Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits > Class Template Reference

non-virtual geometric mapping More...

#include <dune/geometry/genericgeometry/hybridmapping.hh>

Public Member Functions
bool	affine () const
	is this mapping affine?
Dune::GeometryType	type () const
	obtain the name of the reference element
int	numCorners () const
	obtain number of corners of the corresponding reference element
GlobalCoordinate	corner (int i) const
	obtain coordinates of the i-th corner
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...
bool	checkInside (const LocalCoordinate &local) const
	check whether a point lies within the reference element More...
FieldType	integrationElement (const LocalCoordinate &local) const
	obtain the integration element More...
FieldType	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...

Detailed Description

template<class Topology, class GeometryTraits>
class Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >

non-virtual geometric mapping

This is the user-visible class of the generic geometries if the topology type for each codimension is unique.

Member Function Documentation

checkInside()

template<class Topology , class GeometryTraits >

bool Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::checkInside ( const LocalCoordinate &  local ) const

inline

check whether a point lies within the reference element

Parameters

[in]

local

local coordinate of point to check

Note

Historically, this method was part of the geometry interface. It is still required for the GenericReferenceElement.

global()

template<class Topology , class GeometryTraits >

GlobalCoordinate Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::global ( const LocalCoordinate &  local ) const

inline

evaluate the mapping

Parameters

[in]

local

local coordinate to map

Returns

corresponding global coordinate

Referenced by Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::LocalCoordinate().

integrationElement()

template<class Topology , class GeometryTraits >

FieldType Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::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 Topology , class GeometryTraits >

const JacobianInverseTransposed& Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::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()

template<class Topology , class GeometryTraits >

const JacobianTransposed& Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::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.

LocalCoordinate()

template<class Topology , class GeometryTraits >

Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::LocalCoordinate ( const GlobalCoordinate &  global ) const

inline

evaluate the inverse mapping

Parameters

[in]

global

global coorindate to map

Returns

corresponding local coordinate

Note

The returned local coordinate y minimizes

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

References Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::global().

volume()

template<class Topology , class GeometryTraits >

FieldType Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::volume ( ) const

inline

obtain the volume of the mapping's image

Note

The current implementation just returns

integrationElement( baryCenter() ) * ReferenceElement::volume()

which is wrong for n-linear surface maps and other nonlinear maps.

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

• dune/geometry/genericgeometry/hybridmapping.hh