In the style of the dune-fem-school-generator we define here dynamic problem descriptions and an EllipticModel such that an application can switch between example problems at run-time. More...

Classes
struct	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >
	A model for a second order elliptic operator. More...

class	Dune::ACFem::ProblemInterface< FunctionSpace >
	Problem interface which describes a second order elliptic boundary problem: More...

class	Dune::ACFem::TransientProblemInterface< FunctionSpace, TimeProvider >
	problem interface class for time dependent problem descriptions, i.e. More...

Enumerations
enum	Dune::ACFem::ModelTraits< EllipticModel< FunctionSpace, GridPart, Problem > >::ConstituentFlags { Dune::ACFem::ModelTraits< EllipticModel< FunctionSpace, GridPart, Problem > >::hasFlux = true , Dune::ACFem::ModelTraits< EllipticModel< FunctionSpace, GridPart, Problem > >::hasSources = true }

Functions
	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::EllipticModel (const ProblemType &problem)
	Constructor taking problem reference. More...

template<class Entity , class Point >
void	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::flux (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, JacobianRangeType &flux) const

template<class Entity , class Point >
void	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::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	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::source (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, RangeType &result) const

template<class Entity , class Point >
void	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::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	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::robinFlux (const Intersection &intersection, const Point &x, const DomainType &unitOuterNormal, const RangeType &value, RangeType &result) const

template<class Intersection , class Point >
void	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::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	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::fluxDivergence (const Entity &entity, const Point &x, const RangeType &value, const JacobianRangeType &jacobian, const HessianRangeType &hessian, RangeType &result) const

BulkForcesFunctionType	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::bulkForcesFunction (const GridPartType &gridPart) const
	Return a grid functin adapter for the external forces, see class Dune::Fem::GridFunctionAdapter.

DirichletBoundaryFunctionType	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::dirichletBoundaryFunction (const GridPartType &gridPart) const
	Return a grid functin adapter for the Dirichlet boundary values, see class Dune::Fem::GridFunctionAdapter.

DirichletWeightFunctionType	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::dirichletWeightFunction (const GridPartType &gridPart) const
	Return the trivial constant one function as Dirichlet weight.

NeumannBoundaryFunctionType	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::neumannBoundaryFunction (const GridPartType &gridPart) const
	Return a grid functin adapter for the Neumann boundary values, see class Dune::Fem::GridFunctionAdapter.

ExactSolutionFunctionType	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::exactSolutionFunction (const GridPartType &gridPart) const
	Return a grid function for a "exact solution" for experimental convergence tests.

const ProblemType &	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::problem () const
	return reference to problem

virtual bool	Dune::ACFem::ProblemInterface< FunctionSpace >::has (OperatorPartsType what) const
	May be used for optimizations during assembly. More...

virtual void	Dune::ACFem::ProblemInterface< FunctionSpace >::f (const DomainType &x, RangeType &value) const
	the right hand side data (default = 0)

virtual void	Dune::ACFem::ProblemInterface< FunctionSpace >::u (const DomainType &x, RangeType &value) const
	the exact solution (default = 0)

virtual void	Dune::ACFem::ProblemInterface< FunctionSpace >::uJacobian (const DomainType &x, JacobianRangeType &value) const
	the jacobian of the exact solution (default = 0)

virtual bool	Dune::ACFem::ProblemInterface< FunctionSpace >::isDirichletSegment (const int bndId, const DomainType &center) const
	Classification of the kind of boundary conditions which applies to a boundary segment with the given Id. More...

virtual bool	Dune::ACFem::ProblemInterface< FunctionSpace >::isNeumannSegment (const int bndId, const DomainType &center) const
	Classification of the kind of boundary conditions which applies to a boundary segment with the given Id. More...

virtual bool	Dune::ACFem::ProblemInterface< FunctionSpace >::isRobinSegment (const int bndId, const DomainType &center) const
	Classification of the kind of boundary conditions which applies to a boundary segment with the given Id. More...

virtual void	Dune::ACFem::ProblemInterface< FunctionSpace >::dirichletData (const DomainType &x, RangeType &value) const
	The Dirichlet boundary data. More...

virtual void	Dune::ACFem::ProblemInterface< FunctionSpace >::neumannData (const DomainType &x, RangeType &value) const
	The Neumann boundary data. More...

virtual void	Dune::ACFem::ProblemInterface< FunctionSpace >::robinData (const DomainType &x, const RangeType &u, RangeType &value) const
	The Robin boundary data. More...

virtual void	Dune::ACFem::ProblemInterface< FunctionSpace >::secondOrderCoefficient (const DomainType &x, const JacobianRangeType &gradient, JacobianRangeType &result) const
	This method has to implement the second order term for the weak formulation, it needs to compute. More...

virtual void	Dune::ACFem::ProblemInterface< FunctionSpace >::secondOrderCoefficient (const DomainType &x, const JacobianRangeType &Du, const HessianRangeType &D2u, RangeType &result) const
	This method has to implement the second order term for the point-wise operator. More...

virtual void	Dune::ACFem::ProblemInterface< FunctionSpace >::firstOrderCoefficient (const DomainType &x, const RangeType &u, const JacobianRangeType &Du, RangeType &result) const
	First order term with derivative on u. More...

virtual void	Dune::ACFem::ProblemInterface< FunctionSpace >::zeroOrderCoefficient (const DomainType &x, const RangeType &u, RangeType &result) const
	Zero order coefficient. More...

void	Dune::ACFem::ProblemInterface< FunctionSpace >::FunctionWrapper< id >::evaluate (const DomainType &x, RangeType &ret) const
	evaluate function

void	Dune::ACFem::ProblemInterface< FunctionSpace >::FunctionWrapper< id >::jacobian (const DomainType &x, JacobianRangeType &jac) const
	jacobian of the function

	Dune::ACFem::TransientProblemInterface< FunctionSpace, TimeProvider >::TransientProblemInterface (const TimeProviderType &timeProvider, double theta=0.0)
	constructor taking time provider

double	Dune::ACFem::TransientProblemInterface< FunctionSpace, TimeProvider >::time () const
	return current simulation time

double	Dune::ACFem::TransientProblemInterface< FunctionSpace, TimeProvider >::deltaT () const
	return current time step size ( \(\Delta_t\))

const TimeViewType &	Dune::ACFem::TransientProblemInterface< FunctionSpace, TimeProvider >::timeView () const
	return reference to Problem's time provider

TimeViewType &	Dune::ACFem::TransientProblemInterface< FunctionSpace, TimeProvider >::timeView ()
	return reference to Problem's time provider

Variables
const ProblemType &	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::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	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::dirichletFunction_

NeumannBoundaryType	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::neumannFunction_

BulkForcesType	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::bulkForcesFunction_

ExactSolutionType	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::solutionFunction_

DirichletIndicatorType	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::dirichletIndicator_

NeumannIndicatorType	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::neumannIndicator_

RobinIndicatorType	Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::robinIndicator_

Detailed Description

In the style of the dune-fem-school-generator we define here dynamic problem descriptions and an EllipticModel such that an application can switch between example problems at run-time.

In principle, however, this is not the way to go when writing efficient code for a single, well defined problem. In that case one would rather write the operator "germs" at the ModelInterface level directly.

As the EllipticModel takes a ProblemClass as template parameter, it is of course possible to write a new non-virtual Problem-class which provides the same methods as the ProblemInterface class but does not use virtual functions.

Nevertheless, the classes defined here a convenient way to get a start.

Enumeration Type Documentation

◆ ConstituentFlags

template<class FunctionSpace , class GridPart , class Problem >

enum Dune::ACFem::ModelTraits< EllipticModel< FunctionSpace, GridPart, Problem > >::ConstituentFlags

Enumerator
hasFlux	non-zero flux()
hasSources	non-zero sources()

Function Documentation

◆ dirichletData()

template<class FunctionSpace >

virtual void Dune::ACFem::ProblemInterface< FunctionSpace >::dirichletData	(	const DomainType &	x,
		RangeType &	value
	)		const

inlinevirtual

The Dirichlet boundary data.

Calls u() by default.

Parameters

[in]	x	The point of evaluation
[out]	value	The result.

References Dune::ACFem::ProblemInterface< FunctionSpace >::u().

◆ EllipticModel()

template<class FunctionSpace , class GridPart , class Problem = ProblemInterface<FunctionSpace>>

Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::EllipticModel ( const ProblemType & problem )

inline

Constructor taking problem reference.

Parameters

[in] problem An instance of a class derived from class ProblemInterface.

◆ firstOrderCoefficient()

template<class FunctionSpace >

virtual void Dune::ACFem::ProblemInterface< FunctionSpace >::firstOrderCoefficient	(	const DomainType &	x,
		const RangeType &	u,
		const JacobianRangeType &	Du,
		RangeType &	result
	)		const

inlinevirtual

First order term with derivative on u.

For

\[\int\phi\,\nabla\cdot(b\,u) dx\]

this function has to implement

\[\nabla\cdot(b(x)\,u(x)\]

.

Parameters

[in]	x	Point of evaluation.
[in]	u	u(x)
[in]	Du	First derivatives
[out]	result	Guess what.

◆ flux()

template<class FunctionSpace , class GridPart , class Problem = ProblemInterface<FunctionSpace>>

template<class Entity , class Point >

void Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::flux	(	const Entity &	entity,
		const Point &	x,
		const RangeType &	value,
		const JacobianRangeType &	jacobian,
		JacobianRangeType &	flux
	)		const

inline

References Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::flux(), and Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::linearizedFlux().

Referenced by Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::flux(), and Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::linearizedFlux().

◆ fluxDivergence()

template<class FunctionSpace , class GridPart , class Problem = ProblemInterface<FunctionSpace>>

template<class Entity , class Point >

void Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::fluxDivergence	(	const Entity &	entity,
		const Point &	x,
		const RangeType &	value,
		const JacobianRangeType &	jacobian,
		const HessianRangeType &	hessian,
		RangeType &	result
	)		const

inline

References Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::problem_.

◆ has()

template<class FunctionSpace >

virtual bool Dune::ACFem::ProblemInterface< FunctionSpace >::has ( OperatorPartsType what ) const

inlinevirtual

May be used for optimizations during assembly.

A derived class has to be careful to reimplement this method properly.

Parameters

[in] what An Id for the repective part of the operator.

Returns: true if the what is indeed present, for example what(DirichletBoundary) returns true if part of the boundary is subject to Dirichlet boundary conditions and false otherwise.

◆ isDirichletSegment()

template<class FunctionSpace >

virtual bool Dune::ACFem::ProblemInterface< FunctionSpace >::isDirichletSegment	(	const int	bndId,
		const DomainType &	center
	)		const

inlinevirtual

Classification of the kind of boundary conditions which applies to a boundary segment with the given Id.

Parameters

[in]	bndId	The boundary classification from the underlying mesh.
[in]	center	The barycenter of the boundary facet.

Returns: true iff bndId or center belong to a boundary segment subject to Dirichlet conditions.

◆ isNeumannSegment()

template<class FunctionSpace >

virtual bool Dune::ACFem::ProblemInterface< FunctionSpace >::isNeumannSegment	(	const int	bndId,
		const DomainType &	center
	)		const

inlinevirtual

Classification of the kind of boundary conditions which applies to a boundary segment with the given Id.

Parameters

[in]	bndId	The boundary classification from the underlying mesh.
[in]	center	The barycenter of the boundary facet.

Returns: true iff bndId belong to a boundary segment subject to Neumann conditions and neumannData() should be called to compute contributions to the right hand side.

◆ isRobinSegment()

template<class FunctionSpace >

virtual bool Dune::ACFem::ProblemInterface< FunctionSpace >::isRobinSegment	(	const int	bndId,
		const DomainType &	center
	)		const

inlinevirtual

Classification of the kind of boundary conditions which applies to a boundary segment with the given Id.

Parameters

[in]	bndId	The boundary classification from the underlying mesh.
[in]	center	The barycenter of the boundary facet.

Returns: true iff bndId belong to a boundary segment subject to Robin conditions and robinData() should be called to compute contributions to the system matrix.

◆ linearizedFlux()

template<class FunctionSpace , class GridPart , class Problem = ProblemInterface<FunctionSpace>>

template<class Entity , class Point >

void Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::linearizedFlux	(	const RangeType &	uBar,
		const JacobianRangeType &	DuBar,
		const Entity &	entity,
		const Point &	x,
		const RangeType &	value,
		const JacobianRangeType &	jacobian,
		JacobianRangeType &	flux
	)		const

inline

References Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::flux(), and Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::problem_.

Referenced by Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::flux().

◆ linearizedRobinFlux()

template<class FunctionSpace , class GridPart , class Problem = ProblemInterface<FunctionSpace>>

template<class Intersection , class Point >

void Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::linearizedRobinFlux	(	const RangeType &	uBar,
		const Intersection &	intersection,
		const Point &	x,
		const DomainType &	unitOuterNormal,
		const RangeType &	value,
		RangeType &	result
	)		const

inline

References Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::problem_.

Referenced by Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::robinFlux().

◆ linearizedSource()

template<class FunctionSpace , class GridPart , class Problem = ProblemInterface<FunctionSpace>>

template<class Entity , class Point >

void Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::linearizedSource	(	const RangeType &	uBar,
		const JacobianRangeType &	DuBar,
		const Entity &	entity,
		const Point &	x,
		const RangeType &	value,
		const JacobianRangeType &	jacobian,
		RangeType &	result
	)		const

inline

References Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::problem_.

Referenced by Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::source().

◆ neumannData()

template<class FunctionSpace >

virtual void Dune::ACFem::ProblemInterface< FunctionSpace >::neumannData	(	const DomainType &	x,
		RangeType &	value
	)		const

inlinevirtual

The Neumann boundary data.

This is used to compute contributions to the right hand side.

Parameters

[in]	x	The point of evaluation
[out]	value	The result.

◆ robinData()

template<class FunctionSpace >

virtual void Dune::ACFem::ProblemInterface< FunctionSpace >::robinData	(	const DomainType &	x,
		const RangeType &	u,
		RangeType &	value
	)		const

inlinevirtual

The Robin boundary data.

This is used to compute contributions to the system matrix. This function has to compute

\[ \alpha(x)\,u(x) \]

We pass the boundary mormal as additional argument. The default implementation simply returns 0.

Parameters

[in]	x	The point of evaluation
[in]	u	The value of u at x.
[out]	value	The result.

◆ robinFlux()

template<class FunctionSpace , class GridPart , class Problem = ProblemInterface<FunctionSpace>>

template<class Intersection , class Point >

void Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::robinFlux	(	const Intersection &	intersection,
		const Point &	x,
		const DomainType &	unitOuterNormal,
		const RangeType &	value,
		RangeType &	result
	)		const

inline

References Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::linearizedRobinFlux().

◆ secondOrderCoefficient() [1/2]

template<class FunctionSpace >

virtual void Dune::ACFem::ProblemInterface< FunctionSpace >::secondOrderCoefficient	(	const DomainType &	x,
		const JacobianRangeType &	Du,
		const HessianRangeType &	D2u,
		RangeType &	result
	)		const

inlinevirtual

This method has to implement the second order term for the point-wise operator.

This is needed by the error estimator.

\[ -\nabla\cdot(A(x)\nabla u) = (-\nabla\cdot A(x))\cdot\nabla u - A(x) D^2 u \]

Parameters

[in]	x	Point of evaluation.
[in]	Du	First derivatives u.
[in]	D2u	Second derivatives of u.
[out]	result	Guess what.

◆ secondOrderCoefficient() [2/2]

template<class FunctionSpace >

virtual void Dune::ACFem::ProblemInterface< FunctionSpace >::secondOrderCoefficient	(	const DomainType &	x,
		const JacobianRangeType &	gradient,
		JacobianRangeType &	result
	)		const

inlinevirtual

This method has to implement the second order term for the weak formulation, it needs to compute.

\[ A(x)\nabla u(x) \]

Parameters

[in]	x	Point of evaluation.
[in]	gradient	First derivatives.
[out]	result	Guess what.

References Dune::ACFem::gradient().

◆ source()

template<class FunctionSpace , class GridPart , class Problem = ProblemInterface<FunctionSpace>>

template<class Entity , class Point >

void Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::source	(	const Entity &	entity,
		const Point &	x,
		const RangeType &	value,
		const JacobianRangeType &	jacobian,
		RangeType &	result
	)		const

inline

References Dune::ACFem::EllipticModel< FunctionSpace, GridPart, Problem >::linearizedSource().

◆ zeroOrderCoefficient()

template<class FunctionSpace >

virtual void Dune::ACFem::ProblemInterface< FunctionSpace >::zeroOrderCoefficient	(	const DomainType &	x,
		const RangeType &	u,
		RangeType &	result
	)		const

inlinevirtual

Zero order coefficient.

This method has to compute \(c(x)\,u(x)\).

Parameters

[in]	x	Point of evaluation.
[in]	u	u(x)
[out]	result	Guess what.

DUNE Distributed and Unified Numerics Environment

DUNE-ACFEM (2.5.1)

Classes

Enumerations

Functions

Variables

Problem data-instances

Detailed Description

Enumeration Type Documentation

◆ ConstituentFlags

Function Documentation

◆ dirichletData()

◆ EllipticModel()

◆ firstOrderCoefficient()

◆ flux()

◆ fluxDivergence()

◆ has()

◆ isDirichletSegment()

◆ isNeumannSegment()

◆ isRobinSegment()

◆ linearizedFlux()

◆ linearizedRobinFlux()

◆ linearizedSource()

◆ neumannData()

◆ robinData()

◆ robinFlux()

◆ secondOrderCoefficient() [1/2]

◆ secondOrderCoefficient() [2/2]

◆ source()

◆ zeroOrderCoefficient()