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::JacobianTransposed	JacobianTransposed

typedef Base::JacobianInverseTransposed	JacobianInverseTransposed

typedef JacobianInverseTransposed	Jacobian
	For backward-compatibility, export the type JacobianInverseTransposed as Jacobian. More...

Public Member Functions
template<class CornerStorage >
	CachedMultiLinearGeometry (const ReferenceElement &refElement, const CornerStorage &cornerStorage)

template<class CornerStorage >
	CachedMultiLinearGeometry (Dune::GeometryType gt, const CornerStorage &cornerStorage)

bool	affine () const
	is this mapping affine? More...

GlobalCoordinate	center () const
	obtain the centroid of the mapping's image More...

GlobalCoordinate	global (const LocalCoordinate &local) const
	evaluate the mapping More...

LocalCoordinate	local (const GlobalCoordinate &global) const
	evaluate the inverse mapping More...

ctype	integrationElement (const LocalCoordinate &local) const
	obtain the integration element More...

ctype	volume () const
	obtain the volume of the mapping's image More...

const JacobianTransposed &	jacobianTransposed (const LocalCoordinate &local) const
	obtain the transposed of the Jacobian More...

const JacobianInverseTransposed &	jacobianInverseTransposed (const LocalCoordinate &local) const
	obtain the transposed of the Jacobian's inverse More...

Dune::GeometryType	type () const
	obtain the name of the reference element More...

int	corners () const
	obtain number of corners of the corresponding reference element More...

GlobalCoordinate	corner (int i) const
	obtain coordinates of the i-th corner More...

Static Public Attributes
static const int	mydimension = mydim
	geometry dimension More...

static const int	coorddimension = cdim
	coordinate dimension More...

Protected Types
typedef Base::MatrixHelper	MatrixHelper

typedef conditional < hasSingleGeometryType, integral_constant< unsigned int, Traits::template hasSingleGeometryType < mydimension >::topologyId > , unsigned int >::type	TopologyId

typedef Dune::ReferenceElements< ctype, mydimension >	ReferenceElements

Protected Member Functions
const ReferenceElement &	refElement () const

TopologyId	topologyId () const

TopologyId	topologyId (integral_constant< bool, true >) const

unsigned int	topologyId (integral_constant< bool, false >) const

Static Protected Member Functions
template<int dim>
static bool	affine (TopologyId topologyId, integral_constant< int, dim >, CornerIterator &cit, JacobianTransposed &jt)

static bool	affine (TopologyId topologyId, integral_constant< int, 0 >, CornerIterator &cit, JacobianTransposed &jt)

template<bool add, int dim>
static void	global (TopologyId topologyId, integral_constant< int, dim >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, GlobalCoordinate &y)

template<bool add>
static void	global (TopologyId topologyId, integral_constant< int, 0 >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, GlobalCoordinate &y)

template<bool add, int rows, int dim>
static void	jacobianTransposed (TopologyId topologyId, integral_constant< int, dim >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, FieldMatrix< ctype, rows, cdim > &jt)

template<bool add, int rows>
static void	jacobianTransposed (TopologyId topologyId, integral_constant< int, 0 >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, FieldMatrix< ctype, rows, cdim > &jt)

Protected Attributes
JacobianTransposed	jacobianTransposed_

JacobianInverseTransposed	jacobianInverseTransposed_

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

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

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

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

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

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

typedef JacobianInverseTransposed Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::Jacobian

inherited

For backward-compatibility, export the type JacobianInverseTransposed as Jacobian.

Deprecated:: This typedef will be removed after the release of dune 2.3

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

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

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

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

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

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

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

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

protected

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

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

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

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

protectedinherited

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

typedef conditional< hasSingleGeometryType, integral_constant< unsigned int, Traits::template hasSingleGeometryType< mydimension >::topologyId >, unsigned int >::type Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::TopologyId

protectedinherited

Constructor & Destructor Documentation

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

template<class CornerStorage >

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

inline

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

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

template<int dim>

bool Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::affine	(	TopologyId	topologyId,
		integral_constant< int, dim >	,
		CornerIterator &	cit,
		JacobianTransposed &	jt
	)

inlinestaticprotectedinherited

References Dune::GenericGeometry::isPrism().

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

bool Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::affine	(	TopologyId	topologyId,
		integral_constant< int, 0 >	,
		CornerIterator &	cit,
		JacobianTransposed &	jt
	)

inlinestaticprotectedinherited

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?

Referenced by Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::global(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::integrationElement(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianInverseTransposed(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::local(), and Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::volume().

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

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

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

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

inlineinherited

obtain coordinates of the i-th corner

References Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::corners().

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

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

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

inlineinherited

obtain number of corners of the corresponding reference element

References Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::mydimension, Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::refElement(), and Dune::ReferenceElement< ctype, dim >::size().

Referenced by Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::corner().

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

template<bool add, int dim>

void Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::global	(	TopologyId	topologyId,
		integral_constant< int, dim >	,
		CornerIterator &	cit,
		const ctype &	df,
		const LocalCoordinate &	x,
		const ctype &	rf,
		GlobalCoordinate &	y
	)

inlinestaticprotectedinherited

References Dune::GenericGeometry::isPrism(), and Dune::GenericGeometry::isPyramid().

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

template<bool add>

void Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::global	(	TopologyId	topologyId,
		integral_constant< int, 0 >	,
		CornerIterator &	cit,
		const ctype &	df,
		const LocalCoordinate &	x,
		const ctype &	rf,
		GlobalCoordinate &	y
	)

inlinestaticprotectedinherited

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::MultiLinearGeometry< ct, mydim, cdim, Traits >::corner(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::global(), and Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed_.

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

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(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::JacobianInverseTransposed::detInv(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::integrationElement(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianInverseTransposed_, Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed_, and Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::JacobianInverseTransposed::setupDeterminant().

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

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

const 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(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianInverseTransposed(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianInverseTransposed_, Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed_, and Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::JacobianInverseTransposed::setup().

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

template<bool add, int rows, int dim>

void Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed	(	TopologyId	topologyId,
		integral_constant< int, dim >	,
		CornerIterator &	cit,
		const ctype &	df,
		const LocalCoordinate &	x,
		const ctype &	rf,
		FieldMatrix< ctype, rows, cdim > &	jt
	)

inlinestaticprotectedinherited

References Dune::GenericGeometry::isPrism(), and Dune::GenericGeometry::isPyramid().

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

template<bool add, int rows>

void Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed	(	TopologyId	topologyId,
		integral_constant< int, 0 >	,
		CornerIterator &	cit,
		const ctype &	df,
		const LocalCoordinate &	x,
		const ctype &	rf,
		FieldMatrix< ctype, rows, cdim > &	jt
	)

inlinestaticprotectedinherited

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

const 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(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed(), and Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed_.

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()

References Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::affine(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::corner(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianInverseTransposed_, Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed_, and Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::local().

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

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

inlineprotectedinherited

Referenced by Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::center(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::center(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::corners(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::local(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::topologyId(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::volume(), and Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::volume().

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

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

inlineprotectedinherited

Referenced by Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::affine(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::global(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed(), and Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::type().

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

TopologyId Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::topologyId ( integral_constant< bool, true > ) const

inlineprotectedinherited

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

unsigned int Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::topologyId ( integral_constant< bool, false > ) const

inlineprotectedinherited

References Dune::GeometryType::id(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::refElement(), and Dune::ReferenceElement< ctype, dim >::type().

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

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

inlineinherited

obtain the name of the reference element

References Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::mydimension, and Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::topologyId().

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

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

inline

obtain the volume of the mapping's image

References Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::affine(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::integrationElement(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::refElement(), Dune::ReferenceElement< ctype, dim >::volume(), and Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::volume().

Member Data Documentation

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

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

staticinherited

coordinate dimension

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

JacobianInverseTransposed Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianInverseTransposed_

mutableprotectedinherited

Referenced by Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::integrationElement(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianInverseTransposed(), and Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::local().

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

JacobianTransposed Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed_

mutableprotectedinherited

Referenced by Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::affine(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::global(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::integrationElement(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianInverseTransposed(), Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed(), Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::jacobianTransposed(), and Dune::CachedMultiLinearGeometry< ct, mydim, cdim, Traits >::local().

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

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

staticinherited

geometry dimension

Referenced by Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::corners(), and Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::type().

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

Static Protected Member Functions

Protected Attributes

Detailed Description

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

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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