Dune::ACFem::PDEModel::RobinBoundaryModel< FunctionSpace, Indicator > Class Template Reference

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

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

Collaboration diagram for Dune::ACFem::PDEModel::RobinBoundaryModel< FunctionSpace, Indicator >:

Public Member Functions
template<class Intersection >
auto	classifyBoundary (const Intersection &intersection)
auto	linearizedRobinFlux (const DomainType &unitOuterNormal, const RangeType &value) const

FunctionSpaceTypes
Forward some basic type from the supplied function-spaces to the model class. Note that FunctionSpace is defined as a shortcut for RangeFunctionSpace in order to simplify the common case DomainFunctionSpace == RangeFunctionSpace.
using	HessianRangeSelector = typename std::conditional< std::is_convertible< typename FunctionSpace::RangeType, typename FunctionSpace::HessianRangeType >::value, Fem::ExplicitFieldVector< typename FunctionSpace::HessianRangeType::value_type, FunctionSpace::dimRange >, typename FunctionSpace::HessianRangeType >::type
	The type returned by classifyBoundary().
using	RangeFunctionSpaceType = FunctionSpace
	The type returned by classifyBoundary().
using	DomainFunctionSpaceType = FunctionSpace
	The type returned by classifyBoundary().
using	FunctionSpaceType = RangeFunctionSpaceType
	The type returned by classifyBoundary().
using	DomainType = typename FunctionSpaceType::DomainType
	The type returned by classifyBoundary().
using	RangeType = typename FunctionSpaceType::RangeType
	The type returned by classifyBoundary().
using	JacobianRangeType = typename FunctionSpaceType::JacobianRangeType
	The type returned by classifyBoundary().
using	HessianRangeType = HessianRangeSelector< FunctionSpaceType >
	The type returned by classifyBoundary().
using	DomainFieldType = typename FunctionSpaceType::DomainFieldType
	The type returned by classifyBoundary().
using	RangeFieldType = typename FunctionSpaceType::RangeFieldType
	The type returned by classifyBoundary().
using	DomainRangeType = typename DomainFunctionSpaceType::RangeType
	The type returned by classifyBoundary().
using	DomainDomainType = typename DomainFunctionSpaceType::DomainType
	The type returned by classifyBoundary().
using	DomainJacobianRangeType = typename DomainFunctionSpaceType::JacobianRangeType
	The type returned by classifyBoundary().
using	DomainHessianRangeType = HessianRangeSelector< DomainFunctionSpaceType >
	The type returned by classifyBoundary().
using	DomainDomainFieldType = typename DomainFunctionSpaceType::DomainFieldType
	The type returned by classifyBoundary().
using	DomainRangeFieldType = typename DomainFunctionSpaceType::RangeFieldType
	The type returned by classifyBoundary().
using	RangeRangeType = typename RangeFunctionSpaceType::RangeType
	The type returned by classifyBoundary().
using	RangeDomainType = typename RangeFunctionSpaceType::DomainType
	The type returned by classifyBoundary().
using	RangeJacobianRangeType = typename RangeFunctionSpaceType::JacobianRangeType
	The type returned by classifyBoundary().
using	RangeHessianRangeType = HessianRangeSelector< RangeFunctionSpaceType >
	The type returned by classifyBoundary().
using	RangeDomainFieldType = typename RangeFunctionSpaceType::DomainFieldType
	The type returned by classifyBoundary().
using	RangeRangeFieldType = typename RangeFunctionSpaceType::RangeFieldType
	The type returned by classifyBoundary().
using	BoundaryConditionsType = std::pair< bool, std::bitset< dimRange > >
	The type returned by classifyBoundary().
void	bind (const Entity &entity)
	Bind to the given entity. More...
void	unbind ()
	Unbind from the previously bound entity. More...
static constexpr int	dimDomain
	The type returned by classifyBoundary().
static constexpr int	dimRange
	The type returned by classifyBoundary().
static constexpr int	domainDimDomain
	The type returned by classifyBoundary().
static constexpr int	domainDimRange
static constexpr int	rangeDimDomain
	The type returned by classifyBoundary().
static constexpr int	rangeDimRange

Detailed Description

template<class FunctionSpace, class Indicator = EntireBoundaryIndicator>
class Dune::ACFem::PDEModel::RobinBoundaryModel< 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 Function Documentation

bind()

void Dune::ACFem::ModelBase< FunctionSpace , FunctionSpace >::bind ( const Entity &  entity )

inlineinherited

Bind to the given entity.

Parameters

[in]

entity

The entity to bind to.

Warning

Calling any other method without first binding the model results in undefined behaviour.

Models needing this method need to reimplement it. This is just here to obey the "bindable" interface of Dune::Fem.

unbind()

void Dune::ACFem::ModelBase< FunctionSpace , FunctionSpace >::unbind ( )

inlineinherited

Unbind from the previously bound entity.

Warning

Calling this method on an unbound model may cause undefined behaviour.

Models needing this method need to reimplement it. This is just here to obey the "bindable" interface of Dune::Fem.

Member Data Documentation

domainDimRange

constexpr int Dune::ACFem::ModelBase< FunctionSpace , FunctionSpace >::domainDimRange

staticconstexprinherited

rangeDimRange

constexpr int Dune::ACFem::ModelBase< FunctionSpace , FunctionSpace >::rangeDimRange

staticconstexprinherited

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

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