exahype2.api.blockstructured.SommerfeldBoundaryConditions.SommerfeldBoundaryConditions Class Reference

Sommerfeld (radiative, outgoing) boundary conditions: waves leave the domain with little reflection, and the solution approaches a far-field solution towards infinity. More...

Inheritance diagram for exahype2.api.blockstructured.SommerfeldBoundaryConditions.SommerfeldBoundaryConditions:

Collaboration diagram for exahype2.api.blockstructured.SommerfeldBoundaryConditions.SommerfeldBoundaryConditions:

Data Structures
class	Generator
	SommerfeldBoundaryConditions-specific code generation. More...

Public Member Functions
	__init__ (self, str implementation=None, Sequence[float] origin=None, bool stateless=False)
	get_origin (self, int dimensions)
	The origin with one entry per dimension.
Public Member Functions inherited from exahype2.api.PDETerm.PDETerm
str	__repr__ (self)
str	__str__ (self)
"PDETerm.Generator"	generator (self)
	Code generator for this term: an instance of this term's own (possibly subclass-specific) Generator.

Data Fields
	origin
	The origin with one entry per dimension.
Data Fields inherited from exahype2.api.PDETerm.PDETerm
	name
	implementation
	stateless

Static Public Attributes
tuple	SIGNATURE
str	NAME = "sommerfeldFarFieldSolution"
Static Public Attributes inherited from exahype2.api.PDETerm.PDETerm
str	NAME
str	SIGNATURE

Detailed Description

Sommerfeld (radiative, outgoing) boundary conditions: waves leave the domain with little reflection, and the solution approaches a far-field solution towards infinity.

The term is an alternative to exahype2.api.DirichletBoundaryConditions. exahype2::blockstructured::applySommerfeldBoundaryConditions() documents the conditions, their discretisation, and how block-structured schemes realise them. The user specifies the far-field solution \( u_\\infty \):

virtual void sommerfeldFarFieldSolution(
  const tarch::la::Vector<Dimensions, double>& x,
  double* __restrict__                         Q // Q[{{NUMBER_OF_UNKNOWNS}}+{{NUMBER_OF_AUXILIARY_VARIABLES}}]
);

Only the first NUMBER_OF_UNKNOWNS entries of Q are read, i.e. the implementation does not have to set the auxiliary variables.

The wave speed is the solver's maximum eigenvalue along the face normal, i.e. the solver has to hold a non-stateless exahype2.api.MaxEigenvalue term. The ghost cells are initialised with the initial condition (exahype2.api.InitPointWisely) before the first time step.

Different to Dirichlet conditions, there is no separate boundary task in the time step. The Sommerfeld update replaces the roll over of the face data instead (

See also

exahype2.api.fv.actionsets.RollOverUpdatedFaceWithSommerfeldBoundaryConditions and exahype2.api.rkfd4.actionsets.RollOverUpdatedFaceWithSommerfeldBoundaryConditions). Runge-Kutta schemes accept the term only if the time stamps of their stages do not decrease.

A solver needs a boundary condition term if and only if at least one axis of the domain is not periodic (

See also

exahype2.api.blockstructured.BoundaryConditions.get_boundary_conditions()).

Only the non-stateless variant is supported, i.e. the term has to be added with stateless=False.

Definition at line 10 of file SommerfeldBoundaryConditions.py.

Constructor & Destructor Documentation

__init__()

exahype2.api.blockstructured.SommerfeldBoundaryConditions.SommerfeldBoundaryConditions.__init__	(		self,
		str	implementation = None,
		Sequence[float]	origin = None,
		bool	stateless = False
	)

Parameters

implementation	str A C++ snippet that becomes sommerfeldFarFieldSolution()'s body, or None (the default) to leave sommerfeldFarFieldSolution() pure virtual for you to implement by hand.
origin	Sequence[float] Centre of the system, i.e. the point the outgoing spherical waves emanate from. One entry per dimension. None (the default) is the origin of the coordinate system.
stateless	bool Has to be False,

See also

the class documentation.

Reimplemented from exahype2.api.PDETerm.PDETerm.

Definition at line 61 of file SommerfeldBoundaryConditions.py.

References exahype2.api.blockstructured.SommerfeldBoundaryConditions.SommerfeldBoundaryConditions.__init__(), exahype2.api.blockstructured.DirichletBoundaryConditions.DirichletBoundaryConditions.NAME, exahype2.api.blockstructured.SommerfeldBoundaryConditions.SommerfeldBoundaryConditions.NAME, exahype2.api.Flux.Flux.NAME, exahype2.api.GradientRefinement.GradientRefinement.NAME, exahype2.api.InitPointWisely.InitPointWisely.NAME, exahype2.api.MassMatrix.MassMatrix.NAME, exahype2.api.MaxEigenvalue.MaxEigenvalue.NAME, exahype2.api.NonconservativeProduct.NonconservativeProduct.NAME, exahype2.api.PDETerm.PDETerm.NAME, exahype2.api.PointSource.PointSource.NAME, exahype2.api.RefineErasePointwisely.RefineErasePointwisely.NAME, and exahype2.api.VolumetricSource.VolumetricSource.NAME.

Referenced by exahype2.api.blockstructured.SommerfeldBoundaryConditions.SommerfeldBoundaryConditions.__init__().

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Member Function Documentation

get_origin()

exahype2.api.blockstructured.SommerfeldBoundaryConditions.SommerfeldBoundaryConditions.get_origin	(		self,
		int	dimensions
	)

The origin with one entry per dimension.

Parameters

dimensions

int Number of dimensions of the domain.

Returns

List[float]

Definition at line 90 of file SommerfeldBoundaryConditions.py.

References exahype2.api.blockstructured.SommerfeldBoundaryConditions.SommerfeldBoundaryConditions.origin.

Field Documentation

NAME

str exahype2.api.blockstructured.SommerfeldBoundaryConditions.SommerfeldBoundaryConditions.NAME = "sommerfeldFarFieldSolution"

static

Definition at line 59 of file SommerfeldBoundaryConditions.py.

Referenced by exahype2.api.blockstructured.DirichletBoundaryConditions.DirichletBoundaryConditions.__init__(), exahype2.api.Flux.Flux.__init__(), exahype2.api.GradientRefinement.GradientRefinement.__init__(), exahype2.api.InitPointWisely.InitPointWisely.__init__(), exahype2.api.MassMatrix.MassMatrix.__init__(), exahype2.api.MaxEigenvalue.MaxEigenvalue.__init__(), exahype2.api.NonconservativeProduct.NonconservativeProduct.__init__(), exahype2.api.PointSource.PointSource.__init__(), exahype2.api.RefineErasePointwisely.RefineErasePointwisely.__init__(), exahype2.api.VolumetricSource.VolumetricSource.__init__(), and exahype2.api.blockstructured.SommerfeldBoundaryConditions.SommerfeldBoundaryConditions.__init__().

origin

exahype2.api.blockstructured.SommerfeldBoundaryConditions.SommerfeldBoundaryConditions.origin

The origin with one entry per dimension.

Parameters

dimensions

int Number of dimensions of the domain.

Returns

List[float]

Definition at line 88 of file SommerfeldBoundaryConditions.py.

Referenced by exahype2.api.blockstructured.SommerfeldBoundaryConditions.SommerfeldBoundaryConditions.get_origin().

SIGNATURE

tuple exahype2.api.blockstructured.SommerfeldBoundaryConditions.SommerfeldBoundaryConditions.SIGNATURE

static

Initial value:

=  (
        "const tarch::la::Vector<Dimensions, double>& x, " "double* __restrict__ Q"
    )

Definition at line 55 of file SommerfeldBoundaryConditions.py.

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

• src/exahype2/api/blockstructured/SommerfeldBoundaryConditions.py