Implement a MultiLinearGeometry with additional caching. More...

#include <dune/geometry/multilineargeometry.hh>

Inheritance diagram for Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >:

Public Types
typedef Base::ReferenceElement	ReferenceElement
typedef Base::ctype	ctype
typedef Base::LocalCoordinate	LocalCoordinate
typedef Base::GlobalCoordinate	GlobalCoordinate
typedef Base::Volume	Volume
typedef Base::JacobianTransposed	JacobianTransposed
typedef Base::JacobianInverseTransposed	JacobianInverseTransposed
typedef Base::Jacobian	Jacobian
typedef Base::JacobianInverse	JacobianInverse

Public Member Functions
template<class CornerStorage>
	CachedMultiLinearGeometry (const ReferenceElement &referenceElement, const CornerStorage &cornerStorage)
template<class CornerStorage>
	CachedMultiLinearGeometry (Dune::GeometryType gt, const CornerStorage &cornerStorage)
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
LocalCoordinate	local (const GlobalCoordinate &global) const
	evaluate the inverse mapping
ctype	integrationElement (const LocalCoordinate &local) const
	obtain the integration element
Volume	volume () const
	obtain the volume of the mapping's image
JacobianTransposed	jacobianTransposed (const LocalCoordinate &local) const
	obtain the transposed of the Jacobian
JacobianInverseTransposed	jacobianInverseTransposed (const LocalCoordinate &local) const
	obtain the transposed of the Jacobian's inverse
Jacobian	jacobian (const LocalCoordinate &local) const
	Obtain the Jacobian.
JacobianInverse	jacobianInverse (const LocalCoordinate &local) const
	Obtain the Jacobian's inverse.
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

Protected Types
typedef Base::MatrixHelper	MatrixHelper
typedef Dune::ReferenceElements< ctype, mydimension >	ReferenceElements
typedef std::conditional< hasSingleGeometryType, std::integral_constant< unsignedint, MultiLinearGeometryTraits< ct >::templatehasSingleGeometryType< mydimension >::topologyId >, unsignedint >::type	TopologyId

Protected Member Functions
ReferenceElement	refElement () const
TopologyId	topologyId () const

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 Typedef Documentation

◆ ctype

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

typedef Base::ctype Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::ctype

◆ GlobalCoordinate

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

typedef Base::GlobalCoordinate Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::GlobalCoordinate

◆ Jacobian

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

typedef Base::Jacobian Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::Jacobian

◆ JacobianInverse

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

typedef Base::JacobianInverse Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::JacobianInverse

◆ JacobianInverseTransposed

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

typedef Base::JacobianInverseTransposed Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::JacobianInverseTransposed

◆ JacobianTransposed

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

typedef Base::JacobianTransposed Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::JacobianTransposed

◆ LocalCoordinate

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

typedef Base::LocalCoordinate Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::LocalCoordinate

◆ MatrixHelper

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

typedef Base::MatrixHelper Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::MatrixHelper

protected

◆ ReferenceElement

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

typedef Base::ReferenceElement Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::ReferenceElement

◆ ReferenceElements

typedef Dune::ReferenceElements< ctype, mydimension > Dune::MultiLinearGeometry< ct, mydim, cdim, MultiLinearGeometryTraits< ct > >::ReferenceElements

protectedinherited

◆ TopologyId

typedef std::conditional<hasSingleGeometryType,std::integral_constant<unsignedint,MultiLinearGeometryTraits< ct >::templatehasSingleGeometryType<mydimension>::topologyId>,unsignedint>::type Dune::MultiLinearGeometry< ct, mydim, cdim, MultiLinearGeometryTraits< ct > >::TopologyId

protectedinherited

◆ Volume

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

typedef Base::Volume Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::Volume

Constructor & Destructor Documentation

◆ CachedMultiLinearGeometry() [1/2]

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

template<class CornerStorage>

Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::CachedMultiLinearGeometry	(	const ReferenceElement &	referenceElement,
		const CornerStorage &	cornerStorage )

inline

◆ CachedMultiLinearGeometry() [2/2]

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

template<class CornerStorage>

Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::CachedMultiLinearGeometry	(	Dune::GeometryType	gt,
		const CornerStorage &	cornerStorage )

inline

Member Function Documentation

◆ affine()

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

bool Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::affine ( ) const

inline

is this mapping affine?

◆ center()

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

GlobalCoordinate Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::center ( ) const

inline

obtain the centroid of the mapping's image

◆ corner()

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

GlobalCoordinate Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::corner ( int i ) const

inline

obtain coordinates of the i-th corner

◆ corners()

int Dune::MultiLinearGeometry< ct, mydim, cdim, MultiLinearGeometryTraits< ct > >::corners ( ) const

inlineinherited

obtain number of corners of the corresponding reference element

◆ 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

◆ 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.

◆ jacobian()

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

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

inline

Obtain the Jacobian.

Parameters

[in] local local coordinate to evaluate Jacobian in

Returns: a copy of the transposed of the Jacobian

◆ jacobianInverse()

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

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

inline

Obtain the Jacobian's inverse.

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

$\‍[J^{-1}(x) J(x) = I.\‍]$

◆ 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 , the following condition holds:

$\‍[J^{-1}(x) J(x) = I.\‍]$

◆ 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.

◆ local()

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

LocalCoordinate Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::local ( 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()

Dune::CachedMultiLinearGeometry::global
GlobalCoordinate global(const LocalCoordinate &local) const
evaluate the mapping
Definition multilineargeometry.hh:580

◆ refElement()

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

ReferenceElement Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::refElement ( ) const

inlineprotected

◆ topologyId()

TopologyId Dune::MultiLinearGeometry< ct, mydim, cdim, MultiLinearGeometryTraits< ct > >::topologyId ( ) const

inlineprotectedinherited

◆ type()

Dune::GeometryType Dune::MultiLinearGeometry< ct, mydim, cdim, MultiLinearGeometryTraits< ct > >::type ( ) const

inlineinherited

obtain the name of the reference element

◆ volume()

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

Volume Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::volume ( ) const

inline

obtain the volume of the mapping's image

Member Data Documentation

◆ coorddimension

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

const int Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::coorddimension

static

coordinate dimension

◆ mydimension

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

const int Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::mydimension

static

geometry dimension

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

multilineargeometry.hh

Public Types

Public Member Functions

Static Public Attributes

Protected Types

Protected Member Functions

Detailed Description

Member Typedef Documentation

◆ ctype

◆ GlobalCoordinate

◆ Jacobian

◆ JacobianInverse

◆ JacobianInverseTransposed

◆ JacobianTransposed

◆ LocalCoordinate

◆ MatrixHelper

◆ ReferenceElement

◆ ReferenceElements

◆ TopologyId

◆ Volume

Constructor & Destructor Documentation

◆ CachedMultiLinearGeometry() [1/2]

◆ CachedMultiLinearGeometry() [2/2]

Member Function Documentation

◆ affine()

◆ center()

◆ corner()

◆ corners()

◆ global()

◆ integrationElement()

◆ jacobian()

◆ jacobianInverse()

◆ jacobianInverseTransposed()

◆ jacobianTransposed()

◆ local()

◆ refElement()

◆ topologyId()

◆ type()

◆ volume()

Member Data Documentation

◆ coorddimension

◆ mydimension