Dune Core Modules (unstable)
Intersection of a mesh entity of codimension 0 ("element") with a "neighboring" element or with the domain boundary. More...
#include <dune/grid/common/intersection.hh>
Public Types  
enum  { mydimension =GridImp::dimension1 } 
Export dimension of the intersection. More...  
enum  { dimensionworld =GridImp::dimensionworld } 
Export dimension of world. More...  
typedef IntersectionImp  Implementation 
type of underlying implementation More...  
typedef GridImp::template Codim< 0 >::Entity  Entity 
Type of entity that this Intersection belongs to.  
typedef GridImp::template Codim< 1 >::Geometry  Geometry 
Codim 1 geometry returned by geometry()  
typedef Geometry::LocalCoordinate  LocalCoordinate 
Type for vectors of coordinates on the intersection.  
typedef Geometry::GlobalCoordinate  GlobalCoordinate 
Type for normal vectors.  
typedef GridImp::template Codim< 1 >::LocalGeometry  LocalGeometry 
Codim 1 geometry returned by geometryInInside() and geometryInOutside()  
typedef GridImp::ctype  ctype 
Type of individual coefficients of coordinate vectors.  
Public Member Functions  
Implementation &  impl () 
access to the underlying implementation More...  
const Implementation &  impl () const 
access to the underlying implementation More...  
bool  boundary () const 
Return true if intersection is with interior or exterior boundary (see the cases above)  
size_t  boundarySegmentIndex () const 
index of the boundary segment within the macro grid More...  
bool  neighbor () const 
return true if intersection is shared with another element.  
Entity  inside () const 
return Entity on the inside of this intersection. That is the Entity where we started this.  
Entity  outside () const 
return Entity on the outside of this intersection. That is the neighboring Entity. More...  
bool  conforming () const 
Return true if intersection is conforming.  
LocalGeometry  geometryInInside () const 
geometrical information about this intersection in local coordinates of the inside() entity. More...  
LocalGeometry  geometryInOutside () const 
geometrical information about this intersection in local coordinates of the outside() entity. More...  
Geometry  geometry () const 
geometrical information about the intersection in global coordinates. More...  
GeometryType  type () const 
obtain the type of reference element for this intersection  
int  indexInInside () const 
Local index of codim 1 entity in the inside() entity where intersection is contained in. More...  
int  indexInOutside () const 
Local index of codim 1 entity in outside() entity where intersection is contained in. More...  
GlobalCoordinate  outerNormal (const LocalCoordinate &local) const 
Return an outer normal (length not necessarily 1) More...  
GlobalCoordinate  integrationOuterNormal (const LocalCoordinate &local) const 
return unit outer normal scaled with the integration element More...  
GlobalCoordinate  unitOuterNormal (const LocalCoordinate &local) const 
Return unit outer normal (length == 1) More...  
GlobalCoordinate  centerUnitOuterNormal () const 
Return unit outer normal (length == 1) More...  
bool  operator== (const Intersection &other) const 
Compares two intersections for equality.  
bool  operator!= (const Intersection &other) const 
Compares two intersections for inequality.  
Intersection ()  
Default constructor.  
Intersection (const Intersection &other)  
Copy constructor from an existing intersection.  
Intersection (Intersection &&other)  
Move constructor from an existing intersection.  
Intersection &  operator= (const Intersection &other) 
Copy assignment operator from an existing intersection.  
Intersection &  operator= (Intersection &&other) 
Move assignment operator from an existing intersection.  
Implementor interface  
Intersection (const Implementation &impl)  
Intersection (Implementation &&impl)  
Detailed Description
template<class GridImp, class IntersectionImp>
class Dune::Intersection< GridImp, IntersectionImp >
Intersection of a mesh entity of codimension 0 ("element") with a "neighboring" element or with the domain boundary.
 Template Parameters

GridImp Type that is a model of Dune::Grid IntersectionImp Class template that is a model of Dune::Intersection
Overview
Intersections are codimension 1 objects. These intersections are accessed via an Intersection. This allows the implementation of nonmatching grids, as one facet can now consist of several intersections. In a conforming mesh such an intersection corresponds to an entity of codimension 1 but in the general nonconforming case there will be no entity in the mesh that directly corresponds to the intersection. Thus, the Intersection describes these intersections implicitly.
Engine Concept
The Intersection class template wraps an object of type IntersectionImp and forwards all member function calls to corresponding members of this class. In that sense Intersection defines the interface and IntersectionImp supplies the implementation.
Methods neighbor and boundary
The following holds for both the level and the leaf intersection : The intersection 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 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 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:
 Data (like the type of boundary) can be attached to physical boundaries either using global coordinates or the intersection's boundary segment index.
The boundary segment indices form a local, zerobased, contiguous set of integer values. Each boundary segment on the macro level is assigned a unique index from this set, which is inherited by child boundary segments. The size of the boundary segment index set (i.e., the number of boundary indices on the macro level) can be determined through the method Grid::numBoundarySegments.
Note that the boundary segment index is not persistent over dynamic load balancing.  Handling periodic boundaries:
 The Intersection stops at periodic boundaries
 periodic grids are handled in correspondence to parallel grids
 At the periodic boundary one can adjust an overlap or ghostlayer.
 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 stops but neither neighbor() nor boundary() are true.
Geometry of an intersection
The method geometry returns a geometry mapping the intersection as a codim one structure to global coordinates. The methods geometryInInside and geometryInOutside return geometries mapping the intersection into the reference elements of the originating entity and the neighboring entity, respectively. The indexInInside and indexInOutside methods return the codim one subentities which contain the intersection.
Member Typedef Documentation
◆ Implementation
typedef IntersectionImp Dune::Intersection< GridImp, IntersectionImp >::Implementation 
type of underlying implementation
 Warning
 Implementation details may change without prior notification.
Member Enumeration Documentation
◆ anonymous enum
anonymous enum 
◆ anonymous enum
anonymous enum 
Constructor & Destructor Documentation
◆ Intersection() [1/2]

inline 
Copy Constructor from IntersectionImp
◆ Intersection() [2/2]

inline 
Move Constructor from IntersectionImp
Member Function Documentation
◆ boundarySegmentIndex()

inline 
index of the boundary segment within the macro grid
In many applications, special data needs to be attached to the boundary segments of the macro grid (e.g., a function selecting the boundary condition). Usually, this data is inherited by the children of the boundary segment.
In the DUNE framework, data is stored in arrays, addressed by an index, in this case the boundarySegmentIndex. The size of these arrays can be obtained by the Grid::numBoundarySegments method.
The indices returned by this method are consecutive, zero based, and local to the processor. Notice that these indices do not necessarily coincide with the insertion indices of the corresponding boundary segments as provided by the GridFactory.
Referenced by Dune::GridPtr< GridType >::parameters().
◆ centerUnitOuterNormal()

inline 
Return unit outer normal (length == 1)
The returned vector is the normal at the center() of the intersection's geometry. It is scaled to have unit length.
◆ geometry()

inline 
geometrical information about the intersection in global coordinates.
This method returns a Geometry object that provides a mapping from local coordinates of the intersection to global (world) coordinates.
 Note
 If the returned geometry has type none then only a limited set of features is available for the geometry, i.e. center and volume.
 Previously, the geometry was encapsulated in the intersection object and a const reference was returned.
 The returned geometry object is guaranteed to remain valid until the grid is modified (or deleted).
◆ geometryInInside()

inline 
geometrical information about this intersection in local coordinates of the inside() entity.
This method returns a Geometry object that provides a mapping from local coordinates of the intersection to local coordinates of the inside() entity.
 Note
 Previously, the geometry was encapsulated in the intersection object and a const reference was returned.
 The returned geometry object is guaranteed to remain valid until the grid is modified (or deleted).
◆ geometryInOutside()

inline 
geometrical information about this intersection in local coordinates of the outside() entity.
This method returns a Geometry object that provides a mapping from local coordinates of the intersection to local coordinates of the outside() entity.
 Note
 Previously, the geometry was encapsulated in the intersection object and a const reference was returned.
 The returned geometry object is guaranteed to remain valid until the grid is modified (or deleted).
◆ impl() [1/2]

inline 
access to the underlying implementation
 Warning
 Implementation details may change without prior notification.
Referenced by Dune::YaspIntersectionIterator< GridImp >::dereference(), and Dune::YaspIntersectionIterator< GridImp >::increment().
◆ impl() [2/2]

inline 
access to the underlying implementation
 Warning
 Implementation details may change without prior notification.
◆ indexInInside()

inline 
Local index of codim 1 entity in the inside() entity where intersection is contained in.
This method returns the facet number with respect to the generic reference element.
 Note
 This index can be used with the inside entity's
subEntity<1>()
method to obtain the facet.
 Returns
 the index of the inside entity's facet containing this intersection (with respect to the generic reference element)
◆ indexInOutside()

inline 
Local index of codim 1 entity in outside() entity where intersection is contained in.
This method returns the facet number with respect to the generic reference element.
 Note
 This index can be used with the outside entity's
subEntity<1>()
method to obtain the facet.
 Returns
 the index of the outside entity's facet containing this intersection (with respect to the generic reference element)
◆ integrationOuterNormal()

inline 
return unit outer normal scaled with the integration element
The normal is scaled with the integration element of the intersection. This method is redundant but it may be more efficient to use this function rather than computing the integration element via geometry().
The returned vector may depend on local position within the intersection.
◆ outerNormal()

inline 
Return an outer normal (length not necessarily 1)
The returned vector may depend on local position within the intersection.
◆ outside()

inline 
return 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.
◆ unitOuterNormal()

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 files:
 dune/grid/common/grid.hh
 dune/grid/common/intersection.hh