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specialization for dim=0, this is a vertex More...
#include <dune/grid/sgrid.hh>
Public Types | |
typedef GridImp::ctype | ctype |
define type used for coordinates in grid module | |
Public Member Functions | |
GeometryType | type () const |
return the element type identifier | |
bool | affine () const |
here we have always an affine geometry | |
int | corners () const |
return the number of corners of this element. Corners are numbered 0...n-1 | |
FieldVector< ctype, cdim > | corner (const int i) const |
return i'th corner of the geometry | |
FieldVector< ctype, cdim > | center () const |
return center of the geometry | |
void | print (std::ostream &ss, int indent) const |
print internal data | |
void | make (FieldMatrix< ctype, 1, cdim > &__As) |
constructor, makes element from position and direction vectors | |
FieldVector< ctype, cdim > | global (const FieldVector< ctype, 0 > &local) const |
maps a local coordinate within reference element to global coordinate in element | |
FieldVector< ctype, 0 > | local (const FieldVector< ctype, cdim > &global) const |
maps a global coordinate within the element to a local coordinate in its reference element | |
SGeometry () | |
constructor with bool argument makes reference element if true, uninitialized else | |
ctype | volume () const |
This dummy routine always returns 1.0. | |
ctype | integrationElement (const FieldVector< ctype, 0 > &local) const |
This dummy routine always returns 1.0. | |
const FieldMatrix< ctype, 0, cdim > & | jacobianTransposed (const FieldVector< ctype, 0 > &local) const |
const FieldMatrix< ctype, cdim, 0 > & | jacobianInverseTransposed (const FieldVector< ctype, 0 > &local) const |
Protected Attributes | |
FieldVector< ctype, cdim > | s |
position of element |
specialization for dim=0, this is a vertex
typedef GridImp::ctype Dune::SGeometry< 0, cdim, GridImp >::ctype |
define type used for coordinates in grid module
Reimplemented from Dune::GeometryDefaultImplementation< 0, cdim, GridImp, SGeometry >.
Dune::SGeometry< 0, cdim, GridImp >::SGeometry | ( | ) | [inline] |
constructor with bool argument makes reference element if true, uninitialized else
Integration over a general element is done by integrating over the reference element and using the transformation from the reference element to the global element as follows:
where is the local to global mapping and
is the integration element.
For a general map involves partial derivatives of the map (surface element of the first kind if
, determinant of the Jacobian of the transformation for
,
for
).
For linear elements, the derivatives of the map with respect to local coordinates do not depend on the local coordinates and are the same over the whole element.
For a structured mesh where all edges are parallel to the coordinate axes, the computation is the length, area or volume of the element is very simple to compute.
Each grid module implements the integration element with optimal efficieny. This will directly translate in substantial savings in the computation of finite element stiffness matrices. For this specialisation the integrationElement is always 1.
bool Dune::SGeometry< 0, cdim, GridImp >::affine | ( | ) | const [inline] |
here we have always an affine geometry
FieldVector<ctype, cdim > Dune::SGeometry< 0, cdim, GridImp >::center | ( | ) | const [inline] |
return center of the geometry
Reimplemented from Dune::GeometryDefaultImplementation< 0, cdim, GridImp, SGeometry >.
FieldVector<ctype, cdim > Dune::SGeometry< 0, cdim, GridImp >::corner | ( | const int | i | ) | const [inline] |
return i'th corner of the geometry
int Dune::SGeometry< 0, cdim, GridImp >::corners | ( | ) | const [inline] |
return the number of corners of this element. Corners are numbered 0...n-1
FieldVector<ctype, cdim> Dune::SGeometry< 0, cdim, GridImp >::global | ( | const FieldVector< ctype, 0 > & | local | ) | const [inline] |
maps a local coordinate within reference element to global coordinate in element
References Dune::SGeometry< mydim, cdim, GridImp >::corner().
ctype Dune::SGeometry< 0, cdim, GridImp >::integrationElement | ( | const FieldVector< ctype, 0 > & | local | ) | const [inline] |
This dummy routine always returns 1.0.
This routine exists so that algorithms that integrate over grid boundaries can also be compiled for 1d-grids.
References Dune::SGeometry< mydim, cdim, GridImp >::volume().
const FieldMatrix<ctype,cdim,0>& Dune::SGeometry< 0, cdim, GridImp >::jacobianInverseTransposed | ( | const FieldVector< ctype, 0 > & | local | ) | const [inline] |
const FieldMatrix<ctype, 0, cdim >& Dune::SGeometry< 0, cdim, GridImp >::jacobianTransposed | ( | const FieldVector< ctype, 0 > & | local | ) | const [inline] |
FieldVector<ctype, 0> Dune::SGeometry< 0, cdim, GridImp >::local | ( | const FieldVector< ctype, cdim > & | global | ) | const [inline] |
maps a global coordinate within the element to a local coordinate in its reference element
void Dune::SGeometry< 0, cdim, GridImp >::make | ( | FieldMatrix< ctype, 1, cdim > & | __As | ) |
constructor, makes element from position and direction vectors
void Dune::SGeometry< 0, cdim, GridImp >::print | ( | std::ostream & | ss, | |
int | indent | |||
) | const |
print internal data
GeometryType Dune::SGeometry< 0, cdim, GridImp >::type | ( | ) | const [inline] |
return the element type identifier
ctype Dune::SGeometry< 0, cdim, GridImp >::volume | ( | ) | const [inline] |
This dummy routine always returns 1.0.
This routine exists so that algorithms that integrate over grid boundaries can also be compiled for 1d-grids.
Reimplemented from Dune::GeometryDefaultImplementation< 0, cdim, GridImp, SGeometry >.
FieldVector<ctype, cdim> Dune::SGeometry< 0, cdim, GridImp >::s [protected] |
position of element
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