Function space. More...

#include </home/wojtek/Projects/BEM/bempp-sven/bempp/lib/space/space.hpp>

Inheritance diagram for Bempp::Space< BasisFunctionType >:

Public Types
typedef Fiber::ScalarTraits < BasisFunctionType > ::RealType	CoordinateType
	Type used to represent coordinates.

typedef Fiber::ScalarTraits < BasisFunctionType > ::ComplexType	ComplexType
	Equivalent to std::complex<CoordinateType>.

typedef Fiber::CollectionOfShapesetTransformations < CoordinateType >	CollectionOfShapesetTransformations
	Appropriate instantiation of Fiber::CollectionOfShapesetTransformations.

typedef Fiber::CollectionOfBasisTransformations < CoordinateType >	CollectionOfBasisTransformations
	Appropriate instantiation of Fiber::CollectionOfBasisTransformations.

Public Member Functions
	Space (const shared_ptr< const Grid > &grid)
	Constructor. More...

	Space (const Space< BasisFunctionType > &other)
	Copy Constructor.

virtual	~Space ()
	Destructor.

Space< BasisFunctionType > &	operator= (const Space< BasisFunctionType > &other)
	Assignment operator.

virtual void	setElementVariant (const Entity< 0 > &element, ElementVariant variant)=0
	Set the variant of element `element` to `variant`. More...

virtual ElementVariant	elementVariant (const Entity< 0 > &element) const =0
	Return current variant of element `element`. More...

shared_ptr< GeometryFactory >	elementGeometryFactory () const
	Return the GeometryFactory associated with the mesh.

BEMPP_DEPRECATED void	assignDofs ()
	Assign global degrees of freedom to local degrees of freedom. More...

BEMPP_DEPRECATED bool	dofsAssigned () const
	True if global degrees of freedom have been already assigned to local degrees of freedom, false otherwise. More...

virtual size_t	flatLocalDofCount () const =0
	Total number of local degrees of freedom on all elements.

virtual size_t	globalDofCount () const =0
	Number of global degrees of freedom.

virtual void	getGlobalDofs (const Entity< 0 > &element, std::vector< GlobalDofIndex > &dofs) const
	Map local degrees of freedom residing on an element to global degrees of freedom. More...

virtual void	getGlobalDofs (const Entity< 0 > &element, std::vector< GlobalDofIndex > &dofs, std::vector< BasisFunctionType > &localDofWeights) const
	Map local degrees of freedom residing on an element to global degrees of freedom. More...

virtual bool	gridIsIdentical (const Space< BasisFunctionType > &other) const
	Return true if both spaces act on the same grid.

virtual SpaceIdentifier	spaceIdentifier () const =0
	Return the identifier of the space.

virtual bool	spaceIsCompatible (const Space< BasisFunctionType > &other) const =0
	Return true if `other` is compatible to this space, i.e. the global dofs of the two spaces agree with each other.

virtual void	global2localDofs (const std::vector< GlobalDofIndex > &globalDofs, std::vector< std::vector< LocalDof > > &localDofs) const
	Map global degrees of freedom to local degrees of freedom. More...

virtual void	global2localDofs (const std::vector< GlobalDofIndex > &globalDofs, std::vector< std::vector< LocalDof > > &localDofs, std::vector< std::vector< BasisFunctionType > > &localDofWeights) const

virtual void	flatLocal2localDofs (const std::vector< FlatLocalDofIndex > &flatLocalDofs, std::vector< LocalDof > &localDofs) const =0
	Map flat indices of local degrees of freedom to local degrees of freedom. More...

virtual void	getGlobalDofInterpolationPoints (arma::Mat< CoordinateType > &points) const
	Retrieve the interpolation points of the global degrees of freedom. More...

virtual void	getNormalsAtGlobalDofInterpolationPoints (arma::Mat< CoordinateType > &normals) const
	Retrieve the unit vectors normal to the grid at the interpolation points of the global degrees of freedom. More...

virtual void	getGlobalDofInterpolationDirections (arma::Mat< CoordinateType > &directions) const
	Retrieve the interpolation directions of the global degrees of freedom. More...

virtual void	getGlobalDofBoundingBoxes (std::vector< BoundingBox< CoordinateType > > &boundingBoxes) const
	Retrieve bounding boxes of global degrees of freedom. More...

virtual void	getFlatLocalDofBoundingBoxes (std::vector< BoundingBox< CoordinateType > > &boundingBoxes) const
	Retrieve bounding boxes of local degrees of freedom ordered by their flat index. More...

virtual void	getGlobalDofPositions (std::vector< Point3D< CoordinateType > > &positions) const =0
	Retrieve the reference positions of global degrees of freedom. More...

virtual void	getFlatLocalDofPositions (std::vector< Point3D< CoordinateType > > &positions) const =0
	Retrieve the reference positions of local degrees of freedom ordered by their flat index. More...

virtual void	getGlobalDofNormals (std::vector< Point3D< CoordinateType > > &normals) const
	Retrieve the unit vectors normal to the grid at the positions of global degrees of freedom. More...

virtual void	getFlatLocalDofNormals (std::vector< Point3D< CoordinateType > > &normals) const
	Retrieve the unit vectors normal to the grid at the positions of global degrees of freedom. More...

virtual BEMPP_DEPRECATED void	dumpClusterIds (const char *fileName, const std::vector< unsigned int > &clusterIdsOfGlobalDofs) const =0
	Write a VTK file showing the distribution of global or flat local degrees of freedom into clusters. More...

virtual void	dumpClusterIdsEx (const char *fileName, const std::vector< unsigned int > &clusterIdsOfGlobalDofs, DofType dofType) const
	Write a VTK file showing the distribution of global or flat local degrees of freedom into clusters. More...

Attributes
virtual shared_ptr< const Space< BasisFunctionType > >	discontinuousSpace (const shared_ptr< const Space< BasisFunctionType > > &self) const =0
	Return a shared pointer to an appropriate counterpart to this space, with basis functions extending only over single elements. More...

virtual bool	isDiscontinuous () const =0
	Return true if each basis function of this space extends over only a single element, false otherwise.

virtual bool	isBarycentric () const =0
	Return `true` if space is based on a barycentric refinement.

virtual int	domainDimension () const =0
	Dimension of the grid on which functions from this space are defined.

virtual int	codomainDimension () const =0
	Dimension of the codomain of the functions. More...

shared_ptr< const Grid >	grid () const
	Shared pointer to the grid on which the functions from this space are defined.

virtual BEMPP_DEPRECATED const Fiber::Basis < BasisFunctionType > &	basis (const Entity< 0 > &element) const
	Reference to the shapeset attached to the specified element. More...

virtual const Fiber::Shapeset < BasisFunctionType > &	shapeset (const Entity< 0 > &element) const
	Reference to the shapeset attached to the specified element.

virtual BEMPP_DEPRECATED const CollectionOfBasisTransformations &	shapeFunctionValue () const
	Transformation mapping shape functions to basis functions. More...

virtual shared_ptr< const Space< BasisFunctionType > >	barycentricSpace (const shared_ptr< const Space< BasisFunctionType > > &self) const
	Return an equivalent space (in terms of global Dofs), but defined using local dofs on the barycentrically refined grid.

unsigned int	level () const
	Return the grid level of the current space.

int	gridDimension () const
	Return the underlying grid dimension.

int	worldDimension () const
	Return the underlying world dimension.

const GridView &	gridView () const
	Return the grid view of the current space.

virtual const CollectionOfShapesetTransformations &	basisFunctionValue () const
	Transformation mapping shape functions to basis functions. More...

Related Functions
(Note that these are not member functions.)
template<typename BasisFunctionType >
void	getAllShapesets (const Space< BasisFunctionType > &space, std::vector< const Fiber::Shapeset< BasisFunctionType > * > &shapesets)
	Get pointers to Basis objects corresponding to all elements of the grid on which a function space is defined. More...

template<typename BasisFunctionType >
void BEMPP_DEPRECATED	getAllBases (const Space< BasisFunctionType > &space, std::vector< const Fiber::Basis< BasisFunctionType > * > &bases)
	Get pointers to Basis objects corresponding to all elements of the grid on which a function space is defined. More...

template<typename BasisFunctionType >
int	maximumShapesetOrder (const Space< BasisFunctionType > &space)
	Return the maximum polynomial order of the shapesets defined by `space` on the elements of the space's underlying grid.

Detailed Description

template<typename BasisFunctionType>
class Bempp::Space< BasisFunctionType >

Function space.

This class represents a space of functions defined on a grid. The space is spanned by a finite number of scalar- or vector-valued basis functions. The template parameter BasisFunctionType is the type of the values of (the components of) these basis functions, and can be set to float, double, std::complex<float> or std::complex<double>.

The basis functions of a space, also known as global degrees of freedom (DOFs), can have support extending over multiple elements of the grid. They are, however, composed of one or more local basis functions (local degrees of freedom), each of which resides on a single element. The mapping of local to global degrees of freedom is triggered by calling the function assignDofs(). Many other member functions of Space may only be invoked after assignDofs() has beeen called.

Constructor & Destructor Documentation

template<typename BasisFunctionType >

Bempp::Space< BasisFunctionType >::Space ( const shared_ptr< const Grid > & grid )

explicit

Constructor.

Parameters

[in]	grid	Grid on which functions from this space should be defined.
[in]	level	Level of the grid on which the space should be defined.

An exception is thrown if grid is a null pointer.

Member Function Documentation

template<typename BasisFunctionType >

void Bempp::Space< BasisFunctionType >::assignDofs ( )

Assign global degrees of freedom to local degrees of freedom.

Deprecated:: It is not necessary any more to call this function, since DOF assignment is now done automatically in the constructor.

template<typename BasisFunctionType>

virtual BEMPP_DEPRECATED const Fiber::Basis<BasisFunctionType>& Bempp::Space< BasisFunctionType >::basis ( const Entity< 0 > & element ) const

inlinevirtual

Reference to the shapeset attached to the specified element.

Deprecated:: This function is deprecated and will be removed in a future release of BEM++. Use shapeset() instead.

References Bempp::Space< BasisFunctionType >::shapeset().

template<typename BasisFunctionType>

virtual const CollectionOfShapesetTransformations& Bempp::Space< BasisFunctionType >::basisFunctionValue ( ) const

inlinevirtual

Transformation mapping shape functions to basis functions.

This function returns a CollectionOfShapesetTransformations object consisting of a single transformation that maps values of shape functions defined on a reference element to those of basis functions defined on a particular element of the grid.

This transformation is the identity for spaces of scalar-valued functions, but may be more complicated for spaces of vector-valued functions, e.g. $H(\mathrm{curl})$ .

Reimplemented in Bempp::RaviartThomas0VectorSpace< BasisFunctionType >, and Bempp::ScalarSpace< BasisFunctionType >.

Referenced by Bempp::Space< BasisFunctionType >::shapeFunctionValue().

template<typename BasisFunctionType>

virtual int Bempp::Space< BasisFunctionType >::codomainDimension ( ) const

pure virtual

Dimension of the codomain of the functions.

In other words, number of components of the values of the functions. (E.g. H1 space -> 1, H(curl) space on a 2D surface -> 2).

template<typename BasisFunctionType>

virtual shared_ptr<const Space<BasisFunctionType> > Bempp::Space< BasisFunctionType >::discontinuousSpace ( const shared_ptr< const Space< BasisFunctionType > > & self ) const

pure virtual

Return a shared pointer to an appropriate counterpart to this space, with basis functions extending only over single elements.

Let $S = span_{n=1}^N f_n$ denote the function space represented by this object, with $f_n$ its basis functions.

If the functions $f_n$ are scalar-valued, discontinuousSpace() should return a shared pointer to an object representing a space $T = span_{m=1}^M g_m$ with basis functions $g_m$ such that:

.
The support of each basis function is a single element.
Each function has a unique representation in the basis of $\{g_m\}_{m=1}^M$ and each function contributes to exactly one function .

If the values of functions $f_n$ are vectors with $d$ components, discontinuousSpace() should return a shared pointer to an object representing a space $T = span_{m=1}^M g_m$ of with scalar-valued basis functions $g_m$ such that

For each $i = 1, 2, \cdots, d$ it holds that $T \supset span_{n=1}^N (f_n)_i$ , where denotes the th component of .
The support of each basis function is a single element.

Parameters

[in] self This must be a shared pointer to *this.

template<typename BasisFunctionType >

bool Bempp::Space< BasisFunctionType >::dofsAssigned ( ) const

True if global degrees of freedom have been already assigned to local degrees of freedom, false otherwise.

Deprecated:: Since DOF assignment is now done automatically in the constructor, this function always returns true.

template<typename BasisFunctionType>

virtual BEMPP_DEPRECATED void Bempp::Space< BasisFunctionType >::dumpClusterIds	(	const char *	fileName,
		const std::vector< unsigned int > &	clusterIdsOfGlobalDofs
	)		const

pure virtual

Write a VTK file showing the distribution of global or flat local degrees of freedom into clusters.

Parameters

[in]	fileName	Name of the VTK file to be created (without extension).
[in]	clusterIdsOfGlobalDofs	Vector whose ith element contains the identifier of the cluster to which ith global degree of freedom has been assigned.

This function generates a VTK file containing a single data series mapping the ``positions'' (see getGlobalDofPositions()) of global degrees of freedom to the identifiers of the clusters to which these degrees of freedom have been assigned. It is intended for debugging clustering algorithms.

Deprecated:: This function is deprecated. Use dumpClusterIdEx() instead, which supports dumping of cluster identifiers of flat local degrees of freedom in addition to the global ones.

template<typename BasisFunctionType >

void Bempp::Space< BasisFunctionType >::dumpClusterIdsEx	(	const char *	fileName,
		const std::vector< unsigned int > &	clusterIdsOfGlobalDofs,
		DofType	dofType
	)		const

virtual

Write a VTK file showing the distribution of global or flat local degrees of freedom into clusters.

Parameters

[in]	fileName	Name of the VTK file to be created (without extension).
[in]	clusterIdsOfGlobalDofs	Vector whose ith element contains the identifier of the cluster to which ith degree of freedom has been assigned.
[in]	dofType	Type of degrees of freedom (GLOBAL_DOFS or FLAT_LOCAL_DOFS).

This function generates a VTK file containing a single data series mapping the ``positions'' (see getGlobalDofPositions() and getFlatLocalDofPositions()) of the chosen type of degrees of freedom to the identifiers of the clusters to which these degrees of freedom have been assigned. It is intended for debugging clustering algorithms.

This function supersedes dumpClusterIds().

template<typename BasisFunctionType>

virtual ElementVariant Bempp::Space< BasisFunctionType >::elementVariant ( const Entity< 0 > & element ) const

pure virtual

Return current variant of element element.

See the documentation of setElementVariant() for more information.

template<typename BasisFunctionType>

virtual void Bempp::Space< BasisFunctionType >::flatLocal2localDofs	(	const std::vector< FlatLocalDofIndex > &	flatLocalDofs,
		std::vector< LocalDof > &	localDofs
	)		const

pure virtual

Map flat indices of local degrees of freedom to local degrees of freedom.

Parameters

[in]	flatLocalDofs	Vector containing flat indices of local degrees of freedom.
[out]	localDofs	Vector whose `i`th element is the local degree of freedom with flat index given by `flatLocalDofs[i]`.

template<typename BasisFunctionType>

virtual void Bempp::Space< BasisFunctionType >::getFlatLocalDofBoundingBoxes ( std::vector< BoundingBox< CoordinateType > > & boundingBoxes ) const

inlinevirtual

Retrieve bounding boxes of local degrees of freedom ordered by their flat index.

Parameters

[out] boundingBoxes Vector whose ith element contains the bounding box the local degree of freedom with flat index i.

Note: This function is intended as a helper for clustering algorithms used in matrix compression algorithms such as adaptive cross approximation.

template<typename BasisFunctionType>

virtual void Bempp::Space< BasisFunctionType >::getFlatLocalDofNormals ( std::vector< Point3D< CoordinateType > > & normals ) const

inlinevirtual

Retrieve the unit vectors normal to the grid at the positions of global degrees of freedom.

Parameters

[out] normals Vector whose ith element contains the unit vector normal to the grid at the reference position of the local degree of freedom with flat index i.

template<typename BasisFunctionType>

virtual void Bempp::Space< BasisFunctionType >::getFlatLocalDofPositions ( std::vector< Point3D< CoordinateType > > & positions ) const

pure virtual

Retrieve the reference positions of local degrees of freedom ordered by their flat index.

Parameters

[out] positions Vector whose ith element contains the coordinates of the point taken to be the ``reference position'' (in some sense) of the local degree of freedom with flat index i.

Note: This function is intended as a helper for clustering algorithms used in matrix compression algorithms such as adaptive cross approximation.

template<typename BasisFunctionType>

virtual void Bempp::Space< BasisFunctionType >::getGlobalDofBoundingBoxes ( std::vector< BoundingBox< CoordinateType > > & boundingBoxes ) const

inlinevirtual

Retrieve bounding boxes of global degrees of freedom.

Parameters

[out] boundingBoxes Vector whose ith element contains the bounding box of ith global degree of freedom.

Note: This function is intended as a helper for clustering algorithms used in matrix compression algorithms such as adaptive cross approximation.

template<typename BasisFunctionType>

virtual void Bempp::Space< BasisFunctionType >::getGlobalDofInterpolationDirections ( arma::Mat< CoordinateType > & directions ) const

inlinevirtual

Retrieve the interpolation directions of the global degrees of freedom.

This function fills the 2D array points whose (i, j)th element contains the ith component of the vector $d_j$ defined in the documentation of getGlobalDofInterpolationPoints().

Reimplemented in Bempp::ScalarSpace< BasisFunctionType >.

template<typename BasisFunctionType>

virtual void Bempp::Space< BasisFunctionType >::getGlobalDofInterpolationPoints ( arma::Mat< CoordinateType > & points ) const

inlinevirtual

Retrieve the interpolation points of the global degrees of freedom.

This function, along with getNormalsAtGlobalDofInterpolationPoints() and getGlobalDofInterpolationDirections(), can be used in the interpolation of functions in finite-dimensional function spaces represented with classes derived from Space. Let $V$ be a function space defined on grid $\Gamma$ with a basis $(f_i)_{i=1}^N$ of functions $f_i : \Gamma \to \mathbb{R}^n$ (or $\mathbb{C}^n$ . We say that this basis is interpolatory if there exist points $x_j \in \Gamma$ and $n$ -dimensional vectors $d_j$ ( $j = 1, 2, \dots, N$ such that

$f_i(x_j) \cdot d_j = \begin{cases} 1 &\text{for} i = j,\\ 0 &\text{otherwise}. \end{cases}$

For any appropriate function $u$ defined on $Gamma$ the numbers $u(x_i) \cdot d_i$ can then be taken as the expansion coefficients in the basis $(f_i)_{i=1}^N$ of its interpolation. ("Appropriate" means that if, for example, the space $V$ is a space of functions tangential to the grid, then $u$ should also be tangential to the grid.)

This function fills the 2D array points whose (i, j)th element contains the ith coordinate of the interpolation point $x_j$ .

Reimplemented in Bempp::PiecewiseConstantDiscontinuousScalarSpaceBarycentric< BasisFunctionType >, Bempp::PiecewiseConstantScalarSpaceBarycentric< BasisFunctionType >, Bempp::PiecewiseConstantScalarSpace< BasisFunctionType >, and Bempp::PiecewiseLinearScalarSpace< BasisFunctionType >.

template<typename BasisFunctionType>

virtual void Bempp::Space< BasisFunctionType >::getGlobalDofNormals ( std::vector< Point3D< CoordinateType > > & normals ) const

inlinevirtual

Retrieve the unit vectors normal to the grid at the positions of global degrees of freedom.

Parameters

[out] normals Vector whose ith element contains the unit vector normal to the grid at the reference position of ith global degree of freedom.

template<typename BasisFunctionType>

virtual void Bempp::Space< BasisFunctionType >::getGlobalDofPositions ( std::vector< Point3D< CoordinateType > > & positions ) const

pure virtual

Retrieve the reference positions of global degrees of freedom.

Parameters

[out] positions Vector whose ith element contains the coordinates of the point taken to be the "reference position" (in some sense) of ith global degree of freedom.

Note: This function is intended as a helper for clustering algorithms used in matrix compression algorithms such as adaptive cross approximation.

template<typename BasisFunctionType >

void Bempp::Space< BasisFunctionType >::getGlobalDofs	(	const Entity< 0 > &	element,
		std::vector< GlobalDofIndex > &	dofs
	)		const

virtual

Map local degrees of freedom residing on an element to global degrees of freedom.

Parameters

[in]	element	An element of the grid grid().
[out]	dofs	Vector whose ith element is the index of the global degrees of freedom to which the ith local degree of freedom residing on `element` contributes. A negative number means that a given local degree of freedom does not contribute to any global one.

Note: This function is deprecated. Use the other overload taking the additional output parameter localDofWeights.

template<typename BasisFunctionType>

void Bempp::Space< BasisFunctionType >::getGlobalDofs	(	const Entity< 0 > &	element,
		std::vector< GlobalDofIndex > &	dofs,
		std::vector< BasisFunctionType > &	localDofWeights
	)		const

virtual

Map local degrees of freedom residing on an element to global degrees of freedom.

Parameters

[in]	element	An element of the grid grid().
[out]	dofs	Vector whose ith element is the index of the global degrees of freedom to which the ith local degree of freedom residing on `element` contributes. A negative number means that a given local degree of freedom does not contribute to any global one.
[out]	localDofWeights	Vector whose ith element is the weight with which the ith local degree of freedom residing on `element` contributes to "its" global degree of freedom.

Reimplemented in Bempp::RaviartThomas0VectorSpace< BasisFunctionType >.

template<typename BasisFunctionType>

virtual void Bempp::Space< BasisFunctionType >::getNormalsAtGlobalDofInterpolationPoints ( arma::Mat< CoordinateType > & normals ) const

inlinevirtual

Retrieve the unit vectors normal to the grid at the interpolation points of the global degrees of freedom.

This function fills the 2D array normals whose (i, j)th element contains the ith component of the unit vector normal to the grid at the interpolation point $x_j$ defined in the documentation of getGlobalDofInterpolationPoints().

Reimplemented in Bempp::PiecewiseConstantDiscontinuousScalarSpaceBarycentric< BasisFunctionType >, Bempp::PiecewiseConstantScalarSpaceBarycentric< BasisFunctionType >, Bempp::PiecewiseConstantScalarSpace< BasisFunctionType >, and Bempp::PiecewiseLinearScalarSpace< BasisFunctionType >.

template<typename BasisFunctionType >

void Bempp::Space< BasisFunctionType >::global2localDofs	(	const std::vector< GlobalDofIndex > &	globalDofs,
		std::vector< std::vector< LocalDof > > &	localDofs
	)		const

virtual

Map global degrees of freedom to local degrees of freedom.

Parameters

[in]	globalDofs	Vector containing indices of global degrees of freedom.
[out]	localDofs	Vector whose `i`th element is the vector containing all the local degrees of freedom that are mapped to the global degree of freedom `globalDofs[i]`.

Note that a local degree of freedom (LocalDof) is a combination of an EntityIndex and LocalDofIndex, as explained in its documentation.

template<typename BasisFunctionType>

virtual void Bempp::Space< BasisFunctionType >::setElementVariant	(	const Entity< 0 > &	element,
		ElementVariant	variant
	)

pure virtual

Set the variant of element element to variant.

The element variant determines the set of basis functions defined on the element (e.g. maximum polynomial order). Different subclasses of Space interpret the variant argument in different ways; for more information, see the documentation of these subclasses.

Note: Calling this function only makes sense for subclasses implementing adaptive function spaces. Currently there are no such subclasses.

template<typename BasisFunctionType>

virtual BEMPP_DEPRECATED const CollectionOfBasisTransformations& Bempp::Space< BasisFunctionType >::shapeFunctionValue ( ) const

inlinevirtual

Transformation mapping shape functions to basis functions.

Deprecated:: This function is deprecated and will be removed in a future release of BEM++. Use basisFunctionValue() instead.

References Bempp::Space< BasisFunctionType >::basisFunctionValue().

Friends And Related Function Documentation

template<typename BasisFunctionType >

void BEMPP_DEPRECATED getAllBases	(	const Space< BasisFunctionType > &	space,
		std::vector< const Fiber::Basis< BasisFunctionType > * > &	bases
	)

Deprecated:: This function is deprecated. Use getAllShapesets() instead.

template<typename BasisFunctionType >

void getAllShapesets	(	const Space< BasisFunctionType > &	space,
		std::vector< const Fiber::Shapeset< BasisFunctionType > * > &	shapesets
	)

Parameters

[in]	space	A Space object.
[out]	bases	Vector whose ith element is a pointer to the Basis object representing the local degrees of freedom residing on the ith element of the grid on which `space` is defined.

An exception is raised if space.assignDofs() has not been called prior to calling this function.

References Bempp::Mapper::entityIndex(), Bempp::Space< BasisFunctionType >::grid(), and Bempp::Space< BasisFunctionType >::shapeset().

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

/home/wojtek/Projects/BEM/bempp-sven/bempp/lib/assembly/assembled_potential_operator.hpp
/home/wojtek/Projects/BEM/bempp-sven/bempp/lib/space/space.hpp
/home/wojtek/Projects/BEM/bempp-sven/bempp/lib/space/space.cpp

Public Types

Public Member Functions

Related Functions

Detailed Description

template<typename BasisFunctionType> class Bempp::Space< BasisFunctionType >

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

template<typename BasisFunctionType>
class Bempp::Space< BasisFunctionType >