dune-geometry  2.3.0
Classes | Public Types | Public Member Functions | Static Public Attributes | List of all members
Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits > Class Template Reference

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

Inheritance diagram for Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >:
Dune::GenericGeometry::HybridMapping< Topology::dimension, 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 JacobianTransposedjacobianTransposed (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 Baseclone () const
 
virtual Baseclone (char *mappingStorage) const
 
template<int codim>
Codim< codim >::Trace * trace (unsigned int i, char *mappingStorage) const
 
const UserDatauserData () const
 
UserDatauserData ()
 

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
template<class Topology , class GeometryTraits >
virtual GlobalCoordinate Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::center ( ) const
inlinevirtual
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]xlocal 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
template<class Topology , class GeometryTraits >
virtual Base* Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::clone ( char *  mappingStorage) const
inlinevirtual
template<class Topology , class GeometryTraits >
virtual GlobalCoordinate Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::corner ( int  i) const
inlinevirtual
template<class Topology , class GeometryTraits >
virtual GlobalCoordinate Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::global ( const LocalCoordinate x) const
inlinevirtual

evaluate the mapping

Parameters
[in]xlocal 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]xlocal 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]xlocal 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]yglobal 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
template<class Topology , class GeometryTraits >
template<int codim>
Codim< codim >::Trace* Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::trace ( unsigned int  i,
char *  mappingStorage 
) const
inline
template<class Topology , class GeometryTraits >
virtual Dune::GeometryType Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::type ( ) const
inlinevirtual
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 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().

Member Data Documentation

template<class Topology , class GeometryTraits >
const unsigned int Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::dimension = Traits::dimension
static
template<class Topology , class GeometryTraits >
const unsigned int Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::dimWorld = Traits::dimWorld
static

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