Function defined on a grid. More...

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

Public Types
enum	DataType { COEFFICIENTS, PROJECTIONS }

enum	ConstructionMode { APPROXIMATE, INTERPOLATE }

typedef Fiber::ScalarTraits < ResultType >::RealType	CoordinateType

typedef Fiber::ScalarTraits < ResultType >::RealType	MagnitudeType

Public Member Functions
	GridFunction ()
	Constructor. More...

	GridFunction (const shared_ptr< const Context< BasisFunctionType, ResultType > > &context, const shared_ptr< const Space< BasisFunctionType > > &space, const arma::Col< ResultType > &coefficients)

	GridFunction (const shared_ptr< const Context< BasisFunctionType, ResultType > > &context, const shared_ptr< const Space< BasisFunctionType > > &space, const shared_ptr< const Space< BasisFunctionType > > &dualSpace, const arma::Col< ResultType > &projections)

	GridFunction (const shared_ptr< const Context< BasisFunctionType, ResultType > > &context, const shared_ptr< const Space< BasisFunctionType > > &space, const shared_ptr< const Space< BasisFunctionType > > &dualSpace, const Function< ResultType > &function, ConstructionMode mode=APPROXIMATE)
	Constructor. More...

BEMPP_DEPRECATED	GridFunction (const shared_ptr< const Context< BasisFunctionType, ResultType > > &context, const shared_ptr< const Space< BasisFunctionType > > &space, const shared_ptr< const Space< BasisFunctionType > > &dualSpace, const arma::Col< ResultType > &data, DataType dataType)
	Constructor. More...

BEMPP_DEPRECATED	GridFunction (const shared_ptr< const Context< BasisFunctionType, ResultType > > &context, const shared_ptr< const Space< BasisFunctionType > > &space, const shared_ptr< const Space< BasisFunctionType > > &dualSpace, const arma::Col< ResultType > &coefficients, const arma::Col< ResultType > &projections)
	Constructor. More...

bool	isInitialized () const
	Return whether this function has been properly initialized.

bool	wasInitializedFromCoefficients () const
	Returns `true` if the GridFunction was initialized with a list of coefficients and `false` if it was initialized with a list of projections. More...

shared_ptr< const Grid >	grid () const
	Grid on which this function is defined. More...

shared_ptr< const Space < BasisFunctionType > >	space () const
	Space in which this function is expanded.

shared_ptr< const Space < BasisFunctionType > >	dualSpace () const
	Space dual to the space in which this function is expanded. More...

shared_ptr< const Context < BasisFunctionType, ResultType > >	context () const
	Assembly context used to retrieve the strategy for evaluating any necessary integrals.

int	componentCount () const
	Number of components of this function. More...

const arma::Col< ResultType > &	coefficients () const
	Vector of expansion coefficients of this function in the basis of its expansion space. More...

arma::Col< ResultType >	projections (const shared_ptr< const Space< BasisFunctionType > > &dualSpace_) const
	Vector of scalar products of this function with the basis functions of `dualSpace`. More...

void	setCoefficients (const arma::Col< ResultType > &coeffs)
	Reset the expansion coefficients of this function in the basis of its primal space. More...

void	setProjections (const shared_ptr< const Space< BasisFunctionType > > &dualSpace_, const arma::Col< ResultType > &projects)
	Reinitialize the function by specifying the vector of its scalar products with the basis functions of `dualSpace`. More...

MagnitudeType	L2Norm () const
	Return the -norm of the grid function. More...

const Fiber::Shapeset < BasisFunctionType > &	shapeset (const Entity< 0 > &element) const
	Return the shapeset associated with the given element. More...

const BEMPP_DEPRECATED Fiber::Basis < BasisFunctionType > &	basis (const Entity< 0 > &element) const
	Return the shapeset associated with the given element. More...

void	getLocalCoefficients (const Entity< 0 > &element, std::vector< ResultType > &coeffs) const
	Retrieve the expansion coefficients of this function on a single element. More...

void	evaluateAtSpecialPoints (VtkWriter::DataType dataType, arma::Mat< ResultType > &result_) const
	Evaluate function at either vertices or barycentres. More...

void	evaluateAtSpecialPoints (VtkWriter::DataType dataType, arma::Mat< CoordinateType > &points, arma::Mat< ResultType > &values) const

void	evaluate (const Entity< 0 > &element, const arma::Mat< CoordinateType > &local, arma::Mat< ResultType > &values) const
	Evaluate function at specific points lying on a given element. More...

BEMPP_DEPRECATED arma::Col < ResultType >	projections (const Space< BasisFunctionType > &dualSpace_) const
	Vector of scalar products of this function with the basis functions of `dualSpace`. More...

BEMPP_DEPRECATED arma::Col < ResultType >	projections () const
	Vector of scalar products of this function with the basis functions of its dual space. More...

BEMPP_DEPRECATED void	setProjections (const Space< BasisFunctionType > &dualSpace_, const arma::Col< ResultType > &projects)
	Reinitialize the function by specifying the vector of its scalar products with the basis functions of `dualSpace`. More...

BEMPP_DEPRECATED void	setProjections (const arma::Col< ResultType > &projects)
	Reset the vector of scalar products of this function with the basis functions of its dual space. More...

BEMPP_DEPRECATED void	exportToVtk (VtkWriter::DataType dataType, const char dataLabel, const char fileNamesBase, const char *filesPath=0, VtkWriter::OutputType type=VtkWriter::ASCII) const
	Export this function to a VTK file. More...

BEMPP_DEPRECATED void	exportToGmsh (const char dataLabel, const char fileName) const
	Export this function to a Gmsh (.msh) file. More...

Private Member Functions
void	initializeFromCoefficients (const shared_ptr< const Context< BasisFunctionType, ResultType > > &context, const shared_ptr< const Space< BasisFunctionType > > &space, const arma::Col< ResultType > &coefficients)

void	initializeFromProjections (const shared_ptr< const Context< BasisFunctionType, ResultType > > &context, const shared_ptr< const Space< BasisFunctionType > > &space, const shared_ptr< const Space< BasisFunctionType > > &dualSpace, const arma::Col< ResultType > &projections)

void	updateProjectionsFromCoefficients (const shared_ptr< const Space< BasisFunctionType > > &dualSpace_) const

void	updateCoefficientsFromProjections () const

Private Attributes
shared_ptr< const Context < BasisFunctionType, ResultType > >	m_context

shared_ptr< const Space < BasisFunctionType > >	m_space

shared_ptr< const Space < BasisFunctionType > >	m_dualSpace

shared_ptr< const arma::Col < ResultType > >	m_coefficients

shared_ptr< const arma::Col < ResultType > >	m_projections

bool	m_wasInitializedFromCoefficients

Related Functions
(Note that these are not member functions.)
template<typename BasisFunctionType , typename ResultType >
GridFunction < BasisFunctionType, ResultType >	operator+ (const GridFunction< BasisFunctionType, ResultType > &g)
	Return a copy of the passed function `g`.

template<typename BasisFunctionType , typename ResultType >
GridFunction < BasisFunctionType, ResultType >	operator- (const GridFunction< BasisFunctionType, ResultType > &g)
	Return the grid function representing the function `g` multipled by -1. More...

template<typename BasisFunctionType , typename ResultType >
GridFunction < BasisFunctionType, ResultType >	operator+ (const GridFunction< BasisFunctionType, ResultType > &g1, const GridFunction< BasisFunctionType, ResultType > &g2)
	Return a grid function representing the sum of the operands. More...

template<typename BasisFunctionType , typename ResultType >
GridFunction < BasisFunctionType, ResultType >	operator- (const GridFunction< BasisFunctionType, ResultType > &g1, const GridFunction< BasisFunctionType, ResultType > &g2)
	Return a grid function representing the difference of the operands. More...

template<typename BasisFunctionType , typename ResultType , typename ScalarType >
GridFunction < BasisFunctionType, ResultType >	operator* (const GridFunction< BasisFunctionType, ResultType > &g, const ScalarType &scalar)
	Return the grid function representing the function `g` multiplied by `scalar`. More...

template<typename BasisFunctionType , typename ResultType , typename ScalarType >
boost::enable_if< typename boost::mpl::has_key < boost::mpl::set< float, double, std::complex< float > , std::complex< double > >, ScalarType >, GridFunction < BasisFunctionType, ResultType > >::type	operator* (const ScalarType &scalar, const GridFunction< BasisFunctionType, ResultType > &g)
	Return the grid function representing the function `g` multiplied by `scalar`. More...

template<typename BasisFunctionType , typename ResultType , typename ScalarType >
GridFunction < BasisFunctionType, ResultType >	operator/ (const GridFunction< BasisFunctionType, ResultType > &g1, const ScalarType &scalar)
	Return the grid function representing the function `g` divided by `scalar`. More...

template<typename BasisFunctionType , typename ResultType >
void	exportToVtk (const GridFunction< BasisFunctionType, ResultType > &gridFunction, VtkWriter::DataType dataType, const char dataLabel, const char fileNamesBase, const char *filesPath=0, VtkWriter::OutputType type=VtkWriter::ASCII)
	Export this function to a VTK file. More...

template<typename BasisFunctionType , typename ResultType >
void	exportToGmsh (const GridFunction< BasisFunctionType, ResultType > &gridFunction, const char dataLabel, const char fileName)
	Export this function to a Gmsh (.msh) file. More...

template<typename BasisFunctionType , typename ResultType >
ScalarTraits < BasisFunctionType > ::RealType	L2NormOfDifference (const GridFunction< BasisFunctionType, ResultType > &gridFunction, const Fiber::Function< ResultType > &refFunction, const Fiber::QuadratureStrategy< BasisFunctionType, ResultType, GeometryFactory > &quadStrategy, const EvaluationOptions &options=EvaluationOptions())
	Calculate the -norm of the difference between a GridFunction and a Function. More...

template<typename BasisFunctionType , typename ResultType >
void	estimateL2Error (const GridFunction< BasisFunctionType, ResultType > &gridFunction, const Fiber::Function< ResultType > &refFunction, const Fiber::QuadratureStrategy< BasisFunctionType, ResultType, GeometryFactory > &quadStrategy, const EvaluationOptions &options, typename ScalarTraits< BasisFunctionType >::RealType &absError, typename ScalarTraits< BasisFunctionType >::RealType &relError)
	Calculate the absolute and relative errors of a solution. More...

template<typename BasisFunctionType , typename ResultType >
void	estimateL2Error (const GridFunction< BasisFunctionType, ResultType > &gridFunction, const Fiber::Function< ResultType > &refFunction, const Fiber::QuadratureStrategy< BasisFunctionType, ResultType, GeometryFactory > &quadStrategy, typename ScalarTraits< BasisFunctionType >::RealType &absError, typename ScalarTraits< BasisFunctionType >::RealType &relError)
	Calculate the absolute and relative errors of a solution. More...

Detailed Description

template<typename BasisFunctionType, typename ResultType>
class Bempp::GridFunction< BasisFunctionType, ResultType >

Function defined on a grid.

This class represents a function defined on a grid and expanded in a particular function space.

Constructor & Destructor Documentation

template<typename BasisFunctionType , typename ResultType >

Bempp::GridFunction< BasisFunctionType, ResultType >::GridFunction ( )

Constructor.

Construct an uninitialized grid function. The only way to initialize it later is using the assignment operator.

template<typename BasisFunctionType, typename ResultType>

Bempp::GridFunction< BasisFunctionType, ResultType >::GridFunction	(	const shared_ptr< const Context< BasisFunctionType, ResultType > > &	context,
		const shared_ptr< const Space< BasisFunctionType > > &	space,
		const arma::Col< ResultType > &	coefficients
	)

Constructor.

Parameters

[in]	context	Assembly context from which a quadrature strategy can be retrieved.
[in]	space	Function space to expand the grid function in.
[in]	coefficients	Vector of length `space.globalDofCount()` containing the expansion coefficients of the grid function in the space `space`.

This constructor builds a grid function from its coefficients in a function space.

template<typename BasisFunctionType, typename ResultType>

Bempp::GridFunction< BasisFunctionType, ResultType >::GridFunction	(	const shared_ptr< const Context< BasisFunctionType, ResultType > > &	context,
		const shared_ptr< const Space< BasisFunctionType > > &	space,
		const shared_ptr< const Space< BasisFunctionType > > &	dualSpace,
		const arma::Col< ResultType > &	projections
	)

Constructor.

Parameters

[in]	context	Assembly context from which a quadrature strategy can be retrieved.
[in]	space	Function space to expand the grid function in.
[in]	dualSpace	Function space dual to `space`.
[in]	projections	Vector of length `dualSpace.globalDofCount()` containing the scalar products of the grid function and the basis functions of the space `dualSpace`.

This constructor builds a grid function expanded in the basis of the space space from the projections of this function on the basis functions of another space dualSpace. Both spaces must be defined on the same grid.

template<typename BasisFunctionType, typename ResultType>

Bempp::GridFunction< BasisFunctionType, ResultType >::GridFunction	(	const shared_ptr< const Context< BasisFunctionType, ResultType > > &	context,
		const shared_ptr< const Space< BasisFunctionType > > &	space,
		const shared_ptr< const Space< BasisFunctionType > > &	dualSpace,
		const Function< ResultType > &	function,
		ConstructionMode	mode = `APPROXIMATE`
	)

Constructor.

Parameters

[in]	context	Assembly context from which a quadrature strategy can be retrieved.
[in]	space	Function space to expand the grid function in.
[in]	dualSpace	Function space dual to `space`.
[in]	function	Function object whose values on `space.grid()` will be used to construct the new grid function.
[in]	mode	Determines the way the expansion coefficients of the function are determined. Can be set to #APPROXIMATE or #INTERPOLATE. These options are discussed below.

This constructor builds a grid function belonging to the space space and approximating the function $f$ defined by the object function.

If mode is set to #APPROXIMATE, the approximate coefficients $\{f_i\}$ of function in the basis $\{\phi_i\}$ of space are determined by solving the equation

$\sum_j \langle \psi_i, \phi_j \rangle f_i = \langle \psi_i, f \rangle$

in the least-squares sense, with $\{\psi_i\}$ denoting the set of basis functions of dualSpace. The two spaces must be defined on the same grid.

Otherwise (if mode is set to #INTERPOLATE), the approximate coefficients $\{f_i\}$ are determined by evaluating function at the interpolation points of the global degrees of freedom of space (see Space::getGlobalDofInterpolationPoints() for more details).

References Bempp::GridFunction< BasisFunctionType, ResultType >::setCoefficients(), and Bempp::GridFunction< BasisFunctionType, ResultType >::setProjections().

template<typename BasisFunctionType, typename ResultType>

Bempp::GridFunction< BasisFunctionType, ResultType >::GridFunction	(	const shared_ptr< const Context< BasisFunctionType, ResultType > > &	context,
		const shared_ptr< const Space< BasisFunctionType > > &	space,
		const shared_ptr< const Space< BasisFunctionType > > &	dualSpace,
		const arma::Col< ResultType > &	data,
		DataType	dataType
	)

Constructor.

Parameters

[in]	context	Assembly context from which a quadrature strategy can be retrieved.
[in]	space	Function space to expand the grid function in.
[in]	dualSpace	Function space dual to `space`.
[in]	data	If `dataType == COEFFICIENTS`, the vector `data` should have length `space.globalDofCount()` and contain the expansion coefficients of the grid function in the space `space`. Otherwise, if `dataType == PROJECTIONS`, `data` should have length `dualSpace.globalDofCount()` contain the scalar products of the grid function and the basis functions of the space `dualSpace`.
[in]	dataType	Interpretation of the vector passed via the argument `data`.

This constructor builds a grid function from either its coefficients in a function space or from its projections on the basis functions of another (dual) function space. If the other type of data turns out to be needed later (for example, the projections vector if coefficients were supplied in the constructor), it is calculated automatically. The Context object given in the constructor is then used to determine the strategy for evaluating any necessary integrals.

space and dualSpace must be defined on the same grid.

Deprecated:: This constructor is deprecated. In new code, use one of the other constructors.

template<typename BasisFunctionType, typename ResultType>

Bempp::GridFunction< BasisFunctionType, ResultType >::GridFunction	(	const shared_ptr< const Context< BasisFunctionType, ResultType > > &	context,
		const shared_ptr< const Space< BasisFunctionType > > &	space,
		const shared_ptr< const Space< BasisFunctionType > > &	dualSpace,
		const arma::Col< ResultType > &	coefficients,
		const arma::Col< ResultType > &	projections
	)

Constructor.

Parameters

[in]	context	Assembly context from which a quadrature strategy can be retrieved.
[in]	space	Function space to expand the grid function in.
[in]	dualSpace	Function space dual to `space`.
[in]	coefficients	Vector of length `space.globalDofCount()` containing the expansion coefficients of the grid function in the space `space`.
[in]	projections	Vector of length `dualSpace.globalDofCount()` containing the scalar products of the grid function and the basis functions of the space `dualSpace`.

space and dualSpace must be defined on the same grid.

Deprecated:: This constructor is deprecated. In new code, use one of the other constructors.

Member Function Documentation

template<typename BasisFunctionType , typename ResultType >

const Fiber::Basis< BasisFunctionType > & Bempp::GridFunction< BasisFunctionType, ResultType >::basis ( const Entity< 0 > & element ) const

Return the shapeset associated with the given element.

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

template<typename BasisFunctionType , typename ResultType >

const arma::Col< ResultType > & Bempp::GridFunction< BasisFunctionType, ResultType >::coefficients ( ) const

Vector of expansion coefficients of this function in the basis of its expansion space.

An exception is thrown if this function is called on an uninitialized GridFunction object (one constructed with the default constructor).

Referenced by Bempp::AssembledPotentialOperator< BasisFunctionType, ResultType >::apply(), Bempp::BoundaryOperator< BasisFunctionType, ResultType >::apply(), Bempp::GridFunction< BasisFunctionType, ResultType >::operator*(), Bempp::GridFunction< BasisFunctionType, ResultType >::operator+(), and Bempp::GridFunction< BasisFunctionType, ResultType >::operator-().

template<typename BasisFunctionType , typename ResultType >

int Bempp::GridFunction< BasisFunctionType, ResultType >::componentCount ( ) const

Number of components of this function.

Note: An exception is thrown if this function is called on an uninitialized GridFunction object.

Referenced by Bempp::GridFunction< BasisFunctionType, ResultType >::exportToGmsh().

template<typename BasisFunctionType , typename ResultType >

shared_ptr< const Space< BasisFunctionType > > Bempp::GridFunction< BasisFunctionType, ResultType >::dualSpace ( ) const

Space dual to the space in which this function is expanded.

Deprecated:: This function is provided only for backward compatibility reasons. It returns the shared pointer to the dual space of the GridFunction, if one was supplied during the construction of the latter, or a null pointer otherwise.

Referenced by Bempp::GridFunction< BasisFunctionType, ResultType >::operator*(), Bempp::GridFunction< BasisFunctionType, ResultType >::operator+(), and Bempp::GridFunction< BasisFunctionType, ResultType >::operator-().

template<typename BasisFunctionType , typename ResultType>

void Bempp::GridFunction< BasisFunctionType, ResultType >::evaluate	(	const Entity< 0 > &	element,
		const arma::Mat< CoordinateType > &	local,
		arma::Mat< ResultType > &	values
	)		const

Evaluate function at specific points lying on a given element.

Parameters

[in]	element	An element belonging to the grid on which `function` is defined.
[in]	local	A 2D array whose (i,j)th element is the ith coordinate of the jth point at which the grid function should be evaluated, in the local coordinate system of `element`.
[in]	values	A 2D array whose (i,j)th element is the ith component of `function` evaluated at the jth point.

References Fiber::CollectionOfShapesetTransformations< CoordinateType_ >::addDependencies(), Fiber::Shapeset< BasisFunctionType >::evaluate(), Fiber::CollectionOfShapesetTransformations< CoordinateType_ >::evaluate(), Bempp::Entity< 0 >::geometry(), Fiber::CollectionOfShapesetTransformations< CoordinateType_ >::resultDimension(), Fiber::Shapeset< BasisFunctionType >::size(), and Fiber::CollectionOfShapesetTransformations< CoordinateType_ >::transformationCount().

Referenced by Bempp::GridFunction< BasisFunctionType, ResultType >::exportToGmsh().

template<typename BasisFunctionType , typename ResultType>

void Bempp::GridFunction< BasisFunctionType, ResultType >::evaluateAtSpecialPoints	(	VtkWriter::DataType	dataType,
		arma::Mat< ResultType > &	result_
	)		const

Evaluate function at either vertices or barycentres.

Note: The results of calling this function on an uninitialized GridFunction object are undefined.

Referenced by Bempp::GridFunction< BasisFunctionType, ResultType >::exportToVtk().

template<typename BasisFunctionType , typename ResultType >

void Bempp::GridFunction< BasisFunctionType, ResultType >::exportToGmsh	(	const char *	dataLabel,
		const char *	fileName
	)		const

Export this function to a Gmsh (.msh) file.

Parameters

[in]	dataLabel	Label used to identify the function in the Gmsh file.
[in]	fileName	Name of the file to be written.

Note: An exception is thrown if this function is called on an uninitialized GridFunction object.; Currently this function treats all elements as independent from each other, so that for example each internal mesh node is output as many times as there are elements adjacent to it. This makes it possible to export GridFunctions expanded in spaces with discontinuous bases. However, it also means that a .msh file generated by exportToGmsh cannot be imported back by BEM++ and used to create a Grid object.

Deprecated:: This member function is deprecated. Use the standalone function exportToGmsh() instead.

template<typename BasisFunctionType , typename ResultType >

void Bempp::GridFunction< BasisFunctionType, ResultType >::exportToVtk	(	VtkWriter::DataType	dataType,
		const char *	dataLabel,
		const char *	fileNamesBase,
		const char *	filesPath = `0`,
		VtkWriter::OutputType	type = `VtkWriter::ASCII`
	)		const

Export this function to a VTK file.

Parameters

[in]	dataType	Determines whether data are attaches to vertices or cells.
[in]	dataLabel	Label used to identify the function in the VTK file.
[in]	fileNamesBase	Base name of the output files. It should not contain any directory part or filename extensions.
[in]	filesPath	Output directory. Can be set to NULL, in which case the files are output in the current directory.
[in]	type	Output type (default: ASCII). See Dune reference manual for more details.

Note: An exception is thrown if this function is called on an uninitialized GridFunction object.

Deprecated:: This member function is deprecated. Use the standalone function exportToVtk() instead.

template<typename BasisFunctionType , typename ResultType>

void Bempp::GridFunction< BasisFunctionType, ResultType >::getLocalCoefficients	(	const Entity< 0 > &	element,
		std::vector< ResultType > &	coeffs
	)		const

Retrieve the expansion coefficients of this function on a single element.

Parameters

[in]	element	An element belonging to the grid `space.grid()`.
[out]	coeffs	Vector of the expansion coefficients of this function corresponding to the basis functions of the primal space living on element `element`.

Note: The results of calling this function on an uninitialized GridFunction object are undefined.

template<typename BasisFunctionType , typename ResultType >

shared_ptr< const Grid > Bempp::GridFunction< BasisFunctionType, ResultType >::grid ( ) const

Grid on which this function is defined.

Note: An exception is thrown if this function is called on an uninitialized GridFunction object.

Referenced by Bempp::ElementaryPotentialOperator< BasisFunctionType_, KernelType_, ResultType_ >::evaluateAtPoints(), and Bempp::ElementaryPotentialOperator< BasisFunctionType_, KernelType_, ResultType_ >::evaluateOnGrid().

template<typename BasisFunctionType , typename ResultType >

GridFunction< BasisFunctionType, ResultType >::MagnitudeType Bempp::GridFunction< BasisFunctionType, ResultType >::L2Norm ( ) const

Return the $L^2$ -norm of the grid function.

Note: For better accuracy, prefer to use L2NormOfDifference() or estimateL2Error() to calculate the norm of the difference between a grid function and a function defined by an analytical expression.

References Bempp::NO_TRANSPOSE.

template<typename BasisFunctionType, typename ResultType >

arma::Col< ResultType > Bempp::GridFunction< BasisFunctionType, ResultType >::projections ( const shared_ptr< const Space< BasisFunctionType > > & dualSpace_ ) const

Vector of scalar products of this function with the basis functions of dualSpace.

dualSpace must be defined on the same grid as the space in which the GridFunction is expanded.

An exception is thrown if this function is called on an uninitialized GridFunction object (one constructed with the default constructor).

Referenced by Bempp::BoundaryOperator< BasisFunctionType, ResultType >::apply(), Bempp::GridFunction< BasisFunctionType, ResultType >::operator*(), Bempp::GridFunction< BasisFunctionType, ResultType >::operator+(), and Bempp::GridFunction< BasisFunctionType, ResultType >::operator-().

template<typename BasisFunctionType, typename ResultType >

arma::Col< ResultType > Bempp::GridFunction< BasisFunctionType, ResultType >::projections ( const Space< BasisFunctionType > & dualSpace_ ) const

Vector of scalar products of this function with the basis functions of dualSpace.

dualSpace must be defined on the same grid as the space in which the GridFunction is expanded.

An exception is thrown if this function is called on an uninitialized GridFunction object (one constructed with the default constructor).

Deprecated:: This function is deprecated; use the variant taking a shared pointer to the dual space instead.

template<typename BasisFunctionType, typename ResultType >

arma::Col< ResultType > Bempp::GridFunction< BasisFunctionType, ResultType >::projections ( ) const

Vector of scalar products of this function with the basis functions of its dual space.

Deprecated:: This function is provided only for backward compatibility purposes. It works only if the dual space was specified during the construction of the GridFunction. In new code the other overload of projections() should be used.

An exception is thrown if this function is called on an uninitialized GridFunction object (one constructed with the default constructor).

template<typename BasisFunctionType , typename ResultType>

void Bempp::GridFunction< BasisFunctionType, ResultType >::setCoefficients ( const arma::Col< ResultType > & coeffs )

Reset the expansion coefficients of this function in the basis of its primal space.

As a side effect, any internally stored vector of the projections of this grid function on the basis functions of its dual space is marked as invalid and recalculated on the next call to projections().

Referenced by Bempp::GridFunction< BasisFunctionType, ResultType >::GridFunction().

template<typename BasisFunctionType, typename ResultType>

void Bempp::GridFunction< BasisFunctionType, ResultType >::setProjections	(	const shared_ptr< const Space< BasisFunctionType > > &	dualSpace_,
		const arma::Col< ResultType > &	projects
	)

Reinitialize the function by specifying the vector of its scalar products with the basis functions of dualSpace.

dualSpace must be defined on the same grid as the space in which the GridFunction is expanded.

Referenced by Bempp::BoundaryOperator< BasisFunctionType, ResultType >::apply(), and Bempp::GridFunction< BasisFunctionType, ResultType >::GridFunction().

template<typename BasisFunctionType, typename ResultType>

void Bempp::GridFunction< BasisFunctionType, ResultType >::setProjections	(	const Space< BasisFunctionType > &	dualSpace_,
		const arma::Col< ResultType > &	projects
	)

Reinitialize the function by specifying the vector of its scalar products with the basis functions of dualSpace.

dualSpace must be defined on the same grid as the space in which the GridFunction is expanded.

Deprecated:: This function is deprecated. Use the other variant taking a shared pointer to the dual space. If you use this function, it is your responsibility to ensure that dualSpace_ is not destroyed as long as this GridFunction object is alive.

template<typename BasisFunctionType, typename ResultType>

void Bempp::GridFunction< BasisFunctionType, ResultType >::setProjections ( const arma::Col< ResultType > & projects )

Reset the vector of scalar products of this function with the basis functions of its dual space.

Deprecated:: This function is provided only for backward compatibility purposes. It works only if the dual space was specified during the construction of the GridFunction. In new code the other overload of setProjections() should be used.

template<typename BasisFunctionType , typename ResultType >

const Fiber::Shapeset< BasisFunctionType > & Bempp::GridFunction< BasisFunctionType, ResultType >::shapeset ( const Entity< 0 > & element ) const

Return the shapeset associated with the given element.

Note: The results of calling this function on an uninitialized GridFunction object are undefined.

template<typename BasisFunctionType , typename ResultType >

bool Bempp::GridFunction< BasisFunctionType, ResultType >::wasInitializedFromCoefficients ( ) const

Returns true if the GridFunction was initialized with a list of coefficients and false if it was initialized with a list of projections.

This means that the other quantity (projections or coefficients, respectively) is a derived quantity and may therefore be less accurate.

Referenced by Bempp::GridFunction< BasisFunctionType, ResultType >::operator*(), Bempp::GridFunction< BasisFunctionType, ResultType >::operator+(), and Bempp::GridFunction< BasisFunctionType, ResultType >::operator-().

Friends And Related Function Documentation

template<typename BasisFunctionType , typename ResultType >

void estimateL2Error	(	const GridFunction< BasisFunctionType, ResultType > &	gridFunction,
		const Fiber::Function< ResultType > &	refFunction,
		const Fiber::QuadratureStrategy< BasisFunctionType, ResultType, GeometryFactory > &	quadStrategy,
		const EvaluationOptions &	options,
		typename ScalarTraits< BasisFunctionType >::RealType &	absError,
		typename ScalarTraits< BasisFunctionType >::RealType &	relError
	)

This function calculates the absolute and relative $L^2$ norms of the difference between a GridFunction (typically a numerical solution of an integral equation) and a Function (typically a known analytical solution.

The quadrature strategy quadStrategy is used to evaluate any necessary integrals; the options object controls the level of parallelism. The results are returned in the output arguments absError and relError.

Note: If you use the numerical quadrature strategy, you may need to increase the quadrature order for regular integrals on single elements by at least 2 to ensure that this function produces results with sufficient accuracy.

template<typename BasisFunctionType , typename ResultType >

void estimateL2Error	(	const GridFunction< BasisFunctionType, ResultType > &	gridFunction,
		const Fiber::Function< ResultType > &	refFunction,
		const Fiber::QuadratureStrategy< BasisFunctionType, ResultType, GeometryFactory > &	quadStrategy,
		typename ScalarTraits< BasisFunctionType >::RealType &	absError,
		typename ScalarTraits< BasisFunctionType >::RealType &	relError
	)

This is an overloaded version, provided for convenience. It is equivalent to the six-parameter version with options set to EvaluationOptions().

template<typename BasisFunctionType , typename ResultType >

void exportToGmsh	(	const GridFunction< BasisFunctionType, ResultType > &	gridFunction,
		const char *	dataLabel,
		const char *	fileName
	)

Parameters

[in]	dataLabel	Label used to identify the function in the Gmsh file.
[in]	fileName	Name of the file to be written.

Note: An exception is thrown if this function is called on an uninitialized GridFunction object.; Currently this function treats all elements as independent from each other, so that for example each internal mesh node is output as many times as there are elements adjacent to it. This makes it possible to export GridFunctions expanded in spaces with discontinuous bases. However, it also means that a .msh file generated by exportToGmsh cannot be imported back by BEM++ and used to create a Grid object.

References Bempp::GridFunction< BasisFunctionType, ResultType >::componentCount(), Bempp::GridView::entityIterator(), Bempp::GridFunction< BasisFunctionType, ResultType >::evaluate(), Bempp::Entity< 0 >::geometry(), Bempp::Geometry::local2global(), Bempp::GridFunction< BasisFunctionType, ResultType >::space(), and Bempp::Entity< 0 >::type().

template<typename BasisFunctionType , typename ResultType >

void exportToVtk	(	const GridFunction< BasisFunctionType, ResultType > &	gridFunction,
		VtkWriter::DataType	dataType,
		const char *	dataLabel,
		const char *	fileNamesBase,
		const char *	filesPath = `0`,
		VtkWriter::OutputType	type = `VtkWriter::ASCII`
	)

Parameters

[in]	dataType	Determines whether data are attaches to vertices or cells.
[in]	dataLabel	Label used to identify the function in the VTK file.
[in]	fileNamesBase	Base name of the output files. It should not contain any directory part or filename extensions.
[in]	filesPath	Output directory. Can be set to NULL, in which case the files are output in the current directory.
[in]	type	Output type (default: ASCII). See Dune reference manual for more details.

Note: An exception is thrown if this function is called on an uninitialized GridFunction object.

References Bempp::GridFunction< BasisFunctionType, ResultType >::evaluateAtSpecialPoints(), Bempp::GridFunction< BasisFunctionType, ResultType >::space(), and Bempp::GridView::vtkWriter().

template<typename BasisFunctionType , typename ResultType >

ScalarTraits< BasisFunctionType >::RealType L2NormOfDifference	(	const GridFunction< BasisFunctionType, ResultType > &	gridFunction,
		const Fiber::Function< ResultType > &	refFunction,
		const Fiber::QuadratureStrategy< BasisFunctionType, ResultType, GeometryFactory > &	quadStrategy,
		const EvaluationOptions &	options = `EvaluationOptions()`
	)

This function can be used to estimate the absolute error of a numerical solution gridFunction against a known analytical solution refFunction.

The quadrature strategy quadStrategy is used to evaluate any necessary integrals; the options object controls the level of parallelism.

Note: If you use the numerical quadrature strategy, you may need to increase the quadrature order for regular integrals on single elements by at least 2 to ensure that this function produces results with sufficient accuracy.

template<typename BasisFunctionType , typename ResultType , typename ScalarType >

GridFunction< BasisFunctionType, ResultType > operator*	(	const GridFunction< BasisFunctionType, ResultType > &	g,
		const ScalarType &	scalar
	)

Note: An exception is thrown if g is uninitialized.

References Bempp::GridFunction< BasisFunctionType, ResultType >::coefficients(), Bempp::GridFunction< BasisFunctionType, ResultType >::context(), Bempp::GridFunction< BasisFunctionType, ResultType >::dualSpace(), Bempp::GridFunction< BasisFunctionType, ResultType >::projections(), Bempp::GridFunction< BasisFunctionType, ResultType >::space(), and Bempp::GridFunction< BasisFunctionType, ResultType >::wasInitializedFromCoefficients().

template<typename BasisFunctionType , typename ResultType , typename ScalarType >

boost::enable_if< typename boost::mpl::has_key< boost::mpl::set< float, double, std::complex< float >, std::complex< double > >, ScalarType >, GridFunction< BasisFunctionType, ResultType > >::type operator*	(	const ScalarType &	scalar,
		const GridFunction< BasisFunctionType, ResultType > &	g
	)

Note: An exception is thrown if g is uninitialized.

template<typename BasisFunctionType , typename ResultType >

GridFunction< BasisFunctionType, ResultType > operator+	(	const GridFunction< BasisFunctionType, ResultType > &	g1,
		const GridFunction< BasisFunctionType, ResultType > &	g2
	)

Note: Both operands must be initialized and their primal and dual spaces must be identical, otherwise an exception is thrown.

References Bempp::GridFunction< BasisFunctionType, ResultType >::coefficients(), Bempp::GridFunction< BasisFunctionType, ResultType >::context(), Bempp::GridFunction< BasisFunctionType, ResultType >::dualSpace(), Bempp::GridFunction< BasisFunctionType, ResultType >::projections(), Bempp::GridFunction< BasisFunctionType, ResultType >::space(), and Bempp::GridFunction< BasisFunctionType, ResultType >::wasInitializedFromCoefficients().

template<typename BasisFunctionType , typename ResultType >

GridFunction< BasisFunctionType, ResultType > operator- ( const GridFunction< BasisFunctionType, ResultType > & g )

Note: An exception is thrown if g is uninitialized.

template<typename BasisFunctionType , typename ResultType >

GridFunction< BasisFunctionType, ResultType > operator-	(	const GridFunction< BasisFunctionType, ResultType > &	g1,
		const GridFunction< BasisFunctionType, ResultType > &	g2
	)

Note: Both operands must be initialized and their primal and dual spaces must be identical, otherwise an exception is thrown.

References Bempp::GridFunction< BasisFunctionType, ResultType >::coefficients(), Bempp::GridFunction< BasisFunctionType, ResultType >::context(), Bempp::GridFunction< BasisFunctionType, ResultType >::dualSpace(), Bempp::GridFunction< BasisFunctionType, ResultType >::projections(), Bempp::GridFunction< BasisFunctionType, ResultType >::space(), and Bempp::GridFunction< BasisFunctionType, ResultType >::wasInitializedFromCoefficients().

template<typename BasisFunctionType , typename ResultType , typename ScalarType >

GridFunction< BasisFunctionType, ResultType > operator/	(	const GridFunction< BasisFunctionType, ResultType > &	g1,
		const ScalarType &	scalar
	)

Note: An exception is thrown if g is uninitialized.

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/assembly/grid_function.hpp
/home/wojtek/Projects/BEM/bempp-sven/bempp/lib/assembly/grid_function.cpp
/home/wojtek/Projects/BEM/bempp-sven/bempp/lib/assembly/l2_norm.hpp

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Related Functions

Detailed Description

template<typename BasisFunctionType, typename ResultType> class Bempp::GridFunction< BasisFunctionType, ResultType >

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

template<typename BasisFunctionType, typename ResultType>
class Bempp::GridFunction< BasisFunctionType, ResultType >