Dune::IntersectionIterator< GridImp, IntersectionIteratorImp > Class Template Reference
[IntersectionIterator]
#include <intersectioniterator.hh>
Detailed Description
template<class GridImp, template< class > class IntersectionIteratorImp>
class Dune::IntersectionIterator< GridImp, IntersectionIteratorImp >
Mesh entities of codimension 0 ("elements") allow to visit all intersections with "neighboring" elements and with the domain boundary.
Template parameters are:
GridImp
Type that is a model of Dune::GridIntersectionIteratorImp
Class template that is a model of Dune::IntersectionIterator
- Warning:
- The name IntersectionIterator may be somewhat misleading. This class has neither an operator* nor an operator->. It iterates over codimension 1 intersections with other entities and the (sub-)domain boundary.
The number of neigbors may be different from the number of faces/edges of an element!
Overview
Intersections are codimension 1 objects. These intersections are accessed via an IntersectionIterator. This allows the implementation of non-matching grids, as one face can now consist of several intersections. In a conforming mesh such an intersection corresponds to an entity of codimension 1 but in the general non-conforming case there will be no entity in the mesh that directly corresponds to the intersection. Thus, the IntersectionIterator describes these intersections implicitly.
Engine Concept
The IntersectionIterator class template wraps an object of type IntersectionIteratorImp and forwards all member function calls to corresponding members of this class. In that sense IntersectionIterator defines the interface and IntersectionIteratorImp supplies the implementation.
Intersections, leaf grid and level grid
On an entity e of codimension zero there are two ways to create IntersectionIterators by either using ilevelbegin() / ilevelend() or ileafbegin()/ileafend(). In the first case intersections with neighboring entities having the same level as e are traversed; in the second case ileafbegin()==ileafend() if e is not a leaf otherwise all intersections with neighboring leaf entities are traversed.
Consider a situation where two elements a and b have a common intersection. Element b has been refined into an element c and d, while a has not been refined. In one space dimension this situation is depicted in the figure below.

IntersectionIterator in a locally refined mesh.
Here the rule is the following: The LevelIntersectionIterator delivers all intersections with elements on the same level, the LeafIntersectionIterator delivers the intersections with all leaf elements if it has been started on a leaf element. Both iterators also stop at intersections with the grid boundary. According to this rule the level intersection iterator started at element a in the example above delivers an intersection with b and the left grid boundary, whereas the leaf intersection iterator returns c instead of b. Starting on entity c the level intersection iterator returns d and the intersection with the left boundary of the level 1 grid, but the leaf intersection iterator returns both d and a. Finally, starting on b the level intersection iterator returns a and the right boundary, but the leaf intersection iterator is empty since b is not a leaf entity of the grid. Starting on d both the level and the leaf intersection iterators will return the element c together with the right grid boundary.
Methods neighbor and boundary
The following holds for both the level and the leaf intersection iterator: The intersection iterator is started on a codimension 0 entity of the grid. If this entity belongs to the interior or the overlap region (see. ???) then the union of all intersections is identical to the boundary of the entity. On ghost elements the iterator only stops on the border of the domain, i.e., only on the intersections with entities in the interior region. Depending on the boolean values returned by the methods boundary() and neighbor() one can detect the position of an intersection relative to the boundary. In general the method boundary() returns true if and only if the intersection is part of the physical boundary of the domain. The method neighbor() returns true only if the method outside() has a well defined return value.
The following cases are possible if the intersection iterator is started on an entity in the interior or overlap region. More details are given below:
intersection | neighbor() | boundary() | outside() | |
1 | with inner, overlap or ghost entity | true | false | the neighbor entity |
2 | on domain boundary | false | true | undefined |
3 | on periodic boundary | true | true | Ghost-/Overlap cell (with transformed geometry) |
4 | on processor boundary | false if grid has no ghosts true otherwise | false | ghost entity (if it exists) |
- Inner Intersections:
The type of the neighboring entity can be determined through methods defined on the outside entity. - Handling physical boundaries: Different types of physical boundaries can be modeled using either the global coordinates of the intersection or by using the boundaryID method. On some grids (AluGrid, AlbertaGrid) this method returns an integer value which can be individually assigned to each boundary intersection of the macro grid and which is prolonged to higher levels during grid refinement. A more general concept will be included in latter releases along the following guidelines:
- We require differently constructed geometries outside the domain
- The kind of construction depends on the discrete problem
- Therefor these constructions can't be part of the Grid interface
- Utility classes are required to do this construction
- The utility classes must be parameterized with the intersection (in our case the IntersectionIterator)
- The utility classes return a suitable transformation of the inner() entitys geometry (with respect to the intersection), e.g., reflection at the intersection point reflection reflection combined with translation...
- Handling periodic boundaries:
- The IntersectionIterator stops at periodic boundaries
- periodic grids are handled in correspondence to parallel grids
- At the periodic boundary one can adjust an overlap- or ghost-layer.
- outer() returns a ghost or overlap cell (for ghost and overlap look into the documentation of the parallel grid interface)
- outer() cell has a periodically transformed geometry (so that one does not see a jump or something like that)
- outer() cell has its own index
- outer() cell has the same id as the corresponding "original" cell
- Processor boundaries:
At processor boundaries, i.e. when an element has an intersection with another element in the sequential grid but this element is only stored in other processors the intersection iterator stops but neither neighbor() nor boundary() are true.Geometry of an intersection
The method intersectionGlobal returns a geometry mapping the intersection as a codim one structure to global coordinates. The methods intersectionSelfLocal and intersectionNeighborLocal return geometries mapping the intersection into the reference elements of the originating entity and the neighboring entity, respectively. The numberInSelf and numberInNeighbor methods return the codim one subentities which contain the intersection.
Public Types | |
enum | { dimension = dim } |
Export grid dimension. More... | |
enum | { dimensionworld = dimworld } |
Export dimension of world. More... | |
typedef GridImp::template Codim< 0 >::Entity | Entity |
Type of entity that this IntersectionIterator belongs to. | |
typedef GridImp::template Codim< 0 >::EntityPointer | EntityPointer |
Pointer to the type of entities that this IntersectionIterator belongs to. | |
typedef GridImp::template Codim< 1 >::Geometry | Geometry |
Codim 1 geometry returned by intersectionGlobal(). | |
typedef GridImp::template Codim< 1 >::LocalGeometry | LocalGeometry |
Codim 1 geometry returned by intersectionSelfLocal() and intersectionNeighborLocal(). | |
typedef IntersectionIterator < GridImp, IntersectionIteratorImp > | Intersection |
typedef GridImp::ctype | ctype |
define type used for coordinates in grid module | |
Public Member Functions | |
const Intersection & | operator* () const |
Dereferencing operator. | |
const Intersection * | operator-> () const |
Pointer operator. | |
IntersectionIterator & | operator++ () |
Preincrement operator. Proceed to next intersection. | |
bool | boundary () const |
return true if intersection is with interior or exterior boundary (see the cases above) | |
int | boundaryId () const |
Identifier for boundary segment from macro grid. | |
bool | neighbor () const |
return true if intersection is shared with another element. | |
EntityPointer | inside () const |
return EntityPointer to the Entity on the inside of this intersection. That is the Entity where we started this Iterator. | |
EntityPointer | outside () const |
return EntityPointer to the Entity on the outside of this intersection. That is the neighboring Entity. | |
const LocalGeometry & | intersectionSelfLocal () const |
geometrical information about this intersection in local coordinates of the inside() entity. | |
const LocalGeometry & | intersectionNeighborLocal () const |
geometrical information about this intersection in local coordinates of the outside() entity. | |
const Geometry & | intersectionGlobal () const |
geometrical information about this intersection in global coordinates. | |
int | numberInSelf () const |
Local number of codim 1 entity in the inside() Entity where intersection is contained in. | |
int | numberInNeighbor () const |
Local number of codim 1 entity in outside() Entity where intersection is contained in. | |
FieldVector< ctype, dimworld > | outerNormal (const FieldVector< ctype, dim-1 > &local) const |
Return an outer normal (length not necessarily 1). | |
FieldVector< ctype, dimworld > | integrationOuterNormal (const FieldVector< ctype, dim-1 > &local) const |
return outer normal scaled with the integration element | |
FieldVector< ctype, dimworld > | unitOuterNormal (const FieldVector< ctype, dim-1 > &local) const |
Return unit outer normal (length == 1). | |
bool | operator== (const IntersectionIterator &rhs) const |
Checks for equality. Only Iterators pointing to the same intersection from the same Entity are equal. Pointing to the same intersection from neighbor is unequal as inside and outside are permuted. | |
bool | operator!= (const IntersectionIterator &rhs) const |
Checks for inequality. Only Iterators pointing to the same intersection from the same Entity are equal. Pointing to the same intersection from neighbor is unequal as inside and outside are permuted. | |
Implementor interface | |
bool | equals (const IntersectionIterator &rhs) const |
forward equality check to realIterator | |
IntersectionIterator (const IntersectionIteratorImp< const GridImp > &i) | |
IntersectionIterator (const IntersectionIterator &i) | |
Protected Member Functions | |
ImplementationType & | getRealImp () |
return reference to the real implementation | |
const ImplementationType & | getRealImp () const |
return reference to the real implementation |
Member Typedef Documentation
typedef IntersectionIterator<GridImp, IntersectionIteratorImp> Dune::IntersectionIterator< GridImp, IntersectionIteratorImp >::Intersection |
forward compatibility to new Dune Intersection's
Member Enumeration Documentation
anonymous enum |
anonymous enum |
Constructor & Destructor Documentation
Dune::IntersectionIterator< GridImp, IntersectionIteratorImp >::IntersectionIterator | ( | const IntersectionIteratorImp< const GridImp > & | i | ) | [inline] |
Copy Constructor from IntersectionIteratorImp
Dune::IntersectionIterator< GridImp, IntersectionIteratorImp >::IntersectionIterator | ( | const IntersectionIterator< GridImp, IntersectionIteratorImp > & | i | ) | [inline] |
Copy constructor
Member Function Documentation
int Dune::IntersectionIterator< GridImp, IntersectionIteratorImp >::boundaryId | ( | ) | const [inline] |
Identifier for boundary segment from macro grid.
One can attach a boundary Id to a boundary segment on the macro grid. This Id will also be used for all fragments of these boundary segments.
The numbering is defined as:
- Id==0 for all intersections without boundary()==false
- Id>=0 for all intersections without boundary()==true
The way the Identifiers are attached to the grid may differ between the different grid implementations.
EntityPointer Dune::IntersectionIterator< GridImp, IntersectionIteratorImp >::outside | ( | ) | const [inline] |
return EntityPointer to the Entity on the outside of this intersection. That is the neighboring Entity.
- Warning:
- Don't call this method if there is no neighboring Entity (neighbor() returns false). In this case the result is undefined.
const LocalGeometry& Dune::IntersectionIterator< GridImp, IntersectionIteratorImp >::intersectionSelfLocal | ( | ) | const [inline] |
const LocalGeometry& Dune::IntersectionIterator< GridImp, IntersectionIteratorImp >::intersectionNeighborLocal | ( | ) | const [inline] |
const Geometry& Dune::IntersectionIterator< GridImp, IntersectionIteratorImp >::intersectionGlobal | ( | ) | const [inline] |
geometrical information about this intersection in global coordinates.
This method returns a Geometry object that provides a mapping from local coordinates of the intersection to global (world) coordinates.
FieldVector<ctype, dimworld> Dune::IntersectionIterator< GridImp, IntersectionIteratorImp >::outerNormal | ( | const FieldVector< ctype, dim-1 > & | local | ) | const [inline] |
Return an outer normal (length not necessarily 1).
The returned vector may depend on local position within the intersection.
FieldVector<ctype, dimworld> Dune::IntersectionIterator< GridImp, IntersectionIteratorImp >::integrationOuterNormal | ( | const FieldVector< ctype, dim-1 > & | local | ) | const [inline] |
return outer normal scaled with the integration element
Return an outer normal (length not necessarily 1).
The returned vector may depend on local position within the intersection. The normal is scaled with the integration element of the intersection. This method is redundant but it may be more efficent to use this function rather than computing the integration element via intersectionGlobal().
FieldVector<ctype, dimworld> Dune::IntersectionIterator< GridImp, IntersectionIteratorImp >::unitOuterNormal | ( | const FieldVector< ctype, dim-1 > & | local | ) | const [inline] |
Return unit outer normal (length == 1).
The returned vector may depend on the local position within the intersection. It is scaled to have unit length.
The documentation for this class was generated from the following file: