Part of the far-field pattern of a radiating solution of the Helmholtz equation in 3D. More...

#include </home/wojtek/Projects/BEM/bempp-sven/bempp/lib/assembly/helmholtz_3d_far_field_double_layer_potential_operator.hpp>

Inheritance diagram for Bempp::Helmholtz3dFarFieldDoubleLayerPotentialOperator< BasisFunctionType_ >:

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

typedef Base::KernelType	KernelType
	Type of the values of kernel functions. More...

typedef Base::ResultType	ResultType
	Type of the values of the potential. More...

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

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

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

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

Public Types inherited from Bempp::Helmholtz3dPotentialOperatorBase< Helmholtz3dFarFieldDoubleLayerPotentialOperatorImpl< BasisFunctionType_ >, BasisFunctionType_ >
typedef Base::BasisFunctionType	BasisFunctionType
	Type of the values of the basis functions into which functions acted upon by the operator are expanded.

typedef Base::KernelType	KernelType
	Type of the values of kernel functions.

typedef Base::ResultType	ResultType
	Type of the values of the potential.

typedef Base::CoordinateType	CoordinateType

typedef Base::CollectionOfBasisTransformations	CollectionOfBasisTransformations

typedef Base::CollectionOfKernels	CollectionOfKernels

typedef Base::KernelTrialIntegral	KernelTrialIntegral

Public Types inherited from Bempp::ElementaryPotentialOperator< BasisFunctionType_, ScalarTraits< BasisFunctionType_ >::ComplexType, ScalarTraits< BasisFunctionType_ >::ComplexType >
typedef Base::BasisFunctionType	BasisFunctionType

typedef ScalarTraits < BasisFunctionType_ > ::ComplexType	KernelType
	Type of the values of the (components of the) kernel functions.

typedef Base::ResultType	ResultType

typedef Base::CoordinateType	CoordinateType

typedef Base::QuadratureStrategy	QuadratureStrategy

typedef Fiber::EvaluatorForIntegralOperators < ResultType >	Evaluator
	Type of the appropriate instantiation of Fiber::EvaluatorForIntegralOperators.

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

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

Public Types inherited from Bempp::PotentialOperator< BasisFunctionType_, ScalarTraits< BasisFunctionType_ >::ComplexType >
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 ScalarTraits < BasisFunctionType_ > ::ComplexType	ResultType
	Type of the values of the (components of the) potential.

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
	Helmholtz3dFarFieldDoubleLayerPotentialOperator (KernelType waveNumber)
	Constructor. More...

virtual	~Helmholtz3dFarFieldDoubleLayerPotentialOperator ()
	Destructor. More...

Public Member Functions inherited from Bempp::Helmholtz3dPotentialOperatorBase< Helmholtz3dFarFieldDoubleLayerPotentialOperatorImpl< BasisFunctionType_ >, BasisFunctionType_ >
	Helmholtz3dPotentialOperatorBase (KernelType waveNumber)
	Constructor. More...

	Helmholtz3dPotentialOperatorBase (const Helmholtz3dPotentialOperatorBase &other)
	Copy constructor.

virtual	~Helmholtz3dPotentialOperatorBase ()
	Destructor.

Helmholtz3dPotentialOperatorBase &	operator= (const Helmholtz3dPotentialOperatorBase &rhs)
	Assignment operator.

KernelType	waveNumber () const
	Return the wave number set previously in the constructor.

Public Member Functions inherited from Bempp::ElementaryPotentialOperator< BasisFunctionType_, ScalarTraits< BasisFunctionType_ >::ComplexType, ScalarTraits< BasisFunctionType_ >::ComplexType >
virtual std::auto_ptr < InterpolatedFunction < ScalarTraits < BasisFunctionType_ > ::ComplexType > >	evaluateOnGrid (const GridFunction< BasisFunctionType, ResultType > &argument, const Grid &evaluationGrid, const QuadratureStrategy &quadStrategy, const EvaluationOptions &options) const
	Evaluate the potential of a given charge distribution on a prescribed grid. More...

virtual arma::Mat < ScalarTraits < BasisFunctionType_ > ::ComplexType >	evaluateAtPoints (const GridFunction< BasisFunctionType, ResultType > &argument, const arma::Mat< CoordinateType > &evaluationPoints, const QuadratureStrategy &quadStrategy, const EvaluationOptions &options) const
	Evaluate the potential of a given charge distribution at prescribed points. More...

virtual AssembledPotentialOperator < BasisFunctionType_, ScalarTraits < BasisFunctionType_ > ::ComplexType >	assemble (const shared_ptr< const Space< BasisFunctionType > > &space, const shared_ptr< const arma::Mat< CoordinateType > > &evaluationPoints, const QuadratureStrategy &quadStrategy, const EvaluationOptions &options) const
	Create and return an AssembledPotentialOperator object. More...

virtual int	componentCount () const
	Number of components of the values of the potential. More...

Public Member Functions inherited from Bempp::PotentialOperator< BasisFunctionType_, ScalarTraits< BasisFunctionType_ >::ComplexType >
virtual	~PotentialOperator ()
	Destructor.

Private Types
typedef Helmholtz3dPotentialOperatorBase < Helmholtz3dFarFieldDoubleLayerPotentialOperatorImpl < BasisFunctionType_ > , BasisFunctionType_ >	Base

Detailed Description

template<typename BasisFunctionType_>
class Bempp::Helmholtz3dFarFieldDoubleLayerPotentialOperator< BasisFunctionType_ >

Part of the far-field pattern of a radiating solution of the Helmholtz equation in 3D.

The far-field pattern of a radiating solution to the Helmholtz equation in 3D is given by (Colton and Kress, p. 21)

$u_\infty(\hat x) = -u_{\infty,\mathrm{SL}}(\hat x) + u_{\infty,\mathrm{DL}}(\hat x),$

where $\hat x$ is a vector lying on the unit sphere,

$u_{\infty,\mathrm{SL}} = \frac{1}{4\pi} \int_S e^{-i k \hat x \cdot y} \frac{\partial u}{\partial n(y)}\, dS(y)$

and

$u_{\infty,\mathrm{DL}} = \frac{1}{4\pi} \int_S \frac{\partial e^{-i k \hat x \cdot y}}{\partial n_(y)} u(y)\, dS(y),$

with $n(y)$ denoting the unit vector normal to S at y.

This operator, applied to a grid function $u(y)$ defined on a surface S, and evaluated at a point $\hat x$ lying on the unit sphere, yields $u_{\infty,\mathrm{DL}}(\hat x)$ as defined above.

Template Parameters

BasisFunctionType_ Type of the values of the basis functions into which functions acted upon by the operator are expanded. It can take the following values: float, double, std::complex<float> and std::complex<double>.

See Also: Helmholtz equation in 3D