Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits > Class Template Reference

Implement a MultiLinearGeometry with additional caching. More...

#include <dune/geometry/multilineargeometry.hh>

Public Member Functions
bool	affine () const
	is this mapping affine?
GlobalCoordinate	center () const
	obtain the centroid of the mapping's image
GlobalCoordinate	global (const LocalCoordinate &local) const
	evaluate the mapping More...
	LocalCoordinate (const GlobalCoordinate &global) const
	evaluate the inverse mapping More...
ctype	integrationElement (const LocalCoordinate &local) const
	obtain the integration element More...
Volume	volume () const
	obtain the volume of the mapping's image
JacobianTransposed	jacobianTransposed (const LocalCoordinate &local) const
	obtain the transposed of the Jacobian More...
JacobianInverseTransposed	jacobianInverseTransposed (const LocalCoordinate &local) const
	obtain the transposed of the Jacobian's inverse More...
GlobalCoordinate	corner (int i) const
	obtain coordinates of the i-th corner
Dune::GeometryType	type () const
	obtain the name of the reference element
int	corners () const
	obtain number of corners of the corresponding reference element

Static Public Attributes
static const int	mydimension
	geometry dimension
static const int	coorddimension
	coordinate dimension

Detailed Description

template<class ct, int mydim, int cdim, class Traits = MultiLinearGeometryTraits< ct >>
class Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >

Implement a MultiLinearGeometry with additional caching.

This class implements the same interface and functionality as MultiLinearGeometry. However, it additionally implements caching for various results.

Template Parameters

ct	coordinate type
mydim	geometry dimension
cdim	coordinate dimension
Traits	traits allowing to tweak some implementation details (optional)

Member Function Documentation

global()

template<class ct , int mydim, int cdim, class Traits = MultiLinearGeometryTraits< ct >>

GlobalCoordinate Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::global ( const LocalCoordinate &  local ) const

inline

evaluate the mapping

Parameters

[in]

local

local coordinate to map

Returns

corresponding global coordinate

References Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::affine(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::corner(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::global(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::global(), and Dune::DenseMatrix< MAT >::umtv().

Referenced by Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::center(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::global(), and Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::LocalCoordinate().

integrationElement()

template<class ct , int mydim, int cdim, class Traits = MultiLinearGeometryTraits< ct >>

ctype Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::integrationElement ( const LocalCoordinate &  local ) const

inline

obtain the integration element

If the Jacobian of the mapping is denoted by $J(x)$, the integration integration element \(\mu(x)\) is given by

\[ \mu(x) = \sqrt{|\det (J^T(x) J(x))|}.\]

Parameters

[in]

local

local coordinate to evaluate the integration element in

Returns

the integration element \(\mu(x)\).

Note

For affine mappings, it is more efficient to call jacobianInverseTransposed before integrationElement, if both are required.

References Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::affine(), and Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::integrationElement().

Referenced by Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::volume().

jacobianInverseTransposed()

template<class ct , int mydim, int cdim, class Traits = MultiLinearGeometryTraits< ct >>

JacobianInverseTransposed Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianInverseTransposed ( const LocalCoordinate &  local ) const

inline

obtain the transposed of the Jacobian's inverse

The Jacobian's inverse is defined as a pseudo-inverse. If we denote the Jacobian by \(J(x)\), the following condition holds:

\[J^{-1}(x) J(x) = I.\]

References Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::affine(), and Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianInverseTransposed().

jacobianTransposed()

template<class ct , int mydim, int cdim, class Traits = MultiLinearGeometryTraits< ct >>

JacobianTransposed Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed ( const LocalCoordinate &  local ) const

inline

obtain the transposed of the Jacobian

Parameters

[in]

local

local coordinate to evaluate Jacobian in

Returns

a reference to the transposed of the Jacobian

Note

The returned reference is reused on the next call to JacobianTransposed, destroying the previous value.

References Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::affine(), and Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed().

LocalCoordinate()

template<class ct , int mydim, int cdim, class Traits = MultiLinearGeometryTraits< ct >>

Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::LocalCoordinate ( const GlobalCoordinate &  global ) const

inline

evaluate the inverse mapping

Parameters

[in]

global

global coordinate to map

Returns

corresponding local coordinate

Note

For given global coordinate y the returned local coordinate x that minimizes the following function over the local coordinate space spanned by the reference element.

(global( x ) - y).two_norm()

References Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::affine(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::corner(), and Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::global().

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The documentation for this class was generated from the following file:

• dune/geometry/multilineargeometry.hh