Dune::GenericGeometry::HybridMapping< dim, GeometryTraits > Class Template Reference

abstract base class for generic mapping More...

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

Public Member Functions
virtual bool	affine () const =0
	is this mapping affine?
virtual Dune::GeometryType	type () const =0
	obtain the name of the reference element
virtual int	numCorners () const =0
	obtain number of corners of the corresponding reference element
virtual GlobalCoordinate	corner (int i) const =0
	obtain coordinates of the i-th corner
virtual GlobalCoordinate	center () const =0
	obtain the centroid of the mapping's image
virtual GlobalCoordinate	global (const LocalCoordinate &x) const =0
	evaluate the mapping More...
virtual	LocalCoordinate (const GlobalCoordinate &y) const =0
	evaluate the inverse mapping More...
virtual bool	checkInside (const LocalCoordinate &x) const =0
	check whether a point lies within the reference element More...
virtual FieldType	integrationElement (const LocalCoordinate &x) const =0
	obtain the integration element More...
virtual FieldType	volume () const =0
	obtain the volume of the mapping's image More...
virtual const JacobianTransposed &	jacobianTransposed (const LocalCoordinate &x) const =0
	obtain the transposed of the Jacobian More...
virtual const JacobianInverseTransposed &	jacobianInverseTransposed (const LocalCoordinate &x) const =0
	obtain the transposed of the Jacobian's inverse More...

Detailed Description

template<unsigned int dim, class GeometryTraits>
class Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >

abstract base class for generic mapping

This is the user-visible class of the generic geometries if the topology type for each codimension is not unique.

Member Function Documentation

checkInside()

template<unsigned int dim, class GeometryTraits >

virtual bool Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::checkInside ( const LocalCoordinate &  x ) const

pure virtual

check whether a point lies within the reference element

Parameters

[in]

x

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<unsigned int dim, class GeometryTraits >

virtual GlobalCoordinate Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::global ( const LocalCoordinate &  x ) const

pure virtual

evaluate the mapping

Parameters

[in]

x

local coordinate to map

Returns

corresponding global coordinate

integrationElement()

template<unsigned int dim, class GeometryTraits >

virtual FieldType Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::integrationElement ( const LocalCoordinate &  x ) const

pure virtual

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]

x

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<unsigned int dim, class GeometryTraits >

virtual const JacobianInverseTransposed& Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::jacobianInverseTransposed ( const LocalCoordinate &  x ) const

pure virtual

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<unsigned int dim, class GeometryTraits >

virtual const JacobianTransposed& Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::jacobianTransposed ( const LocalCoordinate &  x ) const

pure virtual

obtain the transposed of the Jacobian

Parameters

[in]

x

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<unsigned int dim, class GeometryTraits >

virtual Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::LocalCoordinate ( const GlobalCoordinate &  y ) const

pure virtual

evaluate the inverse mapping

Parameters

[in]

y

global coordinate to map

Returns

corresponding local coordinate

Note

The returned local coordinate y minimizes

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

volume()

template<unsigned int dim, class GeometryTraits >

virtual FieldType Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::volume ( ) const

pure virtual

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