DUNE-ACFEM (2.5.1)

Public Types | Public Member Functions | List of all members
Dune::ACFem::RobinBoundaryOperatorParts< FunctionSpace, Indicator > Class Template Reference
PDE-Models » Model Building Blocks » Building Blocks for Boundary Conditions

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]IndicatorThe 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

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