dune-grid
2.1.1
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#include <dune/grid/genericgeometry/hybridmapping.hh>
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 |
Public Member Functions | |
template<class CoordVector > | |
VirtualMapping (const CoordVector &coordVector) | |
virtual unsigned int | topologyId () const |
virtual const GlobalCoordinate & | corner (int i) const |
virtual int | numCorners () const |
virtual GlobalCoordinate | center () const |
virtual GlobalCoordinate | global (const LocalCoordinate &local) const |
virtual LocalCoordinate | local (const GlobalCoordinate &global) const |
virtual bool | checkInside (const LocalCoordinate &local) const |
virtual bool | affine () const |
virtual FieldType | integrationElement (const LocalCoordinate &local) const |
virtual FieldType | volume () const |
virtual const JacobianTransposed & | jacobianTransposed (const LocalCoordinate &local) const |
virtual const JacobianInverseTransposed & | jacobianInverseTransposed (const LocalCoordinate &local) const |
virtual Base * | clone () const |
virtual Base * | clone (char *mappingStorage) const |
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 |
typedef GeometryTraits::Caching Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::Caching |
Reimplemented from Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
typedef Traits::FieldType Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::FieldType |
Reimplemented from Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
typedef Traits::GlobalCoordinate Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::GlobalCoordinate |
Reimplemented from Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
typedef Base::JacobianInverseTransposed Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::JacobianInverseTransposed |
Reimplemented from Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
typedef Base::JacobianTransposed Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::JacobianTransposed |
Reimplemented from Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
typedef Traits::LocalCoordinate Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::LocalCoordinate |
Reimplemented from Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
typedef Mapping::ReferenceElement Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::ReferenceElement |
Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::VirtualMapping | ( | const CoordVector & | coordVector | ) | [inline, explicit] |
virtual bool Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::affine | ( | ) | const [inline, virtual] |
is this mapping affine?
Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::affine().
virtual GlobalCoordinate Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::center | ( | ) | const [inline, virtual] |
obtain the centroid of the mapping's image
Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::center().
virtual bool Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::checkInside | ( | const LocalCoordinate & | x | ) | const [inline, virtual] |
check whether a point lies within the reference element
[in] | x | local coorinate of point to check |
Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::checkInside().
virtual Base* Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::clone | ( | ) | const [inline, virtual] |
virtual Base* Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::clone | ( | char * | mappingStorage | ) | const [inline, virtual] |
virtual const GlobalCoordinate& Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::corner | ( | int | i | ) | const [inline, virtual] |
virtual GlobalCoordinate Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::global | ( | const LocalCoordinate & | x | ) | const [inline, virtual] |
evaluate the mapping
[in] | x | local coordinate to map |
Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::global().
virtual FieldType Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::integrationElement | ( | const LocalCoordinate & | x | ) | const [inline, 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 |
Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::integrationElement().
virtual const JacobianInverseTransposed& Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::jacobianInverseTransposed | ( | const LocalCoordinate & | x | ) | const [inline, 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:
Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::jacobianInverseTransposed().
virtual const JacobianTransposed& Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::jacobianTransposed | ( | const LocalCoordinate & | x | ) | const [inline, virtual] |
obtain the transposed of the Jacobian
[in] | x | local coordinate to evaluate Jacobian in |
Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::jacobianTransposed().
virtual LocalCoordinate Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::local | ( | const GlobalCoordinate & | y | ) | const [inline, virtual] |
evaluate the inverse mapping
[in] | y | global coorindate to map |
(global( x ) - y).two_norm()
Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::local().
virtual int Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::numCorners | ( | ) | const [inline, virtual] |
obtain number of corners of the corresponding reference element
Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::numCorners().
virtual unsigned int Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::topologyId | ( | ) | const [inline, virtual] |
obtain topology id of the corresponding reference element
Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::topologyId().
Codim< codim >::Trace* Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::trace | ( | unsigned int | i, |
char * | mappingStorage | ||
) | const [inline] |
Reimplemented from Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
virtual FieldType Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::volume | ( | ) | const [inline, virtual] |
obtain the volume of the mapping's image
integrationElement( baryCenter() ) * ReferenceElement::volume()
Implements Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
References Dune::GenericGeometry::CachedMapping< Topology, GeometryTraits >::volume().
const unsigned int Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::dimension = Traits :: dimension [static] |
Reimplemented from Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.
const unsigned int Dune::GenericGeometry::VirtualMapping< Topology, GeometryTraits >::dimWorld = Traits :: dimWorld [static] |
Reimplemented from Dune::GenericGeometry::HybridMapping< Topology::dimension, GeometryTraits >.