dune-geometry  2.2.0
Classes | Public Types | Public Member Functions | Static Public Attributes | Protected Types
Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits > Class Template Reference

non-virtual geometric mapping More...

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

List of all members.

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 Mapping::ReferenceElement ReferenceElement
typedef GeometryTraits::Caching Caching
typedef GeometryTraits::UserData UserData

Public Member Functions

template<class CoordVector >
 NonHybridMapping (const CoordVector &coordVector)
bool affine () const
 is this mapping affine?
Dune::GeometryType type () const
 obtain the name of the reference element
unsigned int topologyId () const
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
LocalCoordinate local (const GlobalCoordinate &global) const
 evaluate the inverse mapping
bool checkInside (const LocalCoordinate &local) const
 check whether a point lies within the reference element
FieldType integrationElement (const LocalCoordinate &local) const
 obtain the integration element
FieldType volume () const
 obtain the volume of the mapping's image
const JacobianTransposedjacobianTransposed (const LocalCoordinate &local) const
 obtain the transposed of the Jacobian
const JacobianInverseTransposedjacobianInverseTransposed (const LocalCoordinate &local) const
 obtain the transposed of the Jacobian's inverse
Thisclone () const
Thisclone (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

Protected Types

typedef MappingTraits
< typename
GeometryTraits::CoordTraits,
Topology::dimension,
GeometryTraits::dimWorld > 
Traits
typedef CachedMapping
< Topology, GeometryTraits > 
Mapping

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 Typedef Documentation

template<class Topology , class GeometryTraits >
typedef GeometryTraits::Caching Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::Caching
template<class Topology , class GeometryTraits >
typedef Traits::FieldType Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::FieldType
template<class Topology , class GeometryTraits >
typedef Traits::GlobalCoordinate Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::GlobalCoordinate
template<class Topology , class GeometryTraits >
typedef CachedJacobianInverseTransposed< dimension, GeometryTraits > Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::JacobianInverseTransposed
template<class Topology , class GeometryTraits >
typedef CachedJacobianTransposed< dimension, GeometryTraits > Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::JacobianTransposed
template<class Topology , class GeometryTraits >
typedef Traits::LocalCoordinate Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::LocalCoordinate
template<class Topology , class GeometryTraits >
typedef CachedMapping< Topology, GeometryTraits > Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::Mapping [protected]
template<class Topology , class GeometryTraits >
typedef Mapping::ReferenceElement Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::ReferenceElement
template<class Topology , class GeometryTraits >
typedef MappingTraits< typename GeometryTraits::CoordTraits, Topology::dimension, GeometryTraits::dimWorld > Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::Traits [protected]
template<class Topology , class GeometryTraits >
typedef GeometryTraits::UserData Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::UserData

Constructor & Destructor Documentation

template<class Topology , class GeometryTraits >
template<class CoordVector >
Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::NonHybridMapping ( const CoordVector &  coordVector) [inline, explicit]

Member Function Documentation

template<class Topology , class GeometryTraits >
bool Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::affine ( ) const [inline]
template<class Topology , class GeometryTraits >
GlobalCoordinate Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::center ( ) const [inline]

obtain the centroid of the mapping's image

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

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]locallocal coordinate of point to check
Note:
Historically, this method was part of the geometry interface. It is still required for the GenericReferenceElement.

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

template<class Topology , class GeometryTraits >
This* Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::clone ( ) const [inline]
template<class Topology , class GeometryTraits >
This* Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::clone ( char *  mappingStorage) const [inline]
template<class Topology , class GeometryTraits >
GlobalCoordinate Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::corner ( int  i) const [inline]

obtain coordinates of the i-th corner

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

template<class Topology , class GeometryTraits >
GlobalCoordinate Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::global ( const LocalCoordinate local) const [inline]

evaluate the mapping

Parameters:
[in]locallocal coordinate to map
Returns:
corresponding global coordinate

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

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]locallocal 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.

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

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:

\[J^{-1}(x) J(x) = I.\]

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

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]locallocal 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.

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

template<class Topology , class GeometryTraits >
LocalCoordinate Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::local ( const GlobalCoordinate global) const [inline]

evaluate the inverse mapping

Parameters:
[in]globalglobal coorindate to map
Returns:
corresponding local coordinate
Note:
The returned local coordinate y minimizes
  (global( x ) - y).two_norm()

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

template<class Topology , class GeometryTraits >
int Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::numCorners ( ) const [inline]

obtain number of corners of the corresponding reference element

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

template<class Topology , class GeometryTraits >
unsigned int Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::topologyId ( ) const [inline]
template<class Topology , class GeometryTraits >
template<int codim>
Codim< codim >::Trace* Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::trace ( unsigned int  i,
char *  mappingStorage 
) const [inline]
template<class Topology , class GeometryTraits >
Dune::GeometryType Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::type ( ) const [inline]
template<class Topology , class GeometryTraits >
const UserData& Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::userData ( ) const [inline]
template<class Topology , class GeometryTraits >
UserData& Dune::GenericGeometry::NonHybridMapping< Topology, GeometryTraits >::userData ( ) [inline]
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 which is wrong for n-linear surface maps and other nonlinear maps.

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


Member Data Documentation

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

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