"Identity operator" for Maxwell equations in 3D. More...

#include </home/wojtek/Projects/BEM/bempp-sven/bempp/lib/assembly/maxwell_3d_identity_operator.hpp>

Inheritance diagram for Bempp::Maxwell3dIdentityOperator< 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...

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

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

Public Types inherited from Bempp::ElementaryLocalOperator< BasisFunctionType_, ResultType_ >
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::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::TestTrialIntegral < BasisFunctionType, ResultType >	TestTrialIntegral
	Type of the appropriate instantiation of Fiber::TestTrialIntegral.

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
	Maxwell3dIdentityOperator (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=NO_SYMMETRY)
	Constructor. More...

Public Member Functions inherited from Bempp::ElementaryLocalOperator< BasisFunctionType_, ResultType_ >
	ElementaryLocalOperator (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 true.

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...

Private Types
typedef ElementaryLocalOperator < BasisFunctionType_, ResultType_ >	Base

Private Member Functions
virtual const CollectionOfBasisTransformations &	testTransformations () const
	Return the collection of test function transformations occurring in the weak form of this operator.

virtual const CollectionOfBasisTransformations &	trialTransformations () const
	Return the collection of trial function transformations occurring in the weak form of this operator.

virtual const TestTrialIntegral &	integral () const
	Return an object representing the integral that is the weak form of this operator. More...

Related Functions
(Note that these are not member functions.)
template<typename BasisFunctionType , typename ResultType >
BoundaryOperator < BasisFunctionType, ResultType >	maxwell3dIdentityOperator (const shared_ptr< const Context< BasisFunctionType, ResultType > > &context, 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=NO_SYMMETRY)
	Construct a BoundaryOperator object wrapping a Maxwell3dIdentityOperator. More...

Additional Inherited Members
Static Public Member Functions inherited from Bempp::AbstractBoundaryOperator< BasisFunctionType_, ResultType_ >
static std::string	uniqueLabel ()
	Generate and return a new unique label "OpN", where N is a number.

Protected Member Functions inherited from Bempp::ElementaryLocalOperator< BasisFunctionType_, ResultType_ >
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.

Detailed Description

template<typename BasisFunctionType_, typename ResultType_>
class Bempp::Maxwell3dIdentityOperator< BasisFunctionType_, ResultType_ >

"Identity operator" for Maxwell equations in 3D.

This class represents an operator $I_{\mathrm{M}}$ whose weak form (under the standard inner product) is

$\langle \boldsymbol u, I_{\mathrm{M}} \boldsymbol v \rangle = \int_\Gamma \boldsymbol u^*(\boldsymbol x) \cdot [\boldsymbol v(\boldsymbol x) \times \boldsymbol n(\boldsymbol x)] \, \mathrm{d}\Gamma(\boldsymbol x),$

where $\boldsymbol n(\boldsymbol x)$ is the outward unit vector normal to the surface $\Gamma$ at the point $\boldsymbol x$ . Thus, the weak form of this operator is identical to the weak form of the standard identity operator under the antisymmetric pseudo-inner product $\langle \cdot, \cdot\rangle_{\boldsymbol\tau, \Gamma}$ defined in Maxwell equations in 3D.