abstract base class for generic mapping More...

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

Inheritance diagram for Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >:

Classes
struct	Codim

Public Types
typedef Traits::FieldType	FieldType

typedef Traits::LocalCoordinate	LocalCoordinate

typedef Traits::GlobalCoordinate	GlobalCoordinate

typedef CachedJacobianTransposed < dimension, GeometryTraits >	JacobianTransposed

typedef CachedJacobianInverseTransposed < dimension, GeometryTraits >	JacobianInverseTransposed

typedef GeometryTraits::Caching	Caching

typedef GeometryTraits::UserData	UserData

Public Member Functions
virtual	~HybridMapping ()

virtual bool	affine () const =0
	is this mapping affine? More...

virtual Dune::GeometryType	type () const =0
	obtain the name of the reference element More...

virtual int	numCorners () const =0
	obtain number of corners of the corresponding reference element More...

virtual GlobalCoordinate	corner (int i) const =0
	obtain coordinates of the i-th corner More...

virtual GlobalCoordinate	center () const =0
	obtain the centroid of the mapping's image More...

virtual GlobalCoordinate	global (const LocalCoordinate &x) const =0
	evaluate the mapping More...

virtual LocalCoordinate	local (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...

virtual This *	clone () const =0

virtual This *	clone (char *mappingStorage) const =0

template<int codim>
Codim< codim >::Trace *	trace (unsigned int i, char *mappingStorage) const

const UserData &	userData () const

UserData &	userData ()

Static Public Attributes
static const unsigned int	dimension = Traits::dimension

static const unsigned int	dimWorld = Traits::dimWorld

Protected Types
typedef MappingTraits < typename GeometryTraits::CoordTraits, dim, GeometryTraits::dimWorld >	Traits

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 Typedef Documentation

template<unsigned int dim, class GeometryTraits>

typedef GeometryTraits::Caching Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::Caching

template<unsigned int dim, class GeometryTraits>

typedef Traits::FieldType Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::FieldType

template<unsigned int dim, class GeometryTraits>

typedef Traits::GlobalCoordinate Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::GlobalCoordinate

template<unsigned int dim, class GeometryTraits>

typedef CachedJacobianInverseTransposed< dimension, GeometryTraits > Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::JacobianInverseTransposed

template<unsigned int dim, class GeometryTraits>

typedef CachedJacobianTransposed< dimension, GeometryTraits > Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::JacobianTransposed

template<unsigned int dim, class GeometryTraits>

typedef Traits::LocalCoordinate Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::LocalCoordinate

template<unsigned int dim, class GeometryTraits>

typedef MappingTraits< typename GeometryTraits::CoordTraits, dim, GeometryTraits::dimWorld > Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::Traits

protected

template<unsigned int dim, class GeometryTraits>

typedef GeometryTraits::UserData Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::UserData

Constructor & Destructor Documentation

template<unsigned int dim, class GeometryTraits>

virtual Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::~HybridMapping ( )

inlinevirtual

Member Function Documentation

template<unsigned int dim, class GeometryTraits>

virtual bool Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::affine ( ) const

pure virtual

is this mapping affine?

Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.

template<unsigned int dim, class GeometryTraits>

virtual GlobalCoordinate Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::center ( ) const

pure virtual

obtain the centroid of the mapping's image

Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.

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.

Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.

template<unsigned int dim, class GeometryTraits>

virtual This* Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::clone ( ) const

pure virtual

Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.

template<unsigned int dim, class GeometryTraits>

virtual This* Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::clone ( char * mappingStorage ) const

pure virtual

Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.

template<unsigned int dim, class GeometryTraits>

virtual GlobalCoordinate Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::corner ( int i ) const

pure virtual

obtain coordinates of the i-th corner

Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.

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

Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.

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.

Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.

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:

$J^{-1}(x) J(x) = I.$

Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.

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.

Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.

template<unsigned int dim, class GeometryTraits>

virtual LocalCoordinate Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::local ( 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()

Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.

template<unsigned int dim, class GeometryTraits>

virtual int Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::numCorners ( ) const

pure virtual

obtain number of corners of the corresponding reference element

Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.

template<unsigned int dim, class GeometryTraits>

template<int codim>

Codim< codim >::Trace* Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::trace	(	unsigned int	i,
		char *	mappingStorage
	)		const

inline

Referenced by Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >::trace().

template<unsigned int dim, class GeometryTraits>

virtual Dune::GeometryType Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::type ( ) const

pure virtual

obtain the name of the reference element

Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.

template<unsigned int dim, class GeometryTraits>

const UserData& Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::userData ( ) const

inline

template<unsigned int dim, class GeometryTraits>

UserData& Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::userData ( )

inline

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.

Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.

Member Data Documentation

template<unsigned int dim, class GeometryTraits>

const unsigned int Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::dimension = Traits::dimension

static

template<unsigned int dim, class GeometryTraits>

const unsigned int Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::dimWorld = Traits::dimWorld

static

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

hybridmapping.hh

Classes

Public Types

Public Member Functions

Static Public Attributes

Protected Types

Detailed Description

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

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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