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

Inheritance diagram for Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >:

Classes
struct	Codim

Public Types
typedef Traits::FieldType	FieldType

typedef Traits::LocalCoordinate	LocalCoordinate

typedef Traits::GlobalCoordinate	GlobalCoordinate

typedef Base::JacobianTransposed	JacobianTransposed

typedef Base::JacobianInverseTransposed	JacobianInverseTransposed

typedef Mapping::ReferenceElement	ReferenceElement

typedef GeometryTraits::Caching	Caching

typedef GeometryTraits::UserData	UserData

Public Member Functions
template<class CoordVector >
	VirtualMapping (const CoordVector &coordVector)

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

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

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

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

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

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

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

virtual bool	checkInside (const LocalCoordinate &local) const
	check whether a point lies within the reference element More...

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

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

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

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

virtual Base *	clone () const

virtual Base *	clone (char *mappingStorage) const

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

Member Typedef Documentation

template<class Topology , class GeometryTraits >

typedef GeometryTraits::Caching Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::Caching

template<class Topology , class GeometryTraits >

typedef Traits::FieldType Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::FieldType

template<class Topology , class GeometryTraits >

typedef Traits::GlobalCoordinate Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::GlobalCoordinate

template<class Topology , class GeometryTraits >

typedef Base::JacobianInverseTransposed Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::JacobianInverseTransposed

template<class Topology , class GeometryTraits >

typedef Base::JacobianTransposed Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::JacobianTransposed

template<class Topology , class GeometryTraits >

typedef Traits::LocalCoordinate Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::LocalCoordinate

template<class Topology , class GeometryTraits >

typedef Mapping::ReferenceElement Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::ReferenceElement

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

inherited

Constructor & Destructor Documentation

template<class Topology , class GeometryTraits >

template<class CoordVector >

Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::VirtualMapping ( const CoordVector & coordVector )

inlineexplicit

Member Function Documentation

template<class Topology , class GeometryTraits >

virtual bool Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::affine ( ) const

inlinevirtual

is this mapping affine?

Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.

References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::affine().

template<class Topology , class GeometryTraits >

virtual GlobalCoordinate Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::center ( ) const

inlinevirtual

obtain the centroid of the mapping's image

Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.

References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::center().

template<class Topology , class GeometryTraits >

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

inlinevirtual

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.

Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.

References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::checkInside().

template<class Topology , class GeometryTraits >

virtual Base* Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::clone ( ) const

inlinevirtual

Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.

template<class Topology , class GeometryTraits >

virtual Base* Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::clone ( char * mappingStorage ) const

inlinevirtual

Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.

template<class Topology , class GeometryTraits >

virtual GlobalCoordinate Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::corner ( int i ) const

inlinevirtual

obtain coordinates of the i-th corner

Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.

References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::corner().

template<class Topology , class GeometryTraits >

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

inlinevirtual

evaluate the mapping

Parameters

[in] x local coordinate to map

Returns: corresponding global coordinate

Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.

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

template<class Topology , class GeometryTraits >

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

inlinevirtual

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.

Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.

References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::integrationElement().

template<class Topology , class GeometryTraits >

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

inlinevirtual

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:

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

Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.

References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::jacobianInverseTransposed().

template<class Topology , class GeometryTraits >

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

inlinevirtual

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.

Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.

References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::jacobianTransposed().

template<class Topology , class GeometryTraits >

virtual LocalCoordinate Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::local ( const GlobalCoordinate & y ) const

inlinevirtual

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()

Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.

References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::local().

template<class Topology , class GeometryTraits >

virtual int Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::numCorners ( ) const

inlinevirtual

obtain number of corners of the corresponding reference element

Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.

References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::numCorners().

template<class Topology , class GeometryTraits >

template<int codim>

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

inline

References Dune::GenericGeometry::TraceProvider< Topology, GeometryTraits, codim, forceHybrid >::construct(), and Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::mapping().

template<class Topology , class GeometryTraits >

virtual Dune::GeometryType Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::type ( ) const

inlinevirtual

obtain the name of the reference element

Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.

References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::type().

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

inlineinherited

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

inlineinherited

template<class Topology , class GeometryTraits >

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

inlinevirtual

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.

Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.

References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::volume().