dune-geometry
2.2.0
|
abstract base class for generic mapping More...
#include <dune/geometry/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 |
typedef GeometryTraits::UserData | UserData |
Public Member Functions | |
virtual | ~HybridMapping () |
virtual bool | affine () const =0 |
is this mapping affine? | |
virtual Dune::GeometryType | type () const =0 |
obtain the name of the reference element | |
unsigned int | topologyId () const |
virtual int | numCorners () const =0 |
obtain number of corners of the corresponding reference element | |
virtual GlobalCoordinate | corner (int i) const =0 |
obtain coordinates of the i-th corner | |
virtual GlobalCoordinate | center () const =0 |
obtain the centroid of the mapping's image | |
virtual GlobalCoordinate | global (const LocalCoordinate &x) const =0 |
evaluate the mapping | |
virtual LocalCoordinate | local (const GlobalCoordinate &y) const =0 |
evaluate the inverse mapping | |
virtual bool | checkInside (const LocalCoordinate &x) const =0 |
check whether a point lies within the reference element | |
virtual FieldType | integrationElement (const LocalCoordinate &x) const =0 |
obtain the integration element | |
virtual FieldType | volume () const =0 |
obtain the volume of the mapping's image | |
virtual const JacobianTransposed & | jacobianTransposed (const LocalCoordinate &x) const =0 |
obtain the transposed of the Jacobian | |
virtual const JacobianInverseTransposed & | jacobianInverseTransposed (const LocalCoordinate &x) const =0 |
obtain the transposed of the Jacobian's inverse | |
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 |
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.
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] |
typedef GeometryTraits::UserData Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::UserData |
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 coordinate 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 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 >.
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 coordinate 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 >.
unsigned int Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::topologyId | ( | ) | const [inline] |
Codim< codim >::Trace* Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::trace | ( | unsigned int | i, |
char * | mappingStorage | ||
) | const [inline] |
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 >.
Referenced by Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >::topologyId().
const UserData& Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::userData | ( | ) | const [inline] |
UserData& Dune::GenericGeometry::HybridMapping< dim, GeometryTraits >::userData | ( | ) | [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 >.