Hypersingular integral boundary operator. More...

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

Inheritance diagram for Bempp::HypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >:

Public Types
typedef Base::BasisFunctionType	BasisFunctionType
	Type of the values of the (components of the) basis functions into which functions acted upon by the operator are expanded. More...

typedef Base::ResultType	ResultType
	Type used to represent elements of the weak form of the operator. More...

typedef Base::CoordinateType	CoordinateType
	Type used to represent coordinates. More...

typedef Base::QuadratureStrategy	QuadratureStrategy
	Type of the appropriate instantiation of Fiber::QuadratureStrategy. More...

typedef Fiber::LocalAssemblerForIntegralOperators < ResultType >	LocalAssembler
	Type of the appropriate instantiation of Fiber::LocalAssemblerForOperators.

typedef KernelType_	KernelType
	Type of the values of the (components of the) kernel functions.

typedef Fiber::CollectionOfShapesetTransformations < CoordinateType >	CollectionOfShapesetTransformations
	Type of the appropriate instantiation of Fiber::CollectionOfShapesetTransformations.

typedef Fiber::CollectionOfShapesetTransformations < CoordinateType >	CollectionOfBasisTransformations
	Type of the appropriate instantiation of Fiber::CollectionOfBasisTransformations. More...

typedef Fiber::CollectionOfKernels < KernelType >	CollectionOfKernels
	Type of the appropriate instantiation of Fiber::CollectionOfKernels.

typedef Fiber::TestKernelTrialIntegral < BasisFunctionType, KernelType, ResultType >	TestKernelTrialIntegral
	Type of the appropriate instantiation of Fiber::TestKernelTrialIntegral.

Public Types inherited from Bempp::AbstractBoundaryOperator< BasisFunctionType_, ResultType_ >
typedef BasisFunctionType_	BasisFunctionType
	Type of the values of the (components of the) basis functions into which functions acted upon by the operator are expanded.

typedef ResultType_	ResultType
	Type used to represent elements of the weak form of the operator.

typedef ScalarTraits < ResultType >::RealType	CoordinateType
	Type used to represent coordinates.

typedef Fiber::QuadratureStrategy < BasisFunctionType, ResultType, GeometryFactory >	QuadratureStrategy
	Type of the appropriate instantiation of Fiber::QuadratureStrategy.

Public Member Functions
	HypersingularIntegralOperator (const shared_ptr< const Space< BasisFunctionType > > &domain, const shared_ptr< const Space< BasisFunctionType > > &range, const shared_ptr< const Space< BasisFunctionType > > &dualToRange, const std::string &label, int symmetry)
	Constructor. More...

virtual bool	isLocal () const
	Return false.

Public Member Functions inherited from Bempp::AbstractBoundaryOperator< BasisFunctionType_, ResultType_ >
	AbstractBoundaryOperator (const shared_ptr< const Space< BasisFunctionType > > &domain, const shared_ptr< const Space< BasisFunctionType > > &range, const shared_ptr< const Space< BasisFunctionType > > &dualToRange, const std::string &label, int symmetry)
	Constructor. More...

virtual	~AbstractBoundaryOperator ()
	Destructor.

virtual BEMPP_DEPRECATED shared_ptr< const AbstractBoundaryOperatorId >	id () const
	Return the identifier of this operator. More...

shared_ptr< const Space < BasisFunctionType > >	domain () const
	Domain. More...

shared_ptr< const Space < BasisFunctionType > >	range () const
	Range. More...

shared_ptr< const Space < BasisFunctionType > >	dualToRange () const
	Dual to range. More...

std::string	label () const
	Return the label of the operator.

int	symmetry () const
	Return the symmetry properties of the operator. More...

shared_ptr < DiscreteBoundaryOperator < ResultType_ > >	assembleWeakForm (const Context< BasisFunctionType_, ResultType_ > &context) const
	Assemble and return the operator's weak form. More...

Protected Member Functions
virtual shared_ptr < DiscreteBoundaryOperator < ResultType_ > >	assembleWeakFormImpl (const Context< BasisFunctionType, ResultType > &context) const
	Assemble and return the operator's weak form. More...

Protected Member Functions inherited from Bempp::AbstractBoundaryOperator< BasisFunctionType_, ResultType_ >
void	collectDataForAssemblerConstruction (const AssemblyOptions &options, shared_ptr< Fiber::RawGridGeometry< CoordinateType > > &testRawGeometry, shared_ptr< Fiber::RawGridGeometry< CoordinateType > > &trialRawGeometry, shared_ptr< GeometryFactory > &testGeometryFactory, shared_ptr< GeometryFactory > &trialGeometryFactory, shared_ptr< std::vector< const Fiber::Shapeset< BasisFunctionType_ > * > > &testShapesets, shared_ptr< std::vector< const Fiber::Shapeset< BasisFunctionType_ > * > > &trialShapesets, shared_ptr< Fiber::OpenClHandler > &openClHandler, bool &cacheSingularIntegrals) const
	Given an AssemblyOptions object, construct objects necessary for subsequent local assembler construction.

void	collectOptionsIndependentDataForAssemblerConstruction (shared_ptr< Fiber::RawGridGeometry< CoordinateType > > &testRawGeometry, shared_ptr< Fiber::RawGridGeometry< CoordinateType > > &trialRawGeometry, shared_ptr< GeometryFactory > &testGeometryFactory, shared_ptr< GeometryFactory > &trialGeometryFactory, shared_ptr< std::vector< const Fiber::Shapeset< BasisFunctionType_ > * > > &testShapesets, shared_ptr< std::vector< const Fiber::Shapeset< BasisFunctionType_ > * > > &trialShapesets) const
	Construct those objects necessary for subsequent local assembler construction that are independent from assembly options.

void	collectOptionsDependentDataForAssemblerConstruction (const AssemblyOptions &options, const shared_ptr< Fiber::RawGridGeometry< CoordinateType > > &testRawGeometry, const shared_ptr< Fiber::RawGridGeometry< CoordinateType > > &trialRawGeometry, shared_ptr< Fiber::OpenClHandler > &openClHandler, bool &cacheSingularIntegrals) const
	Construct those objects necessary for subsequent local assembler construction that depend on assembly options.

Private Types
typedef AbstractBoundaryOperator < BasisFunctionType_, ResultType_ >	Base

Private Member Functions
virtual const CollectionOfKernels &	kernels () const =0
	Return the collection of kernel functions occurring in the weak form of this operator.

virtual const CollectionOfShapesetTransformations &	testTransformations () const =0
	Return the collection of test-function transformations occurring in the first representation of the weak form of this operator (valid for all pairs of test and trial functions).

virtual const CollectionOfShapesetTransformations &	trialTransformations () const =0
	Return the collection of trial-function transformations occurring in the first representation of the weak form of this operator (valid for all pairs of test and trial functions).

virtual const TestKernelTrialIntegral &	integral () const =0
	Return an object representing the integral that is the first representation of the weak form of this operator (valid for all pairs of test and trial functions). More...

virtual const CollectionOfKernels &	offDiagonalKernels () const =0
	Return the collection of kernel functions occurring in the in the second representation of the weak form of this operator (valid at least for pairs of test and trial functions with nonoverlapping supports).

virtual const CollectionOfShapesetTransformations &	offDiagonalTestTransformations () const =0
	Return the collection of test-function transformations occurring in the second representation of the weak form of this operator (valid at least for pairs of test and trial functions with nonoverlapping supports). More...

virtual const CollectionOfShapesetTransformations &	offDiagonalTrialTransformations () const =0
	Return the collection of trial-function transformations occurring in the second representation of the weak form of this operator (valid at least for pairs of test and trial functions with nonoverlapping supports). More...

virtual const TestKernelTrialIntegral &	offDiagonalIntegral () const =0
	Return an object representing the integral that is the second representation of the weak form of this operator (valid at least for pairs of test and trial functions with nonoverlapping supports). More...

Detailed Description

template<typename BasisFunctionType_, typename KernelType_, typename ResultType_>
class Bempp::HypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >

Hypersingular integral boundary operator.

This abstract class represents an integral boundary operator $\mathcal A$ providing two alternative ways to evaluate its weak form $\langle \phi, \mathcal A \psi \rangle$ . One of them must be valid for any pair of test and trial functions, $\phi$ and $\psi$ , and it can be expressed by a formula of an arbitrary form; in particular, it can contain differential operators, e.g. surface div and curl, acting on the test and trial functions. The other one needs only be valid for test and trial functions with nonoverlapping support, and it must be of the form

$\int_\Gamma \int_\Sigma \phi^*(x) \, K(x, y) \, \psi(y) \, \mathrm{d}\Gamma(x) \,\mathrm{d}\Sigma(y),$

where $K(x, y)$ is an arbitrary kernel; note that the formula contains "bare" test and trial functions, without any operators acting on them.

When the discrete weak form of an integral operator represented by a subclass of this class is assembled in the hybrid ACA mode (

See Also: AcaOptions::mode), the first representation of the weak form is used in the Assembly of nonadmissible blocks and the second in the Assembly of admissible ("off-diagonal") blocks.

The first representation of the weak form is determined by the implementation of the virtual functions integral(), kernels(), testTransformations() and trialTransformations(). The second representation is determined by the implementation of the virtual functions offDiagonalIntegral(), offDiagonalKernels(), offDiagonalTestTransformations() and offDiagonalTrialTransformations().

Template Parameters

BasisFunctionType_	Type of the values of the (components of the) basis functions into which functions acted upon by the operator are expanded.
KernelType_	Type of the values of the (components of the) kernel functions occurring in the integrand of the operator.
ResultType_	Type used to represent elements of the weak form of the operator.

All three template parameters can take the following values: float, double, std::complex<float> and std::complex<double>. All types must have the same precision: for instance, mixing float with std::complex<double> is not allowed. If either BasisFunctionType_ or KernelType_ is a complex type, then ResultType_ must be set to the same type.

Member Typedef Documentation

template<typename BasisFunctionType_ , typename KernelType_ , typename ResultType_ >

typedef Base::BasisFunctionType Bempp::HypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >::BasisFunctionType

Type of the values of the (components of the) basis functions into which functions acted upon by the operator are expanded.

template<typename BasisFunctionType_ , typename KernelType_ , typename ResultType_ >

typedef Fiber::CollectionOfShapesetTransformations<CoordinateType> Bempp::HypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >::CollectionOfBasisTransformations

Type of the appropriate instantiation of Fiber::CollectionOfBasisTransformations.

Deprecated:: This type is deprecated; use CollectionOfShapesetTransformations instead.

template<typename BasisFunctionType_ , typename KernelType_ , typename ResultType_ >

typedef Base::CoordinateType Bempp::HypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >::CoordinateType

Type used to represent coordinates.

template<typename BasisFunctionType_ , typename KernelType_ , typename ResultType_ >

typedef Base::QuadratureStrategy Bempp::HypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >::QuadratureStrategy

Type of the appropriate instantiation of Fiber::QuadratureStrategy.

template<typename BasisFunctionType_ , typename KernelType_ , typename ResultType_ >

typedef Base::ResultType Bempp::HypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >::ResultType

Type used to represent elements of the weak form of the operator.

Constructor & Destructor Documentation

template<typename BasisFunctionType , typename KernelType , typename ResultType >

Bempp::HypersingularIntegralOperator< BasisFunctionType, KernelType, ResultType >::HypersingularIntegralOperator	(	const shared_ptr< const Space< BasisFunctionType > > &	domain,
		const shared_ptr< const Space< BasisFunctionType > > &	range,
		const shared_ptr< const Space< BasisFunctionType > > &	dualToRange,
		const std::string &	label,
		int	symmetry
	)

Constructor.

Parameters

[in]	domain	Function space being the domain of the operator.
[in]	range	Function space being the range of the operator.
[in]	dualToRange	Function space dual to the the range of the operator.
[in]	label	Textual label of the operator. If empty, a unique label is generated automatically.
[in]	symmetry	Symmetry of the weak form of the operator. Can be any combination of the flags defined in the enumeration type Symmetry.

None of the shared pointers may be null and the spaces range and dualToRange must be defined on the same grid, otherwise an exception is thrown.

Member Function Documentation

template<typename BasisFunctionType , typename KernelType , typename ResultType >

shared_ptr< DiscreteBoundaryOperator< ResultType > > Bempp::HypersingularIntegralOperator< BasisFunctionType, KernelType, ResultType >::assembleWeakFormImpl ( const Context< BasisFunctionType, ResultType > & context ) const

protectedvirtual

Assemble and return the operator's weak form.

This virtual function is invoked by assembleWeakForm() to do the actual work.

Implements Bempp::AbstractBoundaryOperator< BasisFunctionType_, ResultType_ >.

References Bempp::Context< BasisFunctionType, ResultType >::assemblyOptions(), Bempp::Context< BasisFunctionType, ResultType >::quadStrategy(), and Bempp::AssemblyOptions::verbosityLevel().

template<typename BasisFunctionType_ , typename KernelType_ , typename ResultType_ >

virtual const TestKernelTrialIntegral& Bempp::HypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >::integral ( ) const

privatepure virtual

Return an object representing the integral that is the first representation of the weak form of this operator (valid for all pairs of test and trial functions).

Subclasses of TestKernelTrialIntegral implement functions that evaluate the integral using the data provided by a CollectionOfKernels representing the kernel functions occurring in the integrand and a pair of CollectionOfShapesetTransformations objects representing the test and trial function transformations occurring in the integrand.

Implemented in Bempp::GeneralHypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >.

template<typename BasisFunctionType_ , typename KernelType_ , typename ResultType_ >

virtual const TestKernelTrialIntegral& Bempp::HypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >::offDiagonalIntegral ( ) const

privatepure virtual

Return an object representing the integral that is the second representation of the weak form of this operator (valid at least for pairs of test and trial functions with nonoverlapping supports).

Subclasses of TestKernelTrialIntegral implement functions that evaluate the integral using the data provided by a CollectionOfKernels representing the kernel functions occurring in the integrand and a pair of CollectionOfShapesetTransformations objects representing the test and trial basis function transformations occurring in the integrand.

Implemented in Bempp::GeneralHypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >.

template<typename BasisFunctionType_ , typename KernelType_ , typename ResultType_ >

virtual const CollectionOfShapesetTransformations& Bempp::HypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >::offDiagonalTestTransformations ( ) const

privatepure virtual

Return the collection of test-function transformations occurring in the second representation of the weak form of this operator (valid at least for pairs of test and trial functions with nonoverlapping supports).

It should normally be the mapping of shape functions (defined on the reference element) to basis functions (defined on the physical elements).

Implemented in Bempp::GeneralHypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >.

template<typename BasisFunctionType_ , typename KernelType_ , typename ResultType_ >

virtual const CollectionOfShapesetTransformations& Bempp::HypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >::offDiagonalTrialTransformations ( ) const

privatepure virtual

Return the collection of trial-function transformations occurring in the second representation of the weak form of this operator (valid at least for pairs of test and trial functions with nonoverlapping supports).

It should normally be the mapping of shape functions (defined on the reference element) to basis functions (defined on the physical elements).

Implemented in Bempp::GeneralHypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >.

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

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

Public Types

Public Member Functions

Protected Member Functions

Private Types

Private Member Functions

Detailed Description

template<typename BasisFunctionType_, typename KernelType_, typename ResultType_> class Bempp::HypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

template<typename BasisFunctionType_, typename KernelType_, typename ResultType_>
class Bempp::HypersingularIntegralOperator< BasisFunctionType_, KernelType_, ResultType_ >