Dune Core Modules (unstable)

Dune::IdSet< GridImp, IdSetImp, IdTypeImp > Class Template Reference

Id Set Interface. More...

#include <dune/grid/common/indexidset.hh>

Public Types

typedef IdTypeImp IdType
 Type used to represent an id.
 

Public Member Functions

template<class Entity >
IdType id (const Entity &e) const
 Get id of an entity. This method is simpler to use than the one below.
 
template<int cc>
IdType id (const typename std::remove_const< GridImp >::type::Traits::template Codim< cc >::Entity &e) const
 Get id of an entity of codim cc. Unhandy because template parameter must be supplied explicitly.
 
IdType subId (const typename std::remove_const< GridImp >::type::Traits::template Codim< 0 >::Entity &e, int i, unsigned int codim) const
 Get id of subentity i of co-dimension codim of a co-dimension 0 entity.
 

Detailed Description

template<class GridImp, class IdSetImp, class IdTypeImp>
class Dune::IdSet< GridImp, IdSetImp, IdTypeImp >

Id Set Interface.

This class template is used as a base class for all id set implementations. It uses the Barton-Nackman trick to ensure conformity to the interface.

Template Parameters
GridImpType that is a model of Dune::Grid.
IdSetImpType that is a model of Dune::IdSet.
IdTypeImpType used for ids

Overview

An id set provides a map

\[ m : E \to \mathbf{I}\]

where \(E\) is a subset of the entities of a grid and \(\mathbf{I}\) is a finite set of indices. These indices are persistent under grid modifications, i.e. if there exists an entity \(e\) with index \(i\) before grid modification and an entity \(e^\prime\) with index \(i\) after grid modification it is guaranteed that \(e=e^\prime\).

In the terminology of the Dune grid interface, these indices are called 'ids'. Ids are typically numbers, but may be other things, too. If they are numbers, the ids used in a grid are not necessarily positive, and they are usually not consecutive. However, the ids must be usable as keys for STL associative containers, like a std::map or a std::unordered_map. As ids are persistent, they are used to keep data on a grid that undergoes modifications.

Injectivity properties

The id map \(m\) is injective on the entire set of entities of a hierarchical grid. More formally, we have:

  • For any \(e,e^\prime\in E\) we have \(e\neq e^\prime \Rightarrow m(e)\neq m(e^\prime)\).

An exception to this rule holds for entities that are copies of entities on a lower refinement level. An element is a copy of its father element if it is the only son. This concept can be transferred to all higher codimensions because in a nested grid structure the entities of any codimension form a set of trees. However, the roots of these trees are not necessarily on level 0. Thus, we define that an entity is a copy of another entity if it is the only descendant of this entity in the refinement tree. This is illustrated in the following figure where, for example, vertex w is a copy of vertex v.

Sharing of ids.

The copy relation is an equivalence relation. We define that all copies of an entity share the same id. In the example of the figure the vertices v and w would have the same id. This definition is useful to transfer data on the leaf grid during grid modification.

Note: In "Bastian et al.: A Generic Grid Interface for Adaptive and Parallel Scientific Computing. Part I: Abstract Framework, Computing 82 (2-3), 2008, pp. 103-119" it is claimed that the id map should be injective only for entities of the same codimension. This is in contrast to the actual Dune code: in the code, grid implementations are required to provide ids that are injective even on sets of entities with different codimensions.

Properties of the IdTypeImp type

The type IdTypeImp used for ids will be specified by the grid implementation. Conceptually, it can be pretty much anything, but we require that it is usable as key for the std::map and std::unordered_map containers of the standard library. In particular, for std::map this means that IdTypeImp implements

bool operator< ( const IdTypeImp &, const IdTypeImp & );

and that this operator implements a strict weak ordering. For use with std::unordered_map, we additionally require

bool operator== ( const IdTypeImp &, const IdTypeImp & );

and that std::hash<IdType> fulfills the requirements of an stl hash object.

For convenience we further require that

bool operator!= ( const IdTypeImp &, const IdTypeImp & );

is implemented and returns the negation of operator==.

The IdTypeImp must be

  • default-constructible
  • copy-constructible
  • copy-assignable

Finally, for debugging purposes it must be possible to write objects of type IdTypeImp into standard C++ streams. Therefore

template< class C, class T >
std::basic_ostream< C, T > &operator<< ( std::basic_ostream< C, T > &, const IdTypeImp & );

has to exist and do something reasonable.

Global and local id sets

Grids are required to provide two types of id sets. These differ only of the grid is distributed over several processes:

  • A global id set provides ids that are unique over all processes over which the grid is distributed.
  • A local id set provides ids that are unique within one process, but two entities in different processes may have the same id. Obviously, a global id set is also a local id set, but a dedicated local id set implementation may be more efficient.

The documentation for this class was generated from the following files:
EnableIfInterOperable< T1, T2, bool >::type operator<(const RandomAccessIteratorFacade< T1, V1, R1, D > &lhs, const RandomAccessIteratorFacade< T2, V2, R2, D > &rhs)
Comparison operator.
Definition: iteratorfacades.hh:635
constexpr bool operator==(const DebugAllocator< T > &, const DebugAllocator< T > &)
check whether allocators are equivalent
Definition: debugallocator.hh:310
constexpr bool operator!=(const DebugAllocator< T > &, const DebugAllocator< T > &)
check whether allocators are not equivalent
Definition: debugallocator.hh:318
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