_old_dof_indices = false  )

staticinherited

Creates a local projection on coarse_elem, based on the DoF values in global_vector for it's children. Computes a vector of coefficients corresponding to dof_indices for only the single given var

Definition at line 791 of file fe_base.C.

References std::abs(), libMesh::C_ONE, libMesh::Elem::child_ptr(), libMesh::Elem::child_ref_range(), libMesh::DenseMatrix< T >::cholesky_solve(), libMesh::FEType::default_quadrature_rule(), libMesh::Elem::dim(), libMesh::DISCONTINUOUS, libMesh::DofMap::dof_indices(), libMesh::FEInterface::dofs_on_edge(), libMesh::FEInterface::dofs_on_side(), libMesh::Elem::edge_index_range(), libMesh::TensorTools::inner_product(), libMesh::FEInterface::inverse_map(), libMesh::Elem::is_child_on_edge(), libMesh::Elem::is_child_on_side(), libMesh::Elem::is_vertex(), libMesh::Elem::max_descendant_p_level(), libMesh::Elem::n_children(), libMesh::FEInterface::n_dofs(), libMesh::FEInterface::n_dofs_at_node(), n_nodes, libMesh::Elem::n_nodes(), libMesh::DofMap::old_dof_indices(), libMesh::FEType::order, libMesh::Elem::p_level(), libMesh::DenseVector< T >::resize(), libMesh::DenseMatrix< T >::resize(), libMesh::Elem::side_index_range(), libMesh::TOLERANCE, libMesh::Elem::type(), libMesh::DofMap::variable_type(), libMesh::DenseMatrix< T >::zero(), libMesh::DenseVector< T >::zero(), and libMesh::zero.

{
  // Side/edge local DOF indices
  std::vector<unsigned int> new_side_dofs, old_side_dofs;

  // FIXME: what about 2D shells in 3D space?
  unsigned int dim = elem->dim();

  // Cache n_children(); it's a virtual call but it's const.
  const unsigned int n_children = elem->n_children();

  // We use local FE objects for now
  // FIXME: we should use more, external objects instead for efficiency
  const FEType & base_fe_type = dof_map.variable_type(var);
  std::unique_ptr<FEGenericBase<OutputShape>> fe
    (FEGenericBase<OutputShape>::build(dim, base_fe_type));
  std::unique_ptr<FEGenericBase<OutputShape>> fe_coarse
    (FEGenericBase<OutputShape>::build(dim, base_fe_type));

  std::unique_ptr<QBase> qrule     (base_fe_type.default_quadrature_rule(dim));
  std::unique_ptr<QBase> qedgerule (base_fe_type.default_quadrature_rule(1));
  std::unique_ptr<QBase> qsiderule (base_fe_type.default_quadrature_rule(dim-1));
  std::vector<Point> coarse_qpoints;

  // The values of the shape functions at the quadrature
  // points
  const std::vector<std::vector<OutputShape>> & phi_values =
    fe->get_phi();
  const std::vector<std::vector<OutputShape>> & phi_coarse =
    fe_coarse->get_phi();

  // The gradients of the shape functions at the quadrature
  // points on the child element.
  const std::vector<std::vector<OutputGradient>> * dphi_values =
    nullptr;
  const std::vector<std::vector<OutputGradient>> * dphi_coarse =
    nullptr;

  const FEContinuity cont = fe->get_continuity();

  if (cont == C_ONE)
    {
      const std::vector<std::vector<OutputGradient>> &
        ref_dphi_values = fe->get_dphi();
      dphi_values = &ref_dphi_values;
      const std::vector<std::vector<OutputGradient>> &
        ref_dphi_coarse = fe_coarse->get_dphi();
      dphi_coarse = &ref_dphi_coarse;
    }

  // The Jacobian * quadrature weight at the quadrature points
  const std::vector<Real> & JxW =
    fe->get_JxW();

  // The XYZ locations of the quadrature points on the
  // child element
  const std::vector<Point> & xyz_values =
    fe->get_xyz();



  FEType fe_type = base_fe_type, temp_fe_type;
  const ElemType elem_type = elem->type();
  fe_type.order = static_cast<Order>(fe_type.order +
                                     elem->max_descendant_p_level());

  // Number of nodes on parent element
  const unsigned int n_nodes = elem->n_nodes();

  // Number of dofs on parent element
  const unsigned int new_n_dofs =
    FEInterface::n_dofs(dim, fe_type, elem_type);

  // Fixed vs. free DoFs on edge/face projections
  std::vector<char> dof_is_fixed(new_n_dofs, false); // bools
  std::vector<int> free_dof(new_n_dofs, 0);

  DenseMatrix<Real> Ke;
  DenseVector<Number> Fe;
  Ue.resize(new_n_dofs); Ue.zero();


  // When coarsening, in general, we need a series of
  // projections to ensure a unique and continuous
  // solution.  We start by interpolating nodes, then
  // hold those fixed and project edges, then
  // hold those fixed and project faces, then
  // hold those fixed and project interiors

  // Copy node values first
  {
    std::vector<dof_id_type> node_dof_indices;
    if (use_old_dof_indices)
      dof_map.old_dof_indices (elem, node_dof_indices, var);
    else
      dof_map.dof_indices (elem, node_dof_indices, var);

    unsigned int current_dof = 0;
    for (unsigned int n=0; n!= n_nodes; ++n)
      {
        // FIXME: this should go through the DofMap,
        // not duplicate dof_indices code badly!
        const unsigned int my_nc =
          FEInterface::n_dofs_at_node (dim, fe_type,
                                       elem_type, n);
        if (!elem->is_vertex(n))
          {
            current_dof += my_nc;
            continue;
          }

        temp_fe_type = base_fe_type;
        // We're assuming here that child n shares vertex n,
        // which is wrong on non-simplices right now
        // ... but this code isn't necessary except on elements
        // where p refinement creates more vertex dofs; we have
        // no such elements yet.
        /*
          if (elem->child_ptr(n)->p_level() < elem->p_level())
          {
          temp_fe_type.order =
          static_cast<Order>(temp_fe_type.order +
          elem->child_ptr(n)->p_level());
          }
        */
        const unsigned int nc =
          FEInterface::n_dofs_at_node (dim, temp_fe_type,
                                       elem_type, n);
        for (unsigned int i=0; i!= nc; ++i)
          {
            Ue(current_dof) =
              old_vector(node_dof_indices[current_dof]);
            dof_is_fixed[current_dof] = true;
            current_dof++;
          }
      }
  }

  // In 3D, project any edge values next
  if (dim > 2 && cont != DISCONTINUOUS)
    for (auto e : elem->edge_index_range())
      {
        FEInterface::dofs_on_edge(elem, dim, fe_type,
                                  e, new_side_dofs);

        const unsigned int n_new_side_dofs =
          cast_int<unsigned int>(new_side_dofs.size());

        // Some edge dofs are on nodes and already
        // fixed, others are free to calculate
        unsigned int free_dofs = 0;
        for (unsigned int i=0; i != n_new_side_dofs; ++i)
          if (!dof_is_fixed[new_side_dofs[i]])
            free_dof[free_dofs++] = i;
        Ke.resize (free_dofs, free_dofs); Ke.zero();
        Fe.resize (free_dofs); Fe.zero();
        // The new edge coefficients
        DenseVector<Number> Uedge(free_dofs);

        // Add projection terms from each child sharing
        // this edge
        for (unsigned int c=0; c != n_children; ++c)
          {
            if (!elem->is_child_on_edge(c,e))
              continue;
            const Elem * child = elem->child_ptr(c);

            std::vector<dof_id_type> child_dof_indices;
            if (use_old_dof_indices)
              dof_map.old_dof_indices (child,
                                       child_dof_indices, var);
            else
              dof_map.dof_indices (child,
                                   child_dof_indices, var);
            const unsigned int child_n_dofs =
              cast_int<unsigned int>
              (child_dof_indices.size());

            temp_fe_type = base_fe_type;
            temp_fe_type.order =
              static_cast<Order>(temp_fe_type.order +
                                 child->p_level());

            FEInterface::dofs_on_edge(child, dim,
                                      temp_fe_type, e, old_side_dofs);

            // Initialize both child and parent FE data
            // on the child's edge
            fe->attach_quadrature_rule (qedgerule.get());
            fe->edge_reinit (child, e);
            const unsigned int n_qp = qedgerule->n_points();

            FEInterface::inverse_map (dim, fe_type, elem,
                                      xyz_values, coarse_qpoints);

            fe_coarse->reinit(elem, &coarse_qpoints);

            // Loop over the quadrature points
            for (unsigned int qp=0; qp<n_qp; qp++)
              {
                // solution value at the quadrature point
                OutputNumber fineval = libMesh::zero;
                // solution grad at the quadrature point
                OutputNumberGradient finegrad;

                // Sum the solution values * the DOF
                // values at the quadrature point to
                // get the solution value and gradient.
                for (unsigned int i=0; i<child_n_dofs;
                     i++)
                  {
                    fineval +=
                      (old_vector(child_dof_indices[i])*
                       phi_values[i][qp]);
                    if (cont == C_ONE)
                      finegrad += (*dphi_values)[i][qp] *
                        old_vector(child_dof_indices[i]);
                  }

                // Form edge projection matrix
                for (unsigned int sidei=0, freei=0; sidei != n_new_side_dofs; ++sidei)
                  {
                    unsigned int i = new_side_dofs[sidei];
                    // fixed DoFs aren't test functions
                    if (dof_is_fixed[i])
                      continue;
                    for (unsigned int sidej=0, freej=0; sidej != n_new_side_dofs; ++sidej)
                      {
                        unsigned int j =
                          new_side_dofs[sidej];
                        if (dof_is_fixed[j])
                          Fe(freei) -=
                            TensorTools::inner_product(phi_coarse[i][qp],
                                                       phi_coarse[j][qp]) *
                            JxW[qp] * Ue(j);
                        else
                          Ke(freei,freej) +=
                            TensorTools::inner_product(phi_coarse[i][qp],
                                                       phi_coarse[j][qp]) *
                            JxW[qp];
                        if (cont == C_ONE)
                          {
                            if (dof_is_fixed[j])
                              Fe(freei) -=
                                TensorTools::inner_product((*dphi_coarse)[i][qp],
                                                           (*dphi_coarse)[j][qp]) *
                                JxW[qp] * Ue(j);
                            else
                              Ke(freei,freej) +=
                                TensorTools::inner_product((*dphi_coarse)[i][qp],
                                                           (*dphi_coarse)[j][qp]) *
                                JxW[qp];
                          }
                        if (!dof_is_fixed[j])
                          freej++;
                      }
                    Fe(freei) += TensorTools::inner_product(phi_coarse[i][qp],
                                                            fineval) * JxW[qp];
                    if (cont == C_ONE)
                      Fe(freei) +=
                        TensorTools::inner_product(finegrad, (*dphi_coarse)[i][qp]) * JxW[qp];
                    freei++;
                  }
              }
          }
        Ke.cholesky_solve(Fe, Uedge);

        // Transfer new edge solutions to element
        for (unsigned int i=0; i != free_dofs; ++i)
          {
            Number & ui = Ue(new_side_dofs[free_dof[i]]);
            libmesh_assert(std::abs(ui) < TOLERANCE ||
                           std::abs(ui - Uedge(i)) < TOLERANCE);
            ui = Uedge(i);
            dof_is_fixed[new_side_dofs[free_dof[i]]] = true;
          }
      }

  // Project any side values (edges in 2D, faces in 3D)
  if (dim > 1 && cont != DISCONTINUOUS)
    for (auto s : elem->side_index_range())
      {
        FEInterface::dofs_on_side(elem, dim, fe_type,
                                  s, new_side_dofs);

        const unsigned int n_new_side_dofs =
          cast_int<unsigned int>(new_side_dofs.size());

        // Some side dofs are on nodes/edges and already
        // fixed, others are free to calculate
        unsigned int free_dofs = 0;
        for (unsigned int i=0; i != n_new_side_dofs; ++i)
          if (!dof_is_fixed[new_side_dofs[i]])
            free_dof[free_dofs++] = i;
        Ke.resize (free_dofs, free_dofs); Ke.zero();
        Fe.resize (free_dofs); Fe.zero();
        // The new side coefficients
        DenseVector<Number> Uside(free_dofs);

        // Add projection terms from each child sharing
        // this side
        for (unsigned int c=0; c != n_children; ++c)
          {
            if (!elem->is_child_on_side(c,s))
              continue;
            const Elem * child = elem->child_ptr(c);

            std::vector<dof_id_type> child_dof_indices;
            if (use_old_dof_indices)
              dof_map.old_dof_indices (child,
                                       child_dof_indices, var);
            else
              dof_map.dof_indices (child,
                                   child_dof_indices, var);
            const unsigned int child_n_dofs =
              cast_int<unsigned int>
              (child_dof_indices.size());

            temp_fe_type = base_fe_type;
            temp_fe_type.order =
              static_cast<Order>(temp_fe_type.order +
                                 child->p_level());

            FEInterface::dofs_on_side(child, dim,
                                      temp_fe_type, s, old_side_dofs);

            // Initialize both child and parent FE data
            // on the child's side
            fe->attach_quadrature_rule (qsiderule.get());
            fe->reinit (child, s);
            const unsigned int n_qp = qsiderule->n_points();

            FEInterface::inverse_map (dim, fe_type, elem,
                                      xyz_values, coarse_qpoints);

            fe_coarse->reinit(elem, &coarse_qpoints);

            // Loop over the quadrature points
            for (unsigned int qp=0; qp<n_qp; qp++)
              {
                // solution value at the quadrature point
                OutputNumber fineval = libMesh::zero;
                // solution grad at the quadrature point
                OutputNumberGradient finegrad;

                // Sum the solution values * the DOF
                // values at the quadrature point to
                // get the solution value and gradient.
                for (unsigned int i=0; i<child_n_dofs;
                     i++)
                  {
                    fineval +=
                      old_vector(child_dof_indices[i]) *
                      phi_values[i][qp];
                    if (cont == C_ONE)
                      finegrad += (*dphi_values)[i][qp] *
                        old_vector(child_dof_indices[i]);
                  }

                // Form side projection matrix
                for (unsigned int sidei=0, freei=0; sidei != n_new_side_dofs; ++sidei)
                  {
                    unsigned int i = new_side_dofs[sidei];
                    // fixed DoFs aren't test functions
                    if (dof_is_fixed[i])
                      continue;
                    for (unsigned int sidej=0, freej=0; sidej != n_new_side_dofs; ++sidej)
                      {
                        unsigned int j =
                          new_side_dofs[sidej];
                        if (dof_is_fixed[j])
                          Fe(freei) -=
                            TensorTools::inner_product(phi_coarse[i][qp],
                                                       phi_coarse[j][qp]) *
                            JxW[qp] * Ue(j);
                        else
                          Ke(freei,freej) +=
                            TensorTools::inner_product(phi_coarse[i][qp],
                                                       phi_coarse[j][qp]) *
                            JxW[qp];
                        if (cont == C_ONE)
                          {
                            if (dof_is_fixed[j])
                              Fe(freei) -=
                                TensorTools::inner_product((*dphi_coarse)[i][qp],
                                                           (*dphi_coarse)[j][qp]) *
                                JxW[qp] * Ue(j);
                            else
                              Ke(freei,freej) +=
                                TensorTools::inner_product((*dphi_coarse)[i][qp],
                                                           (*dphi_coarse)[j][qp]) *
                                JxW[qp];
                          }
                        if (!dof_is_fixed[j])
                          freej++;
                      }
                    Fe(freei) += TensorTools::inner_product(fineval, phi_coarse[i][qp]) * JxW[qp];
                    if (cont == C_ONE)
                      Fe(freei) +=
                        TensorTools::inner_product(finegrad, (*dphi_coarse)[i][qp]) * JxW[qp];
                    freei++;
                  }
              }
          }
        Ke.cholesky_solve(Fe, Uside);

        // Transfer new side solutions to element
        for (unsigned int i=0; i != free_dofs; ++i)
          {
            Number & ui = Ue(new_side_dofs[free_dof[i]]);
            libmesh_assert(std::abs(ui) < TOLERANCE ||
                           std::abs(ui - Uside(i)) < TOLERANCE);
            ui = Uside(i);
            dof_is_fixed[new_side_dofs[free_dof[i]]] = true;
          }
      }

  // Project the interior values, finally

  // Some interior dofs are on nodes/edges/sides and
  // already fixed, others are free to calculate
  unsigned int free_dofs = 0;
  for (unsigned int i=0; i != new_n_dofs; ++i)
    if (!dof_is_fixed[i])
      free_dof[free_dofs++] = i;
  Ke.resize (free_dofs, free_dofs); Ke.zero();
  Fe.resize (free_dofs); Fe.zero();
  // The new interior coefficients
  DenseVector<Number> Uint(free_dofs);

  // Add projection terms from each child
  for (auto & child : elem->child_ref_range())
    {
      std::vector<dof_id_type> child_dof_indices;
      if (use_old_dof_indices)
        dof_map.old_dof_indices (&child,
                                 child_dof_indices, var);
      else
        dof_map.dof_indices (&child,
                             child_dof_indices, var);
      const unsigned int child_n_dofs =
        cast_int<unsigned int>
        (child_dof_indices.size());

      // Initialize both child and parent FE data
      // on the child's quadrature points
      fe->attach_quadrature_rule (qrule.get());
      fe->reinit (&child);
      const unsigned int n_qp = qrule->n_points();

      FEInterface::inverse_map (dim, fe_type, elem,
                                xyz_values, coarse_qpoints);

      fe_coarse->reinit(elem, &coarse_qpoints);

      // Loop over the quadrature points
      for (unsigned int qp=0; qp<n_qp; qp++)
        {
          // solution value at the quadrature point
          OutputNumber fineval = libMesh::zero;
          // solution grad at the quadrature point
          OutputNumberGradient finegrad;

          // Sum the solution values * the DOF
          // values at the quadrature point to
          // get the solution value and gradient.
          for (unsigned int i=0; i<child_n_dofs; i++)
            {
              fineval +=
                (old_vector(child_dof_indices[i]) *
                 phi_values[i][qp]);
              if (cont == C_ONE)
                finegrad += (*dphi_values)[i][qp] *
                  old_vector(child_dof_indices[i]);
            }

          // Form interior projection matrix
          for (unsigned int i=0, freei=0;
               i != new_n_dofs; ++i)
            {
              // fixed DoFs aren't test functions
              if (dof_is_fixed[i])
                continue;
              for (unsigned int j=0, freej=0; j !=
                     new_n_dofs; ++j)
                {
                  if (dof_is_fixed[j])
                    Fe(freei) -=
                      TensorTools::inner_product(phi_coarse[i][qp],
                                                 phi_coarse[j][qp]) *
                      JxW[qp] * Ue(j);
                  else
                    Ke(freei,freej) +=
                      TensorTools::inner_product(phi_coarse[i][qp],
                                                 phi_coarse[j][qp]) *
                      JxW[qp];
                  if (cont == C_ONE)
                    {
                      if (dof_is_fixed[j])
                        Fe(freei) -=
                          TensorTools::inner_product((*dphi_coarse)[i][qp],
                                                     (*dphi_coarse)[j][qp]) *
                          JxW[qp] * Ue(j);
                      else
                        Ke(freei,freej) +=
                          TensorTools::inner_product((*dphi_coarse)[i][qp],
                                                     (*dphi_coarse)[j][qp]) *
                          JxW[qp];
                    }
                  if (!dof_is_fixed[j])
                    freej++;
                }
              Fe(freei) += TensorTools::inner_product(phi_coarse[i][qp], fineval) *
                JxW[qp];
              if (cont == C_ONE)
                Fe(freei) += TensorTools::inner_product(finegrad, (*dphi_coarse)[i][qp]) * JxW[qp];
              freei++;
            }
        }
    }
  Ke.cholesky_solve(Fe, Uint);

  // Transfer new interior solutions to element
  for (unsigned int i=0; i != free_dofs; ++i)
    {
      Number & ui = Ue(free_dof[i]);
      libmesh_assert(std::abs(ui) < TOLERANCE ||
                     std::abs(ui - Uint(i)) < TOLERANCE);
      ui = Uint(i);
      // We should be fixing all dofs by now; no need to keep track of
      // that unless we're debugging
#ifndef NDEBUG
      dof_is_fixed[free_dof[i]] = true;
#endif
    }

#ifndef NDEBUG
  // Make sure every DoF got reached!
  for (unsigned int i=0; i != new_n_dofs; ++i)
    libmesh_assert(dof_is_fixed[i]);
#endif
}

coarsened_dof_values() [2/2]

void libMesh::FEGenericBase< FEOutputType< T >::type >::coarsened_dof_values ( const NumericVector< Number > &  global_vector, const DofMap &  dof_map, const Elem *  coarse_elem, DenseVector< Number > &  coarse_dofs, const bool  use_old_dof_indices = false  )

staticinherited

Creates a local projection on coarse_elem, based on the DoF values in global_vector for it's children. Computes a vector of coefficients corresponding to all dof_indices.

Definition at line 1343 of file fe_base.C.

References libMesh::DenseVector< T >::append(), libMesh::DofMap::n_variables(), and libMesh::DenseVector< T >::resize().

{
  Ue.resize(0);

  for (unsigned int v=0; v != dof_map.n_variables(); ++v)
    {
      DenseVector<Number> Usub;

      coarsened_dof_values(old_vector, dof_map, elem, Usub,
                           use_old_dof_indices);

      Ue.append (Usub);
    }
}

compute_constraints() [1/29]

template<>

void libMesh::FE< 2, SCALAR >::compute_constraints	(	DofConstraints &	,
		DofMap &	,
		const unsigned	int,
		const Elem *
	)

Definition at line 122 of file fe_scalar.C.

{ }

compute_constraints() [2/29]

template<>

void libMesh::FE< 3, SCALAR >::compute_constraints	(	DofConstraints &	,
		DofMap &	,
		const unsigned	int,
		const Elem *
	)

Definition at line 129 of file fe_scalar.C.

{ }

compute_constraints() [3/29]

template<>

void libMesh::FE< 2, L2_HIERARCHIC >::compute_constraints	(	DofConstraints &	,
		DofMap &	,
		const unsigned	int,
		const Elem *
	)

Definition at line 207 of file fe_l2_hierarchic.C.

{ }

compute_constraints() [4/29]

template<>

void libMesh::FE< 3, L2_HIERARCHIC >::compute_constraints	(	DofConstraints &	,
		DofMap &	,
		const unsigned	int,
		const Elem *
	)

Definition at line 214 of file fe_l2_hierarchic.C.

{ }

compute_constraints() [5/29]

template<>

void libMesh::FE< 2, CLOUGH >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 304 of file fe_clough.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [6/29]

template<>

void libMesh::FE< 3, CLOUGH >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 311 of file fe_clough.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [7/29]

template<>

void libMesh::FE< 2, HERMITE >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 355 of file fe_hermite.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [8/29]

template<>

void libMesh::FE< 3, HERMITE >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 362 of file fe_hermite.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [9/29]

template<>

void libMesh::FE< 2, HIERARCHIC >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 383 of file fe_hierarchic.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [10/29]

template<>

void libMesh::FE< 3, HIERARCHIC >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 390 of file fe_hierarchic.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [11/29]

template<unsigned int Dim, FEFamily T>

static void libMesh::FE< Dim, T >::compute_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const unsigned int  variable_number, const Elem *  elem  )

static

Computes the constraint matrix contributions (for non-conforming adapted meshes) corresponding to variable number var_number, using element-specific optimizations if possible.

Referenced by libMesh::FEInterface::compute_constraints().

compute_constraints() [12/29]

template<>

void libMesh::FE< 2, MONOMIAL >::compute_constraints	(	DofConstraints &	,
		DofMap &	,
		const unsigned	int,
		const Elem *
	)

Definition at line 419 of file fe_monomial.C.

{}

compute_constraints() [13/29]

template<>

void libMesh::FE< 3, MONOMIAL >::compute_constraints	(	DofConstraints &	,
		DofMap &	,
		const unsigned	int,
		const Elem *
	)

Definition at line 420 of file fe_monomial.C.

{}

compute_constraints() [14/29]

template<>

void libMesh::FE< 2, BERNSTEIN >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 450 of file fe_bernstein.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [15/29]

template<>

void libMesh::FE< 3, BERNSTEIN >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 457 of file fe_bernstein.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [16/29]

template<>

void libMesh::FE< 2, L2_LAGRANGE >::compute_constraints	(	DofConstraints &	,
		DofMap &	,
		const unsigned	int,
		const Elem *
	)

Definition at line 495 of file fe_l2_lagrange.C.

{ }

compute_constraints() [17/29]

template<>

void libMesh::FE< 3, L2_LAGRANGE >::compute_constraints	(	DofConstraints &	,
		DofMap &	,
		const unsigned	int,
		const Elem *
	)

Definition at line 502 of file fe_l2_lagrange.C.

{ }

compute_constraints() [18/29]

template<>

void libMesh::FE< 0, NEDELEC_ONE >::compute_constraints	(	DofConstraints &	,
		DofMap &	,
		const unsigned	int,
		const Elem *
	)

Definition at line 563 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

compute_constraints() [19/29]

template<>

void libMesh::FE< 1, NEDELEC_ONE >::compute_constraints	(	DofConstraints &	,
		DofMap &	,
		const unsigned	int,
		const Elem *
	)

Definition at line 570 of file fe_nedelec_one.C.

{ NEDELEC_LOW_D_ERROR_MESSAGE }

compute_constraints() [20/29]

template<>

void libMesh::FE< 2, NEDELEC_ONE >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 577 of file fe_nedelec_one.C.

{ nedelec_one_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/2); }

compute_constraints() [21/29]

template<>

void libMesh::FE< 3, NEDELEC_ONE >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 584 of file fe_nedelec_one.C.

{ nedelec_one_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/3); }

compute_constraints() [22/29]

template<>

void libMesh::FE< 2, LAGRANGE >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 900 of file fe_lagrange.C.

{ lagrange_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/2); }

compute_constraints() [23/29]

template<>

void libMesh::FE< 3, LAGRANGE >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 907 of file fe_lagrange.C.

{ lagrange_compute_constraints(constraints, dof_map, variable_number, elem, /*Dim=*/3); }

compute_constraints() [24/29]

template<>

void libMesh::FE< 2, XYZ >::compute_constraints	(	DofConstraints &	,
		DofMap &	,
		const unsigned	int,
		const Elem *
	)

Definition at line 942 of file fe_xyz.C.

{}

compute_constraints() [25/29]

template<>

void libMesh::FE< 3, XYZ >::compute_constraints	(	DofConstraints &	,
		DofMap &	,
		const unsigned	int,
		const Elem *
	)

Definition at line 943 of file fe_xyz.C.

{}

compute_constraints() [26/29]

template<>

void libMesh::FE< 2, LAGRANGE_VEC >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 950 of file fe_lagrange_vec.C.

{ //libmesh_not_implemented();
  FEVectorBase::compute_proj_constraints(constraints, dof_map, variable_number, elem);
}

compute_constraints() [27/29]

template<>

void libMesh::FE< 3, LAGRANGE_VEC >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 959 of file fe_lagrange_vec.C.

{ //libmesh_not_implemented();
  FEVectorBase::compute_proj_constraints(constraints, dof_map, variable_number, elem);
}

compute_constraints() [28/29]

template<>

void libMesh::FE< 2, SZABAB >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 1287 of file fe_szabab.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_constraints() [29/29]

template<>

void libMesh::FE< 3, SZABAB >::compute_constraints	(	DofConstraints &	constraints,
		DofMap &	dof_map,
		const unsigned int	variable_number,
		const Elem *	elem
	)

Definition at line 1294 of file fe_szabab.C.

{ compute_proj_constraints(constraints, dof_map, variable_number, elem); }

compute_node_constraints()

void libMesh::FEAbstract::compute_node_constraints ( NodeConstraints &  constraints, const Elem *  elem  )

staticinherited

Computes the nodal constraint contributions (for non-conforming adapted meshes), using Lagrange geometry

Definition at line 820 of file fe_abstract.C.

References std::abs(), libMesh::Elem::build_side_ptr(), libMesh::Elem::default_order(), libMesh::Elem::dim(), libMesh::FEAbstract::fe_type, libMesh::FEInterface::inverse_map(), libMesh::LAGRANGE, libMesh::Elem::level(), libMesh::FEInterface::n_dofs(), libMesh::Elem::neighbor_ptr(), libMesh::Elem::parent(), libMesh::Real, libMesh::remote_elem, libMesh::FEInterface::shape(), libMesh::Elem::side_index_range(), libMesh::Threads::spin_mtx, and libMesh::Elem::subactive().

{
  libmesh_assert(elem);

  const unsigned int Dim = elem->dim();

  // Only constrain elements in 2,3D.
  if (Dim == 1)
    return;

  // Only constrain active and ancestor elements
  if (elem->subactive())
    return;

  // We currently always use LAGRANGE mappings for geometry
  const FEType fe_type(elem->default_order(), LAGRANGE);

  // Pull objects out of the loop to reduce heap operations
  std::vector<const Node *> my_nodes, parent_nodes;
  std::unique_ptr<const Elem> my_side, parent_side;

  // Look at the element faces.  Check to see if we need to
  // build constraints.
  for (auto s : elem->side_index_range())
    if (elem->neighbor_ptr(s) != nullptr &&
        elem->neighbor_ptr(s) != remote_elem)
      if (elem->neighbor_ptr(s)->level() < elem->level()) // constrain dofs shared between
        {                                                 // this element and ones coarser
          // than this element.
          // Get pointers to the elements of interest and its parent.
          const Elem * parent = elem->parent();

          // This can't happen...  Only level-0 elements have nullptr
          // parents, and no level-0 elements can be at a higher
          // level than their neighbors!
          libmesh_assert(parent);

          elem->build_side_ptr(my_side, s);
          parent->build_side_ptr(parent_side, s);

          const unsigned int n_side_nodes = my_side->n_nodes();

          my_nodes.clear();
          my_nodes.reserve (n_side_nodes);
          parent_nodes.clear();
          parent_nodes.reserve (n_side_nodes);

          for (unsigned int n=0; n != n_side_nodes; ++n)
            my_nodes.push_back(my_side->node_ptr(n));

          for (unsigned int n=0; n != n_side_nodes; ++n)
            parent_nodes.push_back(parent_side->node_ptr(n));

          for (unsigned int my_side_n=0;
               my_side_n < n_side_nodes;
               my_side_n++)
            {
              libmesh_assert_less (my_side_n, FEInterface::n_dofs(Dim-1, fe_type, my_side->type()));

              const Node * my_node = my_nodes[my_side_n];

              // The support point of the DOF
              const Point & support_point = *my_node;

              // Figure out where my node lies on their reference element.
              const Point mapped_point = FEInterface::inverse_map(Dim-1, fe_type,
                                                                  parent_side.get(),
                                                                  support_point);

              // Compute the parent's side shape function values.
              for (unsigned int their_side_n=0;
                   their_side_n < n_side_nodes;
                   their_side_n++)
                {
                  libmesh_assert_less (their_side_n, FEInterface::n_dofs(Dim-1, fe_type, parent_side->type()));

                  const Node * their_node = parent_nodes[their_side_n];
                  libmesh_assert(their_node);

                  const Real their_value = FEInterface::shape(Dim-1,
                                                              fe_type,
                                                              parent_side->type(),
                                                              their_side_n,
                                                              mapped_point);

                  const Real their_mag = std::abs(their_value);
#ifdef DEBUG
                  // Protect for the case u_i ~= u_j,
                  // in which case i better equal j.
                  if (their_mag > 0.999)
                    {
                      libmesh_assert_equal_to (my_node, their_node);
                      libmesh_assert_less (std::abs(their_value - 1.), 0.001);
                    }
                  else
#endif
                    // To make nodal constraints useful for constructing
                    // sparsity patterns faster, we need to get EVERY
                    // POSSIBLE constraint coupling identified, even if
                    // there is no coupling in the isoparametric
                    // Lagrange case.
                    if (their_mag < 1.e-5)
                      {
                        // since we may be running this method concurrently
                        // on multiple threads we need to acquire a lock
                        // before modifying the shared constraint_row object.
                        Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);

                        // A reference to the constraint row.
                        NodeConstraintRow & constraint_row = constraints[my_node].first;

                        constraint_row.insert(std::make_pair (their_node,
                                                              0.));
                      }
                  // To get nodal coordinate constraints right, only
                  // add non-zero and non-identity values for Lagrange
                  // basis functions.
                    else // (1.e-5 <= their_mag <= .999)
                      {
                        // since we may be running this method concurrently
                        // on multiple threads we need to acquire a lock
                        // before modifying the shared constraint_row object.
                        Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);

                        // A reference to the constraint row.
                        NodeConstraintRow & constraint_row = constraints[my_node].first;

                        constraint_row.insert(std::make_pair (their_node,
                                                              their_value));
                      }
                }
            }
        }
}

compute_periodic_constraints()

void libMesh::FEGenericBase< FEOutputType< T >::type >::compute_periodic_constraints ( DofConstraints &  constraints, DofMap &  dof_map, const PeriodicBoundaries &  boundaries, const MeshBase &  mesh, const PointLocatorBase *  point_locator, const unsigned int  variable_number, const Elem *  elem  )

staticinherited

Computes the constraint matrix contributions (for meshes with periodic boundary conditions) corresponding to variable number var_number, using generic projections.

Definition at line 1650 of file fe_base.C.

References std::abs(), libMesh::TypeVector< T >::absolute_fuzzy_equals(), libMesh::Elem::active(), libMesh::PeriodicBoundaries::boundary(), libMesh::BoundaryInfo::boundary_ids(), libMesh::C_ONE, libMesh::C_ZERO, libMesh::DenseMatrix< T >::cholesky_solve(), libMesh::DofMap::constrain_p_dofs(), libMesh::FEType::default_quadrature_order(), libMesh::Elem::dim(), libMesh::DISCONTINUOUS, libMesh::DofMap::dof_indices(), libMesh::DofObject::dof_number(), libMesh::FEInterface::dofs_on_side(), libMesh::MeshBase::get_boundary_info(), libMesh::PeriodicBoundaryBase::get_corresponding_pos(), libMesh::PeriodicBoundaryBase::get_transformation_matrix(), libMesh::PeriodicBoundaryBase::get_variables(), libMesh::PeriodicBoundaryBase::has_transformation_matrix(), libMesh::Elem::hmin(), libMesh::DofObject::id(), libMesh::index_range(), libMesh::TensorTools::inner_product(), libMesh::DofObject::invalid_id, libMesh::invalid_uint, libMesh::FEInterface::inverse_map(), libMesh::DofMap::is_constrained_dof(), libMesh::Elem::is_edge(), libMesh::Elem::is_face(), libMesh::PeriodicBoundaryBase::is_my_variable(), libMesh::Elem::is_node_on_edge(), libMesh::Elem::is_node_on_side(), libMesh::Elem::is_vertex(), libMesh::Elem::level(), mesh, std::min(), libMesh::Elem::min_p_level_by_neighbor(), libMesh::DofObject::n_comp(), libMesh::Elem::n_edges(), libMesh::Elem::n_nodes(), libMesh::Elem::n_sides(), libMesh::PeriodicBoundaries::neighbor(), libMesh::Elem::neighbor_ptr(), libMesh::Elem::node_ptr(), libMesh::Elem::node_ref(), libMesh::Elem::p_level(), libMesh::PeriodicBoundaryBase::pairedboundary, libMesh::Real, libMesh::DenseVector< T >::resize(), libMesh::DenseMatrix< T >::resize(), libMesh::BoundaryInfo::side_with_boundary_id(), libMesh::Threads::spin_mtx, swap(), libMesh::DofMap::sys_number(), libMesh::TOLERANCE, and libMesh::DofMap::variable_type().

{
  // Only bother if we truly have periodic boundaries
  if (boundaries.empty())
    return;

  libmesh_assert(elem);

  // Only constrain active elements with this method
  if (!elem->active())
    return;

  const unsigned int Dim = elem->dim();

  // We need sys_number and variable_number for DofObject methods
  // later
  const unsigned int sys_number = dof_map.sys_number();

  const FEType & base_fe_type = dof_map.variable_type(variable_number);

  // Construct FE objects for this element and its pseudo-neighbors.
  std::unique_ptr<FEGenericBase<OutputShape>> my_fe
    (FEGenericBase<OutputShape>::build(Dim, base_fe_type));
  const FEContinuity cont = my_fe->get_continuity();

  // We don't need to constrain discontinuous elements
  if (cont == DISCONTINUOUS)
    return;
  libmesh_assert (cont == C_ZERO || cont == C_ONE);

  // We'll use element size to generate relative tolerances later
  const Real primary_hmin = elem->hmin();

  std::unique_ptr<FEGenericBase<OutputShape>> neigh_fe
    (FEGenericBase<OutputShape>::build(Dim, base_fe_type));

  QGauss my_qface(Dim-1, base_fe_type.default_quadrature_order());
  my_fe->attach_quadrature_rule (&my_qface);
  std::vector<Point> neigh_qface;

  const std::vector<Real> & JxW = my_fe->get_JxW();
  const std::vector<Point> & q_point = my_fe->get_xyz();
  const std::vector<std::vector<OutputShape>> & phi = my_fe->get_phi();
  const std::vector<std::vector<OutputShape>> & neigh_phi =
    neigh_fe->get_phi();
  const std::vector<Point> * face_normals = nullptr;
  const std::vector<std::vector<OutputGradient>> * dphi = nullptr;
  const std::vector<std::vector<OutputGradient>> * neigh_dphi = nullptr;
  std::vector<dof_id_type> my_dof_indices, neigh_dof_indices;
  std::vector<unsigned int> my_side_dofs, neigh_side_dofs;

  if (cont != C_ZERO)
    {
      const std::vector<Point> & ref_face_normals =
        my_fe->get_normals();
      face_normals = &ref_face_normals;
      const std::vector<std::vector<OutputGradient>> & ref_dphi =
        my_fe->get_dphi();
      dphi = &ref_dphi;
      const std::vector<std::vector<OutputGradient>> & ref_neigh_dphi =
        neigh_fe->get_dphi();
      neigh_dphi = &ref_neigh_dphi;
    }

  DenseMatrix<Real> Ke;
  DenseVector<Real> Fe;
  std::vector<DenseVector<Real>> Ue;

  // Container to catch the boundary ids that BoundaryInfo hands us.
  std::vector<boundary_id_type> bc_ids;

  // Look at the element faces.  Check to see if we need to
  // build constraints.
  const unsigned short int max_ns = elem->n_sides();
  for (unsigned short int s = 0; s != max_ns; ++s)
    {
      if (elem->neighbor_ptr(s))
        continue;

      mesh.get_boundary_info().boundary_ids (elem, s, bc_ids);

      for (const auto & boundary_id : bc_ids)
        {
          const PeriodicBoundaryBase * periodic = boundaries.boundary(boundary_id);
          if (periodic && periodic->is_my_variable(variable_number))
            {
              libmesh_assert(point_locator);

              // Get pointers to the element's neighbor.
              const Elem * neigh = boundaries.neighbor(boundary_id, *point_locator, elem, s);

              if (neigh == nullptr)
                libmesh_error_msg("PeriodicBoundaries point locator object returned nullptr!");

              // periodic (and possibly h refinement) constraints:
              // constrain dofs shared between
              // this element and ones as coarse
              // as or coarser than this element.
              if (neigh->level() <= elem->level())
                {
                  unsigned int s_neigh =
                    mesh.get_boundary_info().side_with_boundary_id(neigh, periodic->pairedboundary);
                  libmesh_assert_not_equal_to (s_neigh, libMesh::invalid_uint);

#ifdef LIBMESH_ENABLE_AMR
                  // Find the minimum p level; we build the h constraint
                  // matrix with this and then constrain away all higher p
                  // DoFs.
                  libmesh_assert(neigh->active());
                  const unsigned int min_p_level =
                    std::min(elem->p_level(), neigh->p_level());

                  // we may need to make the FE objects reinit with the
                  // minimum shared p_level
                  // FIXME - I hate using const_cast<> and avoiding
                  // accessor functions; there's got to be a
                  // better way to do this!
                  const unsigned int old_elem_level = elem->p_level();
                  if (old_elem_level != min_p_level)
                    (const_cast<Elem *>(elem))->hack_p_level(min_p_level);
                  const unsigned int old_neigh_level = neigh->p_level();
                  if (old_neigh_level != min_p_level)
                    (const_cast<Elem *>(neigh))->hack_p_level(min_p_level);
#endif // #ifdef LIBMESH_ENABLE_AMR

                  // We can do a projection with a single integration,
                  // due to the assumption of nested finite element
                  // subspaces.
                  // FIXME: it might be more efficient to do nodes,
                  // then edges, then side, to reduce the size of the
                  // Cholesky factorization(s)
                  my_fe->reinit(elem, s);

                  dof_map.dof_indices (elem, my_dof_indices,
                                       variable_number);
                  dof_map.dof_indices (neigh, neigh_dof_indices,
                                       variable_number);

                  // We use neigh_dof_indices_all_variables in the case that the
                  // periodic boundary condition involves mappings between multiple
                  // variables.
                  std::vector<std::vector<dof_id_type>> neigh_dof_indices_all_variables;
                  if(periodic->has_transformation_matrix())
                    {
                      const std::set<unsigned int> & variables = periodic->get_variables();
                      neigh_dof_indices_all_variables.resize(variables.size());
                      unsigned int index = 0;
                      for(unsigned int var : variables)
                        {
                          dof_map.dof_indices (neigh, neigh_dof_indices_all_variables[index],
                                               var);
                          index++;
                        }
                    }

                  const unsigned int n_qp = my_qface.n_points();

                  // Translate the quadrature points over to the
                  // neighbor's boundary
                  std::vector<Point> neigh_point(q_point.size());
                  for (auto i : index_range(neigh_point))
                    neigh_point[i] = periodic->get_corresponding_pos(q_point[i]);

                  FEInterface::inverse_map (Dim, base_fe_type, neigh,
                                            neigh_point, neigh_qface);

                  neigh_fe->reinit(neigh, &neigh_qface);

                  // We're only concerned with DOFs whose values (and/or first
                  // derivatives for C1 elements) are supported on side nodes
                  FEInterface::dofs_on_side(elem, Dim, base_fe_type, s, my_side_dofs);
                  FEInterface::dofs_on_side(neigh, Dim, base_fe_type, s_neigh, neigh_side_dofs);

                  // We're done with functions that examine Elem::p_level(),
                  // so let's unhack those levels
#ifdef LIBMESH_ENABLE_AMR
                  if (elem->p_level() != old_elem_level)
                    (const_cast<Elem *>(elem))->hack_p_level(old_elem_level);
                  if (neigh->p_level() != old_neigh_level)
                    (const_cast<Elem *>(neigh))->hack_p_level(old_neigh_level);
#endif // #ifdef LIBMESH_ENABLE_AMR

                  const unsigned int n_side_dofs =
                    cast_int<unsigned int>
                    (my_side_dofs.size());
                  libmesh_assert_equal_to (n_side_dofs, neigh_side_dofs.size());

                  Ke.resize (n_side_dofs, n_side_dofs);
                  Ue.resize(n_side_dofs);

                  // Form the projection matrix, (inner product of fine basis
                  // functions against fine test functions)
                  for (unsigned int is = 0; is != n_side_dofs; ++is)
                    {
                      const unsigned int i = my_side_dofs[is];
                      for (unsigned int js = 0; js != n_side_dofs; ++js)
                        {
                          const unsigned int j = my_side_dofs[js];
                          for (unsigned int qp = 0; qp != n_qp; ++qp)
                            {
                              Ke(is,js) += JxW[qp] *
                                TensorTools::inner_product(phi[i][qp],
                                                           phi[j][qp]);
                              if (cont != C_ZERO)
                                Ke(is,js) += JxW[qp] *
                                  TensorTools::inner_product((*dphi)[i][qp] *
                                                             (*face_normals)[qp],
                                                             (*dphi)[j][qp] *
                                                             (*face_normals)[qp]);
                            }
                        }
                    }

                  // Form the right hand sides, (inner product of coarse basis
                  // functions against fine test functions)
                  for (unsigned int is = 0; is != n_side_dofs; ++is)
                    {
                      const unsigned int i = neigh_side_dofs[is];
                      Fe.resize (n_side_dofs);
                      for (unsigned int js = 0; js != n_side_dofs; ++js)
                        {
                          const unsigned int j = my_side_dofs[js];
                          for (unsigned int qp = 0; qp != n_qp; ++qp)
                            {
                              Fe(js) += JxW[qp] *
                                TensorTools::inner_product(neigh_phi[i][qp],
                                                           phi[j][qp]);
                              if (cont != C_ZERO)
                                Fe(js) += JxW[qp] *
                                  TensorTools::inner_product((*neigh_dphi)[i][qp] *
                                                             (*face_normals)[qp],
                                                             (*dphi)[j][qp] *
                                                             (*face_normals)[qp]);
                            }
                        }
                      Ke.cholesky_solve(Fe, Ue[is]);
                    }

                  // Make sure we're not adding recursive constraints
                  // due to the redundancy in the way we add periodic
                  // boundary constraints
                  //
                  // In order for this to work while threaded or on
                  // distributed meshes, we need a rigorous way to
                  // avoid recursive constraints.  Here it is:
                  //
                  // For vertex DoFs, if there is a "prior" element
                  // (i.e. a coarser element or an equally refined
                  // element with a lower id) on this boundary which
                  // contains the vertex point, then we will avoid
                  // generating constraints; the prior element (or
                  // something prior to it) may do so.  If we are the
                  // most prior (or "primary") element on this
                  // boundary sharing this point, then we look at the
                  // boundary periodic to us, we find the primary
                  // element there, and if that primary is coarser or
                  // equal-but-lower-id, then our vertex dofs are
                  // constrained in terms of that element.
                  //
                  // For edge DoFs, if there is a coarser element
                  // on this boundary sharing this edge, then we will
                  // avoid generating constraints (we will be
                  // constrained indirectly via AMR constraints
                  // connecting us to the coarser element's DoFs).  If
                  // we are the coarsest element sharing this edge,
                  // then we generate constraints if and only if we
                  // are finer than the coarsest element on the
                  // boundary periodic to us sharing the corresponding
                  // periodic edge, or if we are at equal level but
                  // our edge nodes have higher ids than the periodic
                  // edge nodes (sorted from highest to lowest, then
                  // compared lexicographically)
                  //
                  // For face DoFs, we generate constraints if we are
                  // finer than our periodic neighbor, or if we are at
                  // equal level but our element id is higher than its
                  // element id.
                  //
                  // If the primary neighbor is also the current elem
                  // (a 1-element-thick mesh) then we choose which
                  // vertex dofs to constrain via lexicographic
                  // ordering on point locations

                  // FIXME: This code doesn't yet properly handle
                  // cases where multiple different periodic BCs
                  // intersect.
                  std::set<dof_id_type> my_constrained_dofs;

                  // Container to catch boundary IDs handed back by BoundaryInfo.
                  std::vector<boundary_id_type> new_bc_ids;

                  for (unsigned int n = 0; n != elem->n_nodes(); ++n)