Space of continuous, piecewise linear scalar functions. More...

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

Inheritance diagram for Bempp::PiecewiseLinearScalarSpace< BasisFunctionType >:

Public Types
typedef Space < BasisFunctionType > ::CoordinateType	CoordinateType

typedef Space < BasisFunctionType > ::ComplexType	ComplexType

Public Types inherited from Bempp::ScalarSpace< BasisFunctionType >
typedef Base::CoordinateType	CoordinateType

typedef Base::CollectionOfShapesetTransformations	CollectionOfShapesetTransformations

typedef Base::CollectionOfBasisTransformations	CollectionOfBasisTransformations

Public Types inherited from Bempp::Space< BasisFunctionType >
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
	PiecewiseLinearScalarSpace (const shared_ptr< const Grid > &grid)

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

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

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

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

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

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...

Public Member Functions inherited from Bempp::ScalarSpace< BasisFunctionType >
	ScalarSpace (const shared_ptr< const Grid > &grid)

	ScalarSpace (const ScalarSpace &other)
	Copy constructor.

ScalarSpace &	operator= (const ScalarSpace &other)
	Assignment operator.

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

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

Public Member Functions inherited from Bempp::Space< BasisFunctionType >
	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.

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	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...

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.

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 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.

Additional Inherited Members
Related Functions inherited from Bempp::Space< BasisFunctionType >
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::PiecewiseLinearScalarSpace< BasisFunctionType >

Space of continuous, piecewise linear scalar functions.

Member Function Documentation

template<typename BasisFunctionType >

int Bempp::PiecewiseLinearScalarSpace< BasisFunctionType >::codomainDimension ( ) const

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).

Implements Bempp::Space< BasisFunctionType >.

Reimplemented in Bempp::PiecewiseLinearContinuousScalarSpaceBarycentric< BasisFunctionType >.

template<typename BasisFunctionType >

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

virtual

Return the variant of element element.

Possible return values:

2: one-dimensional segment,
3: triangular element,
4: quadrilateral element.

Implements Bempp::Space< BasisFunctionType >.

Reimplemented in Bempp::PiecewiseLinearContinuousScalarSpaceBarycentric< BasisFunctionType >.

References Bempp::Entity< 0 >::type().

template<typename BasisFunctionType >

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

virtual

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 from Bempp::Space< BasisFunctionType >.

template<typename BasisFunctionType >

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

virtual

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 from Bempp::Space< BasisFunctionType >.

template<typename BasisFunctionType >

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

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.

Implements Bempp::Space< BasisFunctionType >.

Reimplemented in Bempp::PiecewiseLinearContinuousScalarSpaceBarycentric< BasisFunctionType >.

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

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

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

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

Member Function Documentation

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