Mappers
[dune-grid]

Detailed Description

What is a Mapper ?

A mapper class is used to attach user-defined data to a subset of the grid entities $E^\prime\subseteq E$ .

It is assumed that the data $D(E^\prime)$ associated with $E^\prime$ is stored in an array. The array can be viewed as a map

$a : I_{E^\prime} \to D(E^\prime)$

from the consecutive, zero-starting index set $I_{E^\prime} = \{0, \ldots, |E^\prime|-1\}$ of $E^\prime$ to the data set.

The mapper class provides a mapping

$m : E^\prime \to I_{E^\prime}$

from the entity set to the index set.

Access from a grid entity $e\in E^\prime$ to its associated data element $d_e$ then is a two step process:

$a(m(e)) = d_e.$

There are different kinds of mappers depending on functionality and efficiency of their implementation. The user selects an appropriate mapper depending on her/his needs. All mappers conform to the same interface.

Index based Mappers

An index-based mapper is allocated for a grid and can be used as long as the grid is not changed (i.e. refined, coarsened or load balanced). The implementation of static mappers is based on a Dune::IndexSet and is typically of $O(1)$

complexity with a very small constant. Index-based mappers are only available for restricted (but usually sufficient) entity sets.

Id based Mappers

An id-based mapper can also be used while a grid changes. For that it has to be implemented on the basis of a Dune::IdSet. This may be relatively slow because the data type used for ids is usually not an int and the non-consecutive ids require more complicated search data structures (typically a map). Access is therefore at least $O(\log |E^\prime|)$ . On the other hand, id-based mappers can treat arbitrary entity sets $E^\prime$ .

Mapper Interface

This interface is implemented by the class template Dune::Mapper. For a full documentation see the description of this class.

The function Dune::Mapper::map delivers the index for an entity. Note that that for performance reasons it is usually not checked whether the entity is really in the entity set.

The functions Dune::Mapper::map delivers the index for a (sub-)entity

The function Dune::Mapper::size returns the size of the entity set, i.e. $|E^\prime|$

The different implementations of the mapper interface are listed below.

Overview of Different Mapper Implementations

Mappers and Mesh Changes


Classes
class	Dune::Mapper< G, MapperImp >
	Mapper interface. More...
class	Dune::MultipleCodimMultipleGeomTypeMapper< G, IS, Layout >
	Implementation class for a multiple codim and multiple geometry type mapper. More...
class	Dune::LeafMultipleCodimMultipleGeomTypeMapper< G, Layout >
	Multiple codim and multiple geometry type mapper for leaf entities. More...
class	Dune::LevelMultipleCodimMultipleGeomTypeMapper< G, Layout >
	Multiple codim and multiple geometry type mapper for entities of one level. More...
class	Dune::SingleCodimSingleGeomTypeMapper< G, IS, c >
	Implementation class for a single codim and single geometry type mapper. More...
class	Dune::LeafSingleCodimSingleGeomTypeMapper< G, c >
	Single codim and single geometry type mapper for leaf entities. More...
class	Dune::LevelSingleCodimSingleGeomTypeMapper< G, c >
	Single codim and single geometry type mapper for entities of one level. More...
class	Dune::UniversalMapper< G, IDS >
	Implements a mapper for an arbitrary subset of entities. More...
class	Dune::GlobalUniversalMapper< G >
	Universal mapper based on global ids. More...
class	Dune::LocalUniversalMapper< G >
	Universal mapper based on local ids. More...

Mappers [dune-grid]