Dune::ACFem::RobinBoundaryOperatorParts< FunctionSpace, Indicator > Class Template Reference

A (homogeneous) Robin-boundary model. More...

#include <dune/acfem/models/modules/robinmodel.hh>

Collaboration diagram for Dune::ACFem::RobinBoundaryOperatorParts< FunctionSpace, Indicator >:

Public Types
enum	StructureFlags
enum	ConstituentFlags
typedef Expression	ExpressionType
	The type of the underlying expression.

Public Member Functions
template<class Intersection , class Point >
void	linearizedRobinFlux (const RangeType &uBar, const Intersection &intersection, const Point &x, const DomainType &unitOuterNormal, const RangeType &value, RangeType &result) const
	The linearized Robin-type flux term. More...
void	setEntity (const Entity &entity) const
void	flux (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, JacobianRangeType &flux) const
void	linearizedFlux (const RangeType &uBar, const JacobianRangeType &DuBar, const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, JacobianRangeType &flux) const
void	source (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, RangeType &result) const
void	linearizedSource (const RangeType &uBar, const JacobianRangeType &DuBar, const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, RangeType &result) const
void	robinFlux (const Intersection &intersection, const Point &x, const DomainType &unitOuterNormal, const RangeType &value, RangeType &result) const
void	fluxDivergence (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, const HessianRangeType &hessian, RangeType &result) const
const ExpressionType &	expression () const
	Return a const reference to the underlying expression.
ExpressionType &	expression ()
	Return a mutable reference to the underlying expression.
ExpressionType	operator* () const
	Return a copy from of the underlying expression.

Detailed Description

template<class FunctionSpace, class Indicator = EntireBoundaryIndicatorType>
class Dune::ACFem::RobinBoundaryOperatorParts< FunctionSpace, Indicator >

A (homogeneous) Robin-boundary model.

(linear) Robin boundary-conditions are in general boundary conditions of the following form

\[ (A(x)\nabla u(x))\cdot\nu(x) = c(x)\,(u^{\text{ext}}(x) - u(x))\text{ on }\Gamma_R \]

where \(A(x)\) is the coefficient matrix of the principle part of an associated PDE of 2nd order, \(c(x)\) is a given wnon-negative cofficient function and \(u^{\text{ext}}(x)\) is some given function.

This models the scenario that the flux of the qunatity u over the boundary is proportional to the difference to some prescribed external temperature distribution with transition coefficient \(c(x)\).

This particular model implements the following homogeneous special case:

\[ (A(x)\nabla u(x))\cdot\nu(x) = - u(x))\text{ on }\Gamma_R \]

The general non-homogeneous case with arbitrary coefficient function can be obtained by subtracting the inhomogeneity from the model and multiplying the resulting non-homogeneous Robin-model with transition coefficent 1 by the desired transition coefficent, which may be a constant, parameter of function.

Parameters

[in]

Indicator

The boundary indicator function which decides on which part of the boundary the Robin boundary conditions is imposed.

Note

Note also that the inhomogeneity uExt is internally incorporated into the Neumann boundary data.

Member Enumeration Documentation

ConstituentFlags

enum Dune::ACFem::DefaultOperatorParts::ConstituentFlags

inherited

StructureFlags

enum Dune::ACFem::DefaultOperatorParts::StructureFlags

inherited

Member Function Documentation

flux()

void Dune::ACFem::DefaultOperatorParts< Expression >::flux ( const Entity &  entity, const Point &  x, const RangeType &  value, const JacobianRangeType &  jacobian, JacobianRangeType &  flux  ) const

inlineinherited

fluxDivergence()

void Dune::ACFem::DefaultOperatorParts< Expression >::fluxDivergence ( const Entity &  entity, const Point &  x, const RangeType &  value, const JacobianRangeType &  jacobian, const HessianRangeType &  hessian, RangeType &  result  ) const

inlineinherited

linearizedFlux()

void Dune::ACFem::DefaultOperatorParts< Expression >::linearizedFlux ( const RangeType &  uBar, const JacobianRangeType &  DuBar, const Entity &  entity, const Point &  x, const RangeType &  value, const JacobianRangeType &  jacobian, JacobianRangeType &  flux  ) const

inlineinherited

linearizedSource()

void Dune::ACFem::DefaultOperatorParts< Expression >::linearizedSource ( const RangeType &  uBar, const JacobianRangeType &  DuBar, const Entity &  entity, const Point &  x, const RangeType &  value, const JacobianRangeType &  jacobian, RangeType &  result  ) const

inlineinherited

robinFlux()

void Dune::ACFem::DefaultOperatorParts< Expression >::robinFlux ( const Intersection &  intersection, const Point &  x, const DomainType &  unitOuterNormal, const RangeType &  value, RangeType &  result  ) const

inlineinherited

setEntity()

void Dune::ACFem::DefaultOperatorParts< Expression >::setEntity ( const Entity &  entity ) const

inlineinherited

source()

void Dune::ACFem::DefaultOperatorParts< Expression >::source ( const Entity &  entity, const Point &  x, const RangeType &  value, const JacobianRangeType &  jacobian, RangeType &  result  ) const

inlineinherited

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

• dune/acfem/models/modules/robinmodel.hh