generic implementation of DUNE geometries More...

#include <dune/geometry/genericgeometry/geometry.hh>

Inheritance diagram for Dune::GenericGeometry::BasicGeometry< mydim, Traits >:

Public Types
typedef CoordTraits::ctype	ctype
	Type used for coordinate components. More...

typedef FieldVector< ctype, mydimension >	LocalCoordinate
	Type used for parameter coordinates. More...

typedef FieldVector< ctype, coorddimension >	GlobalCoordinate
	Type used for world coordinates. More...

typedef Mapping::JacobianTransposed	JacobianTransposed
	Type used for Jacobian matrices. More...

typedef Mapping::JacobianInverseTransposed	Jacobian
	Type used for Jacobian matrices. More...

typedef Jacobian	JacobianInverseTransposed

Public Member Functions
	BasicGeometry ()
	Default constructor. More...

template<class CoordVector >
	BasicGeometry (const GeometryType &type, const CoordVector &coords)
	Constructor using a GeometryType and a list of corner coordinates. More...

template<class CoordVector >
	BasicGeometry (const CoordVector &coords)
	Constructor using a vector of corner coordinates and the dimension. More...

template<int fatherdim>
	BasicGeometry (const BasicGeometry< fatherdim, Traits > &father, int i)
	obtain a geometry for a subentity More...

	BasicGeometry (const BasicGeometry &other)
	Copy constructor. More...

	~BasicGeometry ()
	Destructor. More...

const BasicGeometry &	operator= (const BasicGeometry &other)
	Assignment from other BasicGeometry. More...

	operator bool () const
	bool cast More...

GeometryType	type () const
	Return the topological type of this geometry. More...

int	corners () const
	Return the number of corners. More...

GlobalCoordinate	corner (const int i) const
	Return the world coordinates of the i-th corner. More...

GlobalCoordinate	global (const LocalCoordinate &local) const
	Map local to global coordinates. More...

LocalCoordinate	local (const GlobalCoordinate &global) const
	Map global to local coordinates. More...

GlobalCoordinate	center () const
	return center of element More...

bool	affine () const
	Return true if this is an affine geometry. More...

ctype	integrationElement (const LocalCoordinate &local) const
	Return the factor $\|det F\|$ that appears in the integral transformation formula. More...

ctype	volume () const
	Return the volume of the element. More...

const JacobianTransposed &	jacobianTransposed (const LocalCoordinate &local) const
	Compute the transpose of the Jacobian matrix of the transformation from the reference element into the world space. More...

const JacobianInverseTransposed &	jacobianInverseTransposed (const LocalCoordinate &local) const
	Compute the transpose of the inverse Jacobian matrix of the transformation from the reference element into the world space. More...

Static Public Attributes
static const int	mydimension = mydim
	The dimension of the parameter space of this geometry. More...

static const int	coorddimension = Traits :: dimWorld
	The dimension of the world space of this geometry. More...

Protected Types
typedef conditional< hybrid, Hybrid< true >, NonHybrid < false > >::type::MappingFactory	MappingFactory

typedef MappingFactory::Mapping	Mapping

Friends
template<int , class >
class	BasicGeometry
	Be friend with other instantiations of the same class. More...

Detailed Description

template<int mydim, class Traits>
class Dune::GenericGeometry::BasicGeometry< mydim, Traits >

generic implementation of DUNE geometries

This class is provides a generic implementation of a DUNE geometry.

Parameters shared by all codimensions are summarized in one class parameter called Traits. As a default traits class, the class DefaultGeometryTraits can be used. Alternatively, the user can provide hand-written traits classes (which may, if that helps, derive from DefaultGeometryTraits). Such classes have to provide the following fields:

template< My_Template_Parameters >
struct MyGeometryTraits
{
  // ctype is the type used for coordinate coefficients
  typedef DuneCoordTraits< ctype > CoordTraits;
  // Dimension of the space the geometry maps into
  static const int dimWorld = ...;
  //   hybrid   [ true if reference element type is a run-time parameter ]
  static const bool hybrid = ...;
  //   topologyId [ reference element type, only needed if it is not a run-time parameter ]
  // In this example: a dim-dimensional simplex
  // static const unsigned int topologyId = SimplexTopology< dim >::type::id;
  // explained below
  template< class Topology >
  struct Mapping
  {
    typedef CornerMapping< CoordTraits, Topology, dimWorld > type;
  };
  // Caching behavior
  struct Caching
  {
    static const EvaluationType evaluateJacobianTransposed = ComputeOnDemand;
    static const EvaluationType evaluateJacobianInverseTransposed = ComputeOnDemand;
    static const EvaluationType evaluateIntegrationElement = ComputeOnDemand;
  };
};

The structure specifying the reference mapping is Traits::Mapping::type. An example implementation is the GenericGeometry::CornerMapping which defines the simple mapping taking corners of the reference elements to corner of the entity in space.

The central reference mapping specified by Traits::Mapping::type requires a constructor taking a single argument. The GenericGeometry::BasicGeometry has a constructor with one template argument which is passed on to the constructor of the reference mapping. The interface for the this class is GenericGeometry::Mapping.

To increase the efficiency of the geometry implementation, different strategies for the caching of parts of the geometry data is provided. The specifics are given by the structure Traits::Caching. Possible values are:

ComputeOnDemand: use caching if method called using barycenter
PreCompute: use caching in constructor using barycenter

Note

This class cannot be used directly as an implementation of Dune::Geometry. Its template parameter list differs from what is expected there from the engine. One of the following derived classes can be used instead:

Member Typedef Documentation

template<int mydim, class Traits>

typedef CoordTraits :: ctype Dune::GenericGeometry::BasicGeometry< mydim, Traits >::ctype

Type used for coordinate components.

template<int mydim, class Traits>

typedef FieldVector< ctype, coorddimension > Dune::GenericGeometry::BasicGeometry< mydim, Traits >::GlobalCoordinate

Type used for world coordinates.

template<int mydim, class Traits>

typedef Mapping::JacobianInverseTransposed Dune::GenericGeometry::BasicGeometry< mydim, Traits >::Jacobian

Type used for Jacobian matrices.

Note: This is not a FieldMatrix but a proxy type that can be assigned to a FieldMatrix.

template<int mydim, class Traits>

typedef Jacobian Dune::GenericGeometry::BasicGeometry< mydim, Traits >::JacobianInverseTransposed

template<int mydim, class Traits>

typedef Mapping::JacobianTransposed Dune::GenericGeometry::BasicGeometry< mydim, Traits >::JacobianTransposed

Type used for Jacobian matrices.

Note: This is not a FieldMatrix but a proxy type that can be assigned to a FieldMatrix.

template<int mydim, class Traits>

typedef FieldVector< ctype, mydimension > Dune::GenericGeometry::BasicGeometry< mydim, Traits >::LocalCoordinate

Type used for parameter coordinates.

template<int mydim, class Traits>

typedef MappingFactory::Mapping Dune::GenericGeometry::BasicGeometry< mydim, Traits >::Mapping

protected

template<int mydim, class Traits>

typedef conditional< hybrid, Hybrid< true >, NonHybrid< false > >::type::MappingFactory Dune::GenericGeometry::BasicGeometry< mydim, Traits >::MappingFactory

protected

Constructor & Destructor Documentation

template<int mydim, class Traits>

Dune::GenericGeometry::BasicGeometry< mydim, Traits >::BasicGeometry ( )

inline

Default constructor.

template<int mydim, class Traits>

template<class CoordVector >

Dune::GenericGeometry::BasicGeometry< mydim, Traits >::BasicGeometry	(	const GeometryType &	type,
		const CoordVector &	coords
	)

inline

Constructor using a GeometryType and a list of corner coordinates.

template<int mydim, class Traits>

template<class CoordVector >

Dune::GenericGeometry::BasicGeometry< mydim, Traits >::BasicGeometry ( const CoordVector & coords )

inline

Constructor using a vector of corner coordinates and the dimension.

Note: the geometry type is guessed from the number of vertices, thus this will only work up to dim 3

template<int mydim, class Traits>

template<int fatherdim>

Dune::GenericGeometry::BasicGeometry< mydim, Traits >::BasicGeometry	(	const BasicGeometry< fatherdim, Traits > &	father,
		int	i
	)

inline

obtain a geometry for a subentity

Assume that we have a geometry for some entity d-dimensional E. This method can provide a geometry for the i-th subentity of E (of codimension d - mydimension).

Note: This method can be more efficient than just building up the geometry for the subentity. For example, the subgeometry automatically inherits affinity.

Parameters

[in]	father	geometry of entity E
[in]	i	number of the subentity (in generic numbering)

template<int mydim, class Traits>

Dune::GenericGeometry::BasicGeometry< mydim, Traits >::BasicGeometry ( const BasicGeometry< mydim, Traits > & other )

inline

Copy constructor.

template<int mydim, class Traits>

Dune::GenericGeometry::BasicGeometry< mydim, Traits >::~BasicGeometry ( )

inline

Destructor.

Member Function Documentation

template<int mydim, class Traits>

bool Dune::GenericGeometry::BasicGeometry< mydim, Traits >::affine ( ) const

inline

Return true if this is an affine geometry.

template<int mydim, class Traits>

GlobalCoordinate Dune::GenericGeometry::BasicGeometry< mydim, Traits >::center ( ) const

inline

return center of element

template<int mydim, class Traits>

GlobalCoordinate Dune::GenericGeometry::BasicGeometry< mydim, Traits >::corner ( const int i ) const

inline

Return the world coordinates of the i-th corner.

template<int mydim, class Traits>

int Dune::GenericGeometry::BasicGeometry< mydim, Traits >::corners ( ) const

inline

Return the number of corners.

template<int mydim, class Traits>

GlobalCoordinate Dune::GenericGeometry::BasicGeometry< mydim, Traits >::global ( const LocalCoordinate & local ) const

inline

Map local to global coordinates.

template<int mydim, class Traits>

ctype Dune::GenericGeometry::BasicGeometry< mydim, Traits >::integrationElement ( const LocalCoordinate & local ) const

inline

Return the factor $|det F|$ that appears in the integral transformation formula.

template<int mydim, class Traits>

const JacobianInverseTransposed& Dune::GenericGeometry::BasicGeometry< mydim, Traits >::jacobianInverseTransposed ( const LocalCoordinate & local ) const

inline

Compute the transpose of the inverse Jacobian matrix of the transformation from the reference element into the world space.

Referenced by Dune::MockGeometry< ctype, mydim, coorddim >::jacobianInverseTransposed().

template<int mydim, class Traits>

const JacobianTransposed& Dune::GenericGeometry::BasicGeometry< mydim, Traits >::jacobianTransposed ( const LocalCoordinate & local ) const

inline

Compute the transpose of the Jacobian matrix of the transformation from the reference element into the world space.

Referenced by Dune::MockGeometry< ctype, mydim, coorddim >::jacobianTransposed().

template<int mydim, class Traits>

LocalCoordinate Dune::GenericGeometry::BasicGeometry< mydim, Traits >::local ( const GlobalCoordinate & global ) const

inline

Map global to local coordinates.

template<int mydim, class Traits>

Dune::GenericGeometry::BasicGeometry< mydim, Traits >::operator bool ( ) const

inline

bool cast

Like a pointer, a BasicGeometry casts to true if and only if it is properly initialized. If a geometry casts to false, none of the interface methods may be called.

template<int mydim, class Traits>

const BasicGeometry& Dune::GenericGeometry::BasicGeometry< mydim, Traits >::operator= ( const BasicGeometry< mydim, Traits > & other )

inline

Assignment from other BasicGeometry.

template<int mydim, class Traits>

GeometryType Dune::GenericGeometry::BasicGeometry< mydim, Traits >::type ( ) const

inline

Return the topological type of this geometry.

Referenced by Dune::GenericGeometry::BasicGeometry< mydim, GenericGeometry::DefaultGeometryTraits< ctype, coorddim, coorddim > >::BasicGeometry().

template<int mydim, class Traits>

ctype Dune::GenericGeometry::BasicGeometry< mydim, Traits >::volume ( ) const

inline

Return the volume of the element.

Friends And Related Function Documentation

template<int mydim, class Traits>

template<int , class >

friend class BasicGeometry

friend

Be friend with other instantiations of the same class.

Member Data Documentation

template<int mydim, class Traits>

const int Dune::GenericGeometry::BasicGeometry< mydim, Traits >::coorddimension = Traits :: dimWorld

static

The dimension of the world space of this geometry.

template<int mydim, class Traits>

const int Dune::GenericGeometry::BasicGeometry< mydim, Traits >::mydimension = mydim

static

The dimension of the parameter space of this geometry.

The documentation for this class was generated from the following file:

geometry.hh

Public Types

Public Member Functions

Static Public Attributes

Protected Types

Friends

Detailed Description

template<int mydim, class Traits> class Dune::GenericGeometry::BasicGeometry< mydim, Traits >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

template<int mydim, class Traits>
class Dune::GenericGeometry::BasicGeometry< mydim, Traits >