Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem > Struct Template Reference

A model for a second order elliptic operator. More...

#include <dune/acfem/models/ellipticmodel.hh>

Collaboration diagram for Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >:

Public Member Functions
	EllipticModel (const ProblemType &problem)
	Constructor taking problem reference. More...
template<class Entity , class Point >
void	flux (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, JacobianRangeType &flux) const
template<class Entity , class Point >
void	linearizedFlux (const RangeType &uBar, const JacobianRangeType &DuBar, const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, JacobianRangeType &flux) const
template<class Entity , class Point >
void	source (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, RangeType &result) const
template<class Entity , class Point >
void	linearizedSource (const RangeType &uBar, const JacobianRangeType &DuBar, const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, RangeType &result) const
template<class Intersection , class Point >
void	robinFlux (const Intersection &intersection, const Point &x, const DomainType &unitOuterNormal, const RangeType &value, RangeType &result) const
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
template<class Entity , class Point >
void	fluxDivergence (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, const HessianRangeType &hessian, RangeType &result) const
BulkForcesFunctionType	bulkForcesFunction (const GridPartType &gridPart) const
	Return a grid functin adapter for the external forces, see class Dune::Fem::GridFunctionAdapter.
DirichletBoundaryFunctionType	dirichletBoundaryFunction (const GridPartType &gridPart) const
	Return a grid functin adapter for the Dirichlet boundary values, see class Dune::Fem::GridFunctionAdapter.
DirichletWeightFunctionType	dirichletWeightFunction (const GridPartType &gridPart) const
	Return the trivial constant one function as Dirichlet weight.
NeumannBoundaryFunctionType	neumannBoundaryFunction (const GridPartType &gridPart) const
	Return a grid functin adapter for the Neumann boundary values, see class Dune::Fem::GridFunctionAdapter.
ExactSolutionFunctionType	exactSolutionFunction (const GridPartType &gridPart) const
	Return a grid function for a "exact solution" for experimental convergence tests.
const ProblemType &	problem () const
	return reference to problem
std::string	name () const
	Print a descriptive name for debugging and output.
TraitsType::template ForcesFunctionalTraits< DiscreteFunctionSpace >::FunctionalType	forcesFunctional (const DiscreteFunctionSpace &space) const

Protected Attributes
const ProblemType &	problem_
	Pointer to the underlying problem.
Problem data-instances
In principle it would be possible to use the GridFunction Wrapper to avoid references to temporaries, but simply constructing the data-functions and keep them here is much safer. @[
DirichletBoundaryType	dirichletFunction_
NeumannBoundaryType	neumannFunction_
BulkForcesType	bulkForcesFunction_
ExactSolutionType	solutionFunction_
DirichletIndicatorType	dirichletIndicator_
NeumannIndicatorType	neumannIndicator_
RobinIndicatorType	robinIndicator_

Detailed Description

template<class FunctionSpace, class GridPart, class Problem = ProblemInterface<FunctionSpace>>
struct Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >

A model for a second order elliptic operator.

The model defines the different parts needed to compute the weak form of a second order elliptic operator. The model is constructed in a way that it could be used to implement the linearization of a potentially non-linear operator of the form

\[ \begin{split} -\nabla\cdot (A(x, u)\,\nabla u) + \nabla\cdot(b(x, u)\,u) + c(x, u)\,u &= f(x)\quad \text{ in }\Omega,\\ u &= g_D \text{ on }\Gamma_D,\\ (A(x, u)\nabla u)\cdot\nu + \alpha(x, u)\,u &= g_N \text{ on }\Gamma_R,\\ (A(x, u)\nabla u)\cdot\nu &= g_N \text{ on }\Gamma_N,\\ \end{split} \]

The underlying default problem interface, however, is not suitable for non-linear problems, i.e. it ignores any extra "non-linear" parameters passed to the local functions of the model.

The methods in this class provide all factors of the integrands not involving test functions. The multiplication by the test-functions is added in the class EllipticOperator. The weak formulation then reads:

\[ \int_\Omega (A(x,u)\,\nabla u)\cdot\nabla\phi\,dx + \int_\Omega (\nabla\cdot(b(x, u)\,u) + c(x, u)\,u)\,\phi\,dx + \int_{\Gamma_R} \alpha(x, u)\,u\,\phi\,do - \int_{\Gamma_R\cup\Gamma_N} g_N\,\phi\,do - \int_\Omega f(x)\,\phi\,dx = 0. \]

Parameters

[in]	FunctionSpace	The function space type where everything lives; in particular defining the rang and domain of each function (Note: this is not the discrete function space).
[in]	Problem	A class describing a linear elliptic problem in global coordinates. Defaults to class ProblemInterface.

Member Function Documentation

forcesFunctional()

TraitsType::template ForcesFunctionalTraits< DiscreteFunctionSpace >::FunctionalType Dune::ACFem::DefaultModel< EllipticModel< FunctionSpace, GridPart, ProblemInterface< FunctionSpace > > >::forcesFunctional ( const DiscreteFunctionSpace &  space ) const

inlineinherited

Generate an instance of a class defining a functional which forms part of the force-terms for the model.

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

• dune/acfem/models/ellipticmodel.hh