Adjoint abstract boundary operator. More...

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

Inheritance diagram for Bempp::AdjointAbstractBoundaryOperator< BasisFunctionType_, 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...

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
	AdjointAbstractBoundaryOperator (const BoundaryOperator< BasisFunctionType, ResultType > &boundaryOp, int symmetry=AUTO_SYMMETRY)
	Constructor. More...

	AdjointAbstractBoundaryOperator (const BoundaryOperator< BasisFunctionType, ResultType > &boundaryOp, const shared_ptr< const Space< BasisFunctionType > > &range, int symmetry=AUTO_SYMMETRY)
	Constructor. More...

virtual bool	isLocal () const
	Return whether this operator is local. More...

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 Attributes
BoundaryOperator < BasisFunctionType, ResultType >	m_operator

Detailed Description

template<typename BasisFunctionType_, typename ResultType_>
class Bempp::AdjointAbstractBoundaryOperator< BasisFunctionType_, ResultType_ >

Adjoint abstract boundary operator.

This class represents the adjoint of an abstract boundary operator.

Currently the adjoint operator can be constructed only for operators acting on real-valued basis functions. Let $A$ be such an operator, and let $\mathsf{A}$ be its discrete weak form. Then the discrete weak form of the adjoint of $A$ is the transpose of $\mathsf{A}$ .

Note that this definition is not the one most usual in mathematics (where the conjugate transpose would be used). However, it corresponds to the relation between the double-layer potential boundary operator and adjoint double-layer potential boundary operator for Laplace and Helmholtz equation as defined in standard texts. Hence, for example, the discrete weak forms of the operators B and C in the code snippet below are numerically identical (at least to within quadrature accuracy):

BoundaryOperator<BFT, RT> A =
    helmholtz3dDoubleLayerBoundaryOperator<BFT>(
        context, domain, range, dualToRange, waveNumber);
BoundaryOperator<BFT, RT> B =
    helmholtz3dAdjointDoubleLayerBoundaryOperator<BFT>(
        context, domain, range, dualToRange, waveNumber);
BoundaryOperator<BFT, RT> C = adjoint(A);

See Also: adjoint().

Member Typedef Documentation

template<typename BasisFunctionType_ , typename ResultType_ >

typedef Base::BasisFunctionType Bempp::AdjointAbstractBoundaryOperator< BasisFunctionType_, 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 ResultType_ >

typedef Base::CoordinateType Bempp::AdjointAbstractBoundaryOperator< BasisFunctionType_, ResultType_ >::CoordinateType

Type used to represent coordinates.

template<typename BasisFunctionType_ , typename ResultType_ >

typedef Base::QuadratureStrategy Bempp::AdjointAbstractBoundaryOperator< BasisFunctionType_, ResultType_ >::QuadratureStrategy

Type of the appropriate instantiation of Fiber::QuadratureStrategy.

template<typename BasisFunctionType_ , typename ResultType_ >

typedef Base::ResultType Bempp::AdjointAbstractBoundaryOperator< BasisFunctionType_, ResultType_ >::ResultType

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

Constructor & Destructor Documentation

template<typename BasisFunctionType , typename ResultType >

Bempp::AdjointAbstractBoundaryOperator< BasisFunctionType, ResultType >::AdjointAbstractBoundaryOperator	(	const BoundaryOperator< BasisFunctionType, ResultType > &	boundaryOp,
		int	symmetry = `AUTO_SYMMETRY`
	)

Constructor.

Construct the boundary operator $\alpha L$ , where $\alpha$ is the scalar weight and $L$ is the operator represented by boundaryOp.

By default the symmetry of the weak form of the resulting operator is determined automatically. It can be set manually via the parameter symmetry, which can be any combination of the flags defined in the enumeration type Symmetry.

References Bempp::BoundaryOperator< BasisFunctionType, ResultType >::domain(), Bempp::BoundaryOperator< BasisFunctionType, ResultType >::dualToRange(), and Bempp::BoundaryOperator< BasisFunctionType, ResultType >::range().

template<typename BasisFunctionType , typename ResultType >

Bempp::AdjointAbstractBoundaryOperator< BasisFunctionType, ResultType >::AdjointAbstractBoundaryOperator	(	const BoundaryOperator< BasisFunctionType, ResultType > &	boundaryOp,
		const shared_ptr< const Space< BasisFunctionType > > &	range,
		int	symmetry = `AUTO_SYMMETRY`
	)

Constructor.

This constructor allows to explicitly specify the range space. This is useful if the standard heuristic to detect this space fails. An example is a boundary operator, where the domain and range live on different grids.

Member Function Documentation

template<typename BasisFunctionType , typename ResultType >

shared_ptr< DiscreteBoundaryOperator< ResultType > > Bempp::AdjointAbstractBoundaryOperator< BasisFunctionType, 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::TRANSPOSE.

template<typename BasisFunctionType , typename ResultType >

bool Bempp::AdjointAbstractBoundaryOperator< BasisFunctionType, ResultType >::isLocal ( ) const

virtual

Return whether this operator is local.

Suppose that an operator $A$ acting on a function $f(x)$ produces another function $g(x)$ . We say that $A$ is local if the value of $g$ at any point $x$ depends only on the values of $f$ in an infinitesimal neighbourhood of $x$ .

Multiplicative and differential operators are local and discretization of their weak forms with finite elements leads to sparse matrices. Conversely, integral operators are in general non-local and discretization of their weak forms leads to dense matrices.

Implements Bempp::AbstractBoundaryOperator< BasisFunctionType_, ResultType_ >.

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

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

Public Types

Public Member Functions

Protected Member Functions

Private Types

Private Attributes

Detailed Description

template<typename BasisFunctionType_, typename ResultType_> class Bempp::AdjointAbstractBoundaryOperator< BasisFunctionType_, ResultType_ >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

template<typename BasisFunctionType_, typename ResultType_>
class Bempp::AdjointAbstractBoundaryOperator< BasisFunctionType_, ResultType_ >