A class mapping local vectorial shape function values and gradients to global shape function values and gradients. More...

#include <nedelecspace.hh>

Detailed Description

template<class GridView>
class Kaskade::VectorialConverterBase< GridView >

A class mapping local vectorial shape function values and gradients to global shape function values and gradients.

This converter realizes the transform \( \psi(x) \) and gives the values and derivatives of global shape functions from local shape functions: \( \phi(x) = C \hat \phi(\xi) \). Derived classes shall redefine the method update() in order to provide \( C \).

Template Parameters

Grid	the FE grid class

Definition at line 40 of file nedelecspace.hh.

Inheritance diagram for Kaskade::VectorialConverterBase< GridView >:

Public Member Functions
	VectorialConverterBase ()=default

	VectorialConverterBase (Cell 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
virtual void	update ()=0
	Redefine this to set \( C \). More...

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

◆ VectorialConverterBase() [1/2]

template<class GridView >

Kaskade::VectorialConverterBase< GridView >::VectorialConverterBase ( )

default

◆ VectorialConverterBase() [2/2]

template<class GridView >

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

inline

Definition at line 48 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

inline

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

inline

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

inline

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

inline

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 )

inline

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 )

inline

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