A class mapping local vectorial shape function values and gradients to global shape function values and gradients in \( H(\text{div}) \) conforming FE spaces. More...

#include <nedelecspace.hh>

Detailed Description

template<class GridView>
class Kaskade::HdivConverter< GridView >

A class mapping local vectorial shape function values and gradients to global shape function values and gradients in \( H(\text{div}) \) conforming FE spaces.

For vectorial \( H(\text{div}) \) conforming finite elements, the values of the shape functions transform as

\[ \phi(x) = B^T J^{-1} \hat \phi(\xi), \]

where \( B \) is the Jacobian of the affine transformation from reference element to actual element and \( J \) its determinant. See, e.g., Solin, Segeth, Dolezel: Higher Order Finite Element Methods, Chapman & Hall 2004, p 176.

Template Parameters

GridView the FE grid class

Definition at line 206 of file nedelecspace.hh.

Inheritance diagram for Kaskade::HdivConverter< GridView >:

Public Member Functions
	HdivConverter ()=default

	HdivConverter (typename GridView::template Codim< 0 >::Entity const &cell)

void	moveTo (Cell const &cell)

void	setLocalPosition (Dune::FieldVector< typename GridView::ctype, dim > const &x)

template<class Scalar >
Dune::FieldMatrix< Scalar, dim, 1 >	global (Dune::FieldMatrix< Scalar, dim, 1 > const &sf) const
	Applies the transformation \( \psi(x) \) to shape function value. More...

template<class Scalar >
VariationalArg< Scalar, dim, dim >	global (std::pair< Dune::FieldVector< Scalar, dim >, Dune::FieldMatrix< Scalar, dim, dim > > const &sf) const
	Applies the transformation \( \psi(x) \) to shape function value and derivative. More...

template<class Scalar >
VariationalArg< Scalar, dim, dim >	global (VariationalArg< Scalar, dim, dim > const &sf, int deriv) const
	Applies the transformation \( \psi \) to shape function value, derivative, and Hessian, returning a filled VariationalArg. More...

template<class Scalar >
Dune::FieldMatrix< Scalar, dim, 1 >	local (Dune::FieldMatrix< Scalar, dim, 1 > const &glob) const
	Applies the inverse transform \( \psi^{-1} \) to global shape function values, giving the local shape function value. More...

Protected Member Functions
void	solve (Dune::FieldMatrix< typename GridView::ctype, dim, dim > A, Dune::FieldVector< typename GridView::ctype, dim > &x, Dune::FieldVector< typename GridView::ctype, dim > b) const

Protected Attributes
Cell const *	cell_

Dune::FieldMatrix< typename GridView::ctype, dim, dim >	Btinv

Dune::FieldMatrix< typename GridView::ctype, dim, dim >	C

Constructor & Destructor Documentation

◆ HdivConverter() [1/2]

template<class GridView >

Kaskade::HdivConverter< GridView >::HdivConverter ( )

default

◆ HdivConverter() [2/2]

template<class GridView >

Kaskade::HdivConverter< GridView >::HdivConverter ( typename GridView::template Codim< 0 >::Entity const & cell )

inline

Definition at line 211 of file nedelecspace.hh.

Member Function Documentation

◆ global() [1/3]

template<class GridView >

template<class Scalar >

Dune::FieldMatrix< Scalar, dim, 1 > Kaskade::VectorialConverterBase< GridView >::global ( Dune::FieldMatrix< Scalar, dim, 1 > const & sf ) const

inlineinherited

Applies the transformation \( \psi(x) \) to shape function value.

Definition at line 62 of file nedelecspace.hh.

◆ global() [2/3]

template<class GridView >

template<class Scalar >

VariationalArg< Scalar, dim, dim > Kaskade::VectorialConverterBase< GridView >::global ( std::pair< Dune::FieldVector< Scalar, dim >, Dune::FieldMatrix< Scalar, dim, dim > > const & sf ) const

inlineinherited

Applies the transformation \( \psi(x) \) to shape function value and derivative.

Definition at line 69 of file nedelecspace.hh.

◆ global() [3/3]

template<class GridView >

template<class Scalar >

VariationalArg< Scalar, dim, dim > Kaskade::VectorialConverterBase< GridView >::global	(	VariationalArg< Scalar, dim, dim > const &	sf,
		int	deriv
	)		const

inlineinherited

Applies the transformation \( \psi \) to shape function value, derivative, and Hessian, returning a filled VariationalArg.

Definition at line 85 of file nedelecspace.hh.

◆ local()

template<class GridView >

template<class Scalar >

Dune::FieldMatrix< Scalar, dim, 1 > Kaskade::VectorialConverterBase< GridView >::local ( Dune::FieldMatrix< Scalar, dim, 1 > const & glob ) const

inlineinherited

Applies the inverse transform \( \psi^{-1} \) to global shape function values, giving the local shape function value.

Definition at line 104 of file nedelecspace.hh.

◆ moveTo()

template<class GridView >

void Kaskade::VectorialConverterBase< GridView >::moveTo ( Cell const & cell )

inlineinherited

Definition at line 50 of file nedelecspace.hh.

◆ setLocalPosition()

template<class GridView >

void Kaskade::VectorialConverterBase< GridView >::setLocalPosition ( Dune::FieldVector< typename GridView::ctype, dim > const & x )

inlineinherited

Definition at line 52 of file nedelecspace.hh.

◆ solve()

template<class GridView >

void Kaskade::VectorialConverterBase< GridView >::solve	(	Dune::FieldMatrix< typename GridView::ctype, dim, dim >	A,
		Dune::FieldVector< typename GridView::ctype, dim > &	x,
		Dune::FieldVector< typename GridView::ctype, dim >	b
	)		const