dune-geometry 2.9.1
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generic geometry implementation based on corner coordinates More...
#include <dune/geometry/multilineargeometry.hh>
Classes | |
class | JacobianInverseTransposed |
Public Types | |
typedef ct | ctype |
coordinate type | |
typedef FieldVector< ctype, mydimension > | LocalCoordinate |
type of local coordinates | |
typedef FieldVector< ctype, coorddimension > | GlobalCoordinate |
type of global coordinates | |
typedef ctype | Volume |
type of volume | |
typedef FieldMatrix< ctype, mydimension, coorddimension > | JacobianTransposed |
type of jacobian transposed | |
typedef FieldMatrix< ctype, coorddimension, mydimension > | Jacobian |
Type for the Jacobian matrix. | |
typedef FieldMatrix< ctype, mydimension, coorddimension > | JacobianInverse |
Type for the inverse Jacobian matrix. | |
typedef ReferenceElements::ReferenceElement | ReferenceElement |
type of reference element | |
Public Member Functions | |
template<class Corners > | |
MultiLinearGeometry (const ReferenceElement &refElement, const Corners &corners) | |
constructor | |
template<class Corners > | |
MultiLinearGeometry (Dune::GeometryType gt, const Corners &corners) | |
constructor | |
bool | affine () const |
is this mapping affine? | |
Dune::GeometryType | type () const |
obtain the name of the reference element | |
int | corners () 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 &globalCoord) const |
evaluate the inverse mapping | |
Volume | integrationElement (const LocalCoordinate &local) const |
obtain the integration element | |
Volume | volume () const |
obtain the volume of the mapping's image | |
JacobianTransposed | jacobianTransposed (const LocalCoordinate &local) const |
obtain the transposed of the Jacobian | |
JacobianInverseTransposed | jacobianInverseTransposed (const LocalCoordinate &local) const |
obtain the transposed of the Jacobian's inverse | |
Jacobian | jacobian (const LocalCoordinate &local) const |
Obtain the Jacobian. | |
JacobianInverse | jacobianInverse (const LocalCoordinate &local) const |
Obtain the Jacobian's inverse. | |
Static Public Attributes | |
static const int | mydimension = mydim |
geometry dimension | |
static const int | coorddimension = cdim |
coordinate dimension | |
Protected Types | |
typedef Dune::ReferenceElements< ctype, mydimension > | ReferenceElements |
typedef Traits::MatrixHelper | MatrixHelper |
typedef std::conditional< hasSingleGeometryType, std::integral_constant< unsignedint, Traits::templatehasSingleGeometryType< mydimension >::topologyId >, unsignedint >::type | TopologyId |
Protected Member Functions | |
ReferenceElement | refElement () const |
TopologyId | topologyId () const |
bool | affine (JacobianTransposed &jacobianT) const |
Static Protected Member Functions | |
template<bool add, int dim, class CornerIterator > | |
static void | global (TopologyId topologyId, std::integral_constant< int, dim >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, GlobalCoordinate &y) |
template<bool add, class CornerIterator > | |
static void | global (TopologyId topologyId, std::integral_constant< int, 0 >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, GlobalCoordinate &y) |
template<bool add, int rows, int dim, class CornerIterator > | |
static void | jacobianTransposed (TopologyId topologyId, std::integral_constant< int, dim >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, FieldMatrix< ctype, rows, cdim > &jt) |
template<bool add, int rows, class CornerIterator > | |
static void | jacobianTransposed (TopologyId topologyId, std::integral_constant< int, 0 >, CornerIterator &cit, const ctype &df, const LocalCoordinate &x, const ctype &rf, FieldMatrix< ctype, rows, cdim > &jt) |
template<int dim, class CornerIterator > | |
static bool | affine (TopologyId topologyId, std::integral_constant< int, dim >, CornerIterator &cit, JacobianTransposed &jt) |
template<class CornerIterator > | |
static bool | affine (TopologyId topologyId, std::integral_constant< int, 0 >, CornerIterator &cit, JacobianTransposed &jt) |
generic geometry implementation based on corner coordinates
Based on the recursive definition of the reference elements, the MultiLinearGeometry provides a generic implementation of a geometry given the corner coordinates.
The geometric mapping is multilinear in the classical sense only in the case of cubes; for simplices it is linear. The name is still justified, because the mapping satisfies the important property of begin linear along edges.
ct | coordinate type |
mydim | geometry dimension |
cdim | coordinate dimension |
Traits | traits allowing to tweak some implementation details (optional) |
The requirements on the traits are documented along with their default, MultiLinearGeometryTraits.
typedef ct Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::ctype |
coordinate type
typedef FieldVector< ctype, coorddimension > Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::GlobalCoordinate |
type of global coordinates
typedef FieldMatrix< ctype, coorddimension, mydimension > Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::Jacobian |
Type for the Jacobian matrix.
typedef FieldMatrix< ctype, mydimension, coorddimension > Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::JacobianInverse |
Type for the inverse Jacobian matrix.
typedef FieldMatrix< ctype, mydimension, coorddimension > Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::JacobianTransposed |
type of jacobian transposed
typedef FieldVector< ctype, mydimension > Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::LocalCoordinate |
type of local coordinates
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protected |
typedef ReferenceElements::ReferenceElement Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::ReferenceElement |
type of reference element
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typedef ctype Dune::MultiLinearGeometry< ct, mydim, cdim, Traits >::Volume |
type of volume
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constructor
[in] | refElement | reference element for the geometry |
[in] | corners | corners to store internally |
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constructor
[in] | gt | geometry type |
[in] | corners | corners to store internally |
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is this mapping affine?
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inlineprotected |
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inlinestaticprotected |
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inlinestaticprotected |
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obtain the centroid of the mapping's image
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obtain coordinates of the i-th corner
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obtain number of corners of the corresponding reference element
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evaluate the mapping
[in] | local | local coordinate to map |
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inlinestaticprotected |
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inlinestaticprotected |
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obtain the integration element
If the Jacobian of the mapping is denoted by $J(x)$, the integration integration element
[in] | local | local coordinate to evaluate the integration element in |
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Obtain the Jacobian.
[in] | local | local coordinate to evaluate Jacobian in |
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Obtain the Jacobian's inverse.
The Jacobian's inverse is defined as a pseudo-inverse. If we denote the Jacobian by
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obtain the transposed of the Jacobian's inverse
The Jacobian's inverse is defined as a pseudo-inverse. If we denote the Jacobian by
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obtain the transposed of the Jacobian
[in] | local | local coordinate to evaluate Jacobian in |
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inlinestaticprotected |
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inlinestaticprotected |
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evaluate the inverse mapping
[in] | globalCoord | global coordinate to map |
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inlineprotected |
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inlineprotected |
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obtain the name of the reference element
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obtain the volume of the mapping's image
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static |
coordinate dimension
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geometry dimension