dune-grid
2.1.1
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abstract base class for generic mapping More...
#include <dune/grid/genericgeometry/hybridmapping.hh>
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 |
Public Member Functions | |
virtual | ~HybridMapping () |
virtual unsigned int | topologyId () const =0 |
virtual const GlobalCoordinate & | corner (int i) const =0 |
virtual int | numCorners () const =0 |
virtual GlobalCoordinate | center () const =0 |
virtual GlobalCoordinate | global (const LocalCoordinate &x) const =0 |
virtual LocalCoordinate | local (const GlobalCoordinate &y) const =0 |
virtual bool | checkInside (const LocalCoordinate &x) const =0 |
virtual bool | affine () const =0 |
virtual FieldType | integrationElement (const LocalCoordinate &x) const =0 |
virtual FieldType | volume () const =0 |
virtual const JacobianTransposed & | jacobianTransposed (const LocalCoordinate &x) const =0 |
virtual const JacobianInverseTransposed & | jacobianInverseTransposed (const LocalCoordinate &x) const =0 |
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 |
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 |
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. It is the abstract base class of VirtualMapping, which implements all methods by forwarding them to a CachedMapping for the corresponding topology.
typedef GeometryTraits::Caching Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::Caching |
Reimplemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.
typedef Traits::FieldType Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::FieldType |
Reimplemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.
typedef Traits::GlobalCoordinate Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::GlobalCoordinate |
Reimplemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.
typedef CachedJacobianInverseTransposed< dimension, GeometryTraits > Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::JacobianInverseTransposed |
Reimplemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.
typedef CachedJacobianTransposed< dimension, GeometryTraits > Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::JacobianTransposed |
Reimplemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.
typedef Traits::LocalCoordinate Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::LocalCoordinate |
Reimplemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.
typedef MappingTraits< typename GeometryTraits::CoordTraits, dim, GeometryTraits::dimWorld > Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::Traits [protected] |
virtual Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::~HybridMapping | ( | ) | [inline, virtual] |
virtual bool Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::affine | ( | ) | const [pure virtual] |
is this mapping affine?
Implemented in Dune::GenericGeometry::VirtualMapping< Topology, 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 >.
virtual bool Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::checkInside | ( | const LocalCoordinate & | x | ) | const [pure virtual] |
check whether a point lies within the reference element
[in] | x | local coorinate of point to check |
Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.
virtual This* Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::clone | ( | ) | const [pure virtual] |
virtual This* Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::clone | ( | char * | mappingStorage | ) | const [pure virtual] |
virtual const GlobalCoordinate& Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::corner | ( | int | i | ) | const [pure virtual] |
virtual GlobalCoordinate Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::global | ( | const LocalCoordinate & | x | ) | const [pure virtual] |
evaluate the mapping
[in] | x | local coordinate to map |
Implemented in Dune::GenericGeometry::VirtualMapping< Topology, 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 is given by
[in] | x | local coordinate to evaluate the integration element in |
Implemented in Dune::GenericGeometry::VirtualMapping< Topology, 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 , the following condition holds:
Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.
virtual const JacobianTransposed& Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::jacobianTransposed | ( | const LocalCoordinate & | x | ) | const [pure virtual] |
obtain the transposed of the Jacobian
[in] | x | local coordinate to evaluate Jacobian in |
Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.
virtual LocalCoordinate Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::local | ( | const GlobalCoordinate & | y | ) | const [pure virtual] |
evaluate the inverse mapping
[in] | y | global coorindate to map |
(global( x ) - y).two_norm()
Implemented in Dune::GenericGeometry::VirtualMapping< Topology, 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 >.
virtual unsigned int Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::topologyId | ( | ) | const [pure virtual] |
obtain topology id of the corresponding reference element
Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.
Codim< codim >::Trace* Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::trace | ( | unsigned int | i, |
char * | mappingStorage | ||
) | const [inline] |
virtual FieldType Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::volume | ( | ) | const [pure virtual] |
obtain the volume of the mapping's image
integrationElement( baryCenter() ) * ReferenceElement::volume()
Implemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.
const unsigned int Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::dimension = Traits::dimension [static] |
Reimplemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.
const unsigned int Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::dimWorld = Traits::dimWorld [static] |
Reimplemented in Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >.