Dune::SGeometry< 0, cdim, GridImp > Class Template Reference
#include <sgrid.hh>
Inheritance diagram for Dune::SGeometry< 0, cdim, GridImp >:

Detailed Description
template<int cdim, class GridImp>
class Dune::SGeometry< 0, cdim, GridImp >
specialization for dim=0, this is a vertex
Public Types | |
typedef sgrid_ctype | ctype |
define type used for coordinates in grid module | |
Public Member Functions | |
GeometryType | type () const |
return the element type identifier | |
int | corners () const |
return the number of corners of this element. Corners are numbered 0...n-1 | |
const FieldVector< sgrid_ctype, cdim > & | operator[] (int i) const |
access to coordinates of corners. Index is the number of the corner | |
void | print (std::ostream &ss, int indent) const |
print internal data | |
void | make (FieldMatrix< sgrid_ctype, 1, cdim > &__As) |
constructor, makes element from position and direction vectors | |
FieldVector< sgrid_ctype, cdim > | global (const FieldVector< sgrid_ctype, 0 > &local) const |
maps a local coordinate within reference element to global coordinate in element | |
FieldVector< sgrid_ctype, 0 > | local (const FieldVector< sgrid_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 | |
sgrid_ctype | integrationElement (const FieldVector< sgrid_ctype, 0 > &local) const |
This dummy routine always returns 1.0. | |
bool | checkInside (const FieldVector< sgrid_ctype, 0 > &local) const |
returns always true | |
const FieldMatrix< sgrid_ctype, 0, 0 > & | jacobianInverseTransposed (const FieldVector< sgrid_ctype, 0 > &local) const |
can only be called for dim=dimworld! | |
ctype | volume () const |
return volume of the geometry | |
Protected Attributes | |
FieldVector< sgrid_ctype, cdim > | s |
position of element |
Constructor & Destructor Documentation
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.
Member Function Documentation
sgrid_ctype Dune::SGeometry< 0, cdim, GridImp >::integrationElement | ( | const FieldVector< sgrid_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.
The documentation for this class was generated from the following files:
- sgrid.hh
- sgrid.cc