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

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

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
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, Traits::templatehasSingleGeometryType< mydimension >::topologyId >, unsignedint >::type	TopologyId

Protected Member Functions
ReferenceElement	refElement () const
bool	affine (JacobianTransposed &jacobianT) const
TopologyId	topologyId () const

Static Protected Member Functions
template<int dim, class CornerIterator >
static bool	affine (TopologyId topologyId, std::integral_constant< int, dim >, CornerIterator &cit, JacobianTransposed &jt)
template<class CornerIterator >
static bool	affine (TopologyId topologyId, std::integral_constant< int, 0 >, CornerIterator &cit, JacobianTransposed &jt)
template<bool add, int dim, class CornerIterator >
static void	global (TopologyId topologyId, std::integral_constant< int, dim >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, GlobalCoordinate &y)
template<bool add, class CornerIterator >
static void	global (TopologyId topologyId, std::integral_constant< int, 0 >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, GlobalCoordinate &y)
template<bool add, int rows, int dim, class CornerIterator >
static void	jacobianTransposed (TopologyId topologyId, std::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, class CornerIterator >
static void	jacobianTransposed (TopologyId topologyId, std::integral_constant< int, 0 >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, FieldMatrix< ctype, rows, cdim > &jt)

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

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

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

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

protectedinherited

TopologyId

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

typedef std::conditional<hasSingleGeometryType,std::integral_constant<unsignedint,Traits::templatehasSingleGeometryType<mydimension>::topologyId>,unsignedint>::type Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::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() [1/4]

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?

affine() [2/4]

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

bool Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::affine ( JacobianTransposed &  jacobianT ) const

inlineprotectedinherited

affine() [3/4]

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

template<class CornerIterator >

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

inlinestaticprotectedinherited

affine() [4/4]

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

template<int dim, class CornerIterator >

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

inlinestaticprotectedinherited

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()

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

global() [1/3]

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

global() [2/3]

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

template<bool add, class CornerIterator >

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

inlinestaticprotectedinherited

global() [3/3]

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

template<bool add, int dim, class CornerIterator >

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

inlinestaticprotectedinherited

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.

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:

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

jacobianTransposed() [1/3]

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.

jacobianTransposed() [2/3]

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

template<bool add, int rows, class CornerIterator >

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

inlinestaticprotectedinherited

jacobianTransposed() [3/3]

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

template<bool add, int rows, int dim, class CornerIterator >

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

inlinestaticprotectedinherited

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()

refElement()

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

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

inlineprotected

topologyId()

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

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

inlineprotectedinherited

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

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

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

• multilineargeometry.hh