dune-grid


Detailed Description

The Dune Grid module defines a general interface to a parallel, in general nonconforming, locally refined and hierarchical finite element mesh. The interface is independent of dimension and element type.

Terminology

Entity

An entity is a geometric object that is part of a grid. It is generalized polytope that has the same dimensionality as the grid or a lower dimension.

Dimension

A grid has a fixed dimension $d$ which is the number of coordinates required to specify any point in the grid. The dimension is a template parameter of a grid.

Codimension of an entity

Each entity has a codimension $c$ where $0 \leq c \leq d$ (the dimension of the grid). An entity with codimension $ c$ in a grid of dimension $ d$ is a $d-c$-dimensional object.

Subentity

Entities are hierarchically constructed in the sense that entities of codimension 0 are made up of entities of codimension 1 which are themselves made up of entities of codimension 2 etc. until entities of codimension $d-1$ which consist of entities of codimension $ d$.

Element

An element is an entity of codimension 0.

Vertex

A vertex is an entity of codimension $ d$ (the same as the grid's dimension).

World dimension

Each grid has a world dimension $ w$ with $ w\geq d$. This is the number of coordinates of the positions of the grid's vertices.

Hierarchical grid

The Dune grid interface describes not only a single grid but a sequence of grids with different resolution. This is achieved by beginning with an intentionally coarse grid, the so-called macro grid. Then each element may be individually subdivided to yield new (smaller) elements. This construction is recursive such that each macro element and all the elements that resulted from subdividing it form a tree structure.

Grid refinement

The grid can only be modified in special phases, the so-called refinement phase. In between refinement phases the entities of the grid can not be modified in any way. During refinement currently only the hierachic subdivision can be modified.

Grid level

All elements of the macro grid form level 0 of the grid structure. All elements that are obtained from an $ l$-fold subdivision of a macro element form level $ l$ of the grid structure.

Leaf grid

All elements of a grid that are not subdivided any further make up the leaf grid. The leaf grid is the mesh with the finest resolution.

Assignable

A type is said to be assignable if it has a (public) copy constructor and assignment operator. Note that this definition requires always both methods.

Default-constructible

A type is said to be default-constructible if it has a constructor without arguments.

Copy-constructible from type X

A type is said to be copy constructible from some other type X if it has a copy constructor that takes a reference to an object of type X.

Equality-comparable

A type is said to be equality-comparable if it has an operator==.

LessThan-comparable

A type is lessthan-comparable if it has an operator<.

Dereferenceable

A type is dereferenceable if it has an operator* that delivers a reference to a value type.

Dereferenceable

An iterator is a type that can be dereferenced to yield an object of its value type, i.e. it behaves like a pointer, and that can be incremented to point to the next element in a linear sequence. In that respect it is comparable to ForwardIterator in the Standard Template Library.

Mutable iterator

An iterator is called mutable if the value it refers to can be changed, i.e. it is assignable.

Immutable iterator

An iterator is called immutable if the value referenced by the iterator can not be changed, i. e. the value is not assignable and only methods marked const on the value can be called.

Model

A type M is called a model of another type X if it implements all the methods of X with the intended semantics. Typically X is a type that describes an interface.

Types common to all grid implementations

  • Dune::ReferenceElement describes the topology and geometry of standard entities. Any given entity of the grid can be completely specified by a reference element and a map from this reference element to world coordinate space.

  • Dune::GeometryType defines names for the reference elements.

  • Dune::CollectiveCommunication defines an interface to global communication operations in a portable and transparent way. In particular also for sequential grids.

Types making up a grid implementation

Each implementation of the Dune grid interface consist of a number of related types which together form a model of the grid interface. These types are the following:

  • Grid which is a model of Dune::Grid where the template parameters are at least the dimension and the world dimension. It is a container of entities that allows to access these entities and that knows the number of entities.

  • Entity which is a model of Dune::Entity. This class is parametrized by dimension and codimension. The entity encapsulates the topological part of an entity, i.e. its hierarchical construction from subentities and the relation to other entities. Entities cannot be created, copied or modified by the user. They can only be read-accessed through immutable iterators.

  • Geometry which is a model of Dune::Geometry. This class encapsulates the geometric part of an entity by mapping local coordinates in a reference element to world coordinates.

  • EntityPointer which is a model of Dune::EntityPointer. This is a dereferenceable type that delivers a reference to an entity. Moreover it is immutable, i.e. the referenced entity can not be modified.

  • LevelIterator which is a model of Dune::LevelIterator is an immutable iterator that provides access to all entities of a given codimension and level of the grid. EntityPointer is copy-constructible from a LevelIterator.

  • LeafIterator which is a model of Dune::LeafIterator is an immutable iterator that provides access to all entities of a given codimension of the leaf grid. EntityPointer is copy-constructible from a LeafIterator.

  • HierarchicIterator which is a model of Dune::HierarchicIterator is an immutable iterator that provides access to all entities of codimension 0 that resulted from subdivision of a given entity of codimension 0. EntityPointer is copy-constructible from a HierarchicIterator.

  • IntersectionIterator which is a model of Dune::IntersectionIterator provides access to all entities of codimension 0 that have an intersection of codimension 1 with a given entity of codimension 0. In a conforming mesh these are the face neighbors of an element. For two entities with a common intersection the IntersectionIterator also provides information about the geometric location of the intersection. Furthermore it also provides information about intersections of an entity with the internal or external boundaries.

  • LevelIndexSet and LeafIndexSet which are both models of Dune::IndexSet are used to attach any kind of user-defined data to (subsets of) entities of the grid. This data is supposed to be stored in one-dimensional arrays for reasons of efficiency.

  • LocalIdSet and GlobalIdSet which are both models of Dune::IdSet are used to save user data during a grid refinement phase and during dynamic load balancing in the parallel case.

Overview of basic capabilities of the types

Class Assignable DefaultConstructible EqualityComparable LessThanComparable
Grid no no no no
Entity no no no no
GeometryType yes yes yes yes
Geometry no no no no
EntityPointer yes no yes no
LevelIterator yes no yes no
LeafIterator yes no yes no
HierarchicIterator yes no yes no
IntersectionIterator yes no yes no
IndexSet no no no no
IdSet no no no no


Modules

 The Grid Interface
 Interfaces needed when working with a Dune::Grid.
 Reference Elements
 Classes describing the geometry of the reference elements.
 Mappers
 Grid Implementations
 A list of the different Implementations of the Dune Grid Interface.
 I/O
 Grid Parts
 Grid Developer API
 Interfaces needed to implement a new Dune::Grid.
 Refinement
 Quadrature

Functions

template<class G>
void Dune::gridinfo (const G &grid, std::string prefix="")
 A function to print some information about the grid as a whole.
template<class G>
void Dune::gridlevellist (const G &grid, int level, std::string prefix)
 A function to print info about a grid level and its entities.
template<class G>
void Dune::gridleaflist (const G &grid, std::string prefix)
 A function to print info about a leaf grid and its entities.

Generated on 6 Nov 2008 with Doxygen (ver 1.5.6) [logfile].