Dune::RefinementImp::Simplex Namespace Reference

This namespace contains the Refinement implementation for simplices (triangles, tetrahedrons...). More...

Classes

class  RefinementImp
class  RefinementIteratorSpecial< dimension, CoordType, dimension >
class  RefinementIteratorSpecial< dimension, CoordType, 0 >
class  Geometry
class  MakeableGeometry
class  ReferenceGeometryInstance

Functions

Utilities

int factorial (int n)
 Calculate n!
int binomial (int upper, int lower)
 calculate $\left({upper}\atop{lower}\right)$
template<int dimension>
int pointIndex (const FieldVector< int, dimension > &point)
 calculate the index of a given gridpoint within a Kuhn0 simplex
template<int n>
FieldVector< int, n > getPermutation (int m)
 Calculate permutation from it's index.
template<int dimension, class CoordType >
FieldVector< CoordType, dimension > referenceToKuhn (FieldVector< CoordType, dimension > point, const FieldVector< int, dimension > &kuhn)
 Map from the reference simplex to some Kuhn simplex.
template<int dimension, class CoordType >
FieldVector< CoordType, dimension > kuhnToReference (FieldVector< CoordType, dimension > point, const FieldVector< int, dimension > &kuhn)
 Map from some Kuhn simplex to the reference simplex.

Detailed Description

This namespace contains the Refinement implementation for simplices (triangles, tetrahedrons...).

See Refinement implementation for simplices.


Function Documentation

int Dune::RefinementImp::Simplex::binomial ( int  upper,
int  lower 
) [inline]

calculate $\left({upper}\atop{lower}\right)$

Runtime is of order O(min {lower, upper-lower})

References factorial().

Referenced by Dune::RefinementImp::Simplex::RefinementImp< dimension_, CoordType >::nVertices(), and pointIndex().

template<int n>
FieldVector<int, n> Dune::RefinementImp::Simplex::getPermutation ( int  m  ) 

Calculate permutation from it's index.

Runtime is of order O(n).

template<int dimension, class CoordType >
FieldVector<CoordType, dimension> Dune::RefinementImp::Simplex::kuhnToReference ( FieldVector< CoordType, dimension >  point,
const FieldVector< int, dimension > &  kuhn 
)
template<int dimension>
int Dune::RefinementImp::Simplex::pointIndex ( const FieldVector< int, dimension > &  point  ) 

calculate the index of a given gridpoint within a Kuhn0 simplex

Runtime is of order O(dimension^2) (or better for dimension > the coordinates of the point)

References binomial().

Referenced by Dune::RefinementImp::Simplex::RefinementIteratorSpecial< dimension, CoordType, dimension >::index(), and Dune::RefinementImp::Simplex::RefinementIteratorSpecial< dimension, CoordType, 0 >::vertexIndices().

template<int dimension, class CoordType >
FieldVector<CoordType, dimension> Dune::RefinementImp::Simplex::referenceToKuhn ( FieldVector< CoordType, dimension >  point,
const FieldVector< int, dimension > &  kuhn 
)

Map from the reference simplex to some Kuhn simplex.

Template Parameters:
dimension Dimension of the simplices
CoordType The C++ type of the coordinates

Runtime is of order O(dimension)

Parameters:
point Point to map
kuhn Permutation of the Kuhn simplex to map to

Referenced by Dune::RefinementImp::PyramidTriangulation::RefinementIteratorSpecial< dimension, CoordType, dimension >::coords(), Dune::RefinementImp::PrismTriangulation::RefinementIteratorSpecial< dimension, CoordType, dimension >::coords(), Dune::RefinementImp::HCubeTriangulation::RefinementIteratorSpecial< dimension, CoordType, dimension >::coords(), Dune::RefinementImp::Simplex::Geometry< mydimension, mydimension, GridImp, Geometry >::global(), Dune::RefinementImp::PyramidTriangulation::Geometry< mydimension, coorddimension, GridImp >::global(), Dune::RefinementImp::PrismTriangulation::Geometry< mydimension, coorddimension, GridImp >::global(), Dune::RefinementImp::HCubeTriangulation::Geometry< mydimension, coorddimension, GridImp >::global(), Dune::RefinementImp::Simplex::Geometry< mydimension, mydimension, GridImp, Geometry >::jacobianInverse(), Dune::RefinementImp::Simplex::Geometry< mydimension, mydimension, GridImp, Geometry >::local(), Dune::RefinementImp::PyramidTriangulation::Geometry< mydimension, coorddimension, GridImp >::operator[](), Dune::RefinementImp::PrismTriangulation::Geometry< mydimension, coorddimension, GridImp >::operator[](), and Dune::RefinementImp::HCubeTriangulation::Geometry< mydimension, coorddimension, GridImp >::operator[]().

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