Dune::ACFem::EllipticFemSchemeBase< DiscreteFunction, Model, InitialGuess > Class Template Reference

Adaptive fem-scheme for "elliptic" problems. More...

#include <dune/acfem/algorithms/ellipticfemscheme.hh>

Collaboration diagram for Dune::ACFem::EllipticFemSchemeBase< DiscreteFunction, Model, InitialGuess >:

Public Types
typedef DiscreteFunction	DiscreteFunctionType
	Type of the discrete solution function.
typedef DiscreteFunctionType::GridType	GridType
	type of hierarchic grid
typedef DiscreteFunctionType::GridPartType	GridPartType
	type of the grid view
typedef DiscreteFunctionType::DiscreteFunctionSpaceType	DiscreteFunctionSpaceType
	type of the discrete function space
typedef Model	ModelImplementationType
	type of the mathematical model
typedef DiscreteFunctionSpaceType::FunctionSpaceType	FunctionSpaceType
	type of function space
typedef SolverSelector< DiscreteFunctionType, OperatorPartsType >	SolverSelectorType
	choose type of discrete function, Matrix implementation and solver implementation
typedef Fem::NewtonInverseOperator< LinearOperatorType, LinearInverseOperatorType >	NonLinearInverseOperatorType
	Non-linear solver.
typedef Fem::RestrictProlongDefault< DiscreteFunctionType >	RestrictionProlongationType
	type of restriction/prolongation projection for adaptive simulations (use default here, i.e. More...
typedef Fem::AdaptationManager< GridType, RestrictionProlongationType >	AdaptationManagerType
	type of adaptation manager handling adapation and DoF compression
typedef ModelType::DirichletBoundaryFunctionType	DirichletBoundaryFunctionType
	type of Dirichlet boundary values
typedef ModelType::DirichletWeightFunctionType	DirichletWeightFunctionType
	type of Dirichlet weight function
typedef decltype(std::declval< DirichletBoundaryFunctionType >()/std::declval< typename DirichletWeightFunctionType::GridFunctionType >())	EffectiveDirichletFunctionType
	type of effective Dirichlet values
typedef ModelType::DirichletIndicatorType	DirichletIndicatorType
	types for various data
typedef DirichletConstraints< LinearOperatorType, EffectiveDirichletFunctionType, DirichletIndicatorType >	ConstraintsOperatorType
	type of Dirichlet constraints
typedef DifferentiableEllipticOperator< LinearOperatorType, OperatorPartsType, ConstraintsOperatorType >	OperatorType
	define differential operator
typedef EllipticEstimator< DiscreteFunctionSpaceType, ModelImplementationType >	EstimatorType
	type of error estimator
typedef MarkingStrategy< EstimatorType >	MarkingStrategyType
	type of marking strategy
typedef InitialGuess	InitialGuessType
	Initial guess/exact solution.
typedef GridFunctionConverter< InitialGuessType, GridPartType >::WrappedGridFunctionType	InitialGuessFunctionType
	The wrapped InitialGuessType (no-op if already instrumented with LocalFunction)
typedef std::tuple< DiscreteFunctionType *, const InitialGuessFunctionType * >	IOTupleType
	type of input/output tuple
typedef DataOutput< GridType, IOTupleType >	DataOutputType
	type of data writer
Define the RHS functional. The default for forces and Neumann is a ZeroGridFunction which will result in a ZeroFunctional which simply will do nothing. For assembling, both will be added efficently together using FunctionalExpressions.
typedef ModelType::BulkForcesFunctionType	BulkForcesFunctionType
typedef L2InnerProductFunctional< DiscreteFunctionSpaceType, BulkForcesFunctionType >	BulkForcesFunctional
typedef ModelType::NeumannBoundaryFunctionType	BoundaryFluxFunctionType
typedef L2BoundaryFunctional< DiscreteFunctionSpaceType, BoundaryFluxFunctionType, typename ModelType::NeumannIndicatorType >	BoundaryFluxFunctional

Public Member Functions
virtual void	initialize ()
	initialize solution
virtual void	solve (bool forceMatrixAssembling=true)
	Solve the system. More...
virtual bool	mark (const double tolerance)
	mark elements for adaptation
virtual double	estimate ()
	calculate error estimator
virtual void	adapt ()
	do the adaptation for a given marking
virtual int	output ()
	data I/O
virtual double	residual () const
	calculate residual (in small l^2)
virtual double	error () const
	calculate L2/H1 error
virtual size_t	size () const
	return some measure about the number of DOFs in use

Protected Member Functions
	EllipticFemSchemeBase (DiscreteFunctionType &solution, const ModelType &model, const InitialGuessType &initialGuess, const std::string &name="ellipt")
	Constructor for the elliptic fem-scheme. More...
virtual void	nonLinearSolve (DiscreteFunctionType &rhs)
	Run the full Newton-scheme ...
virtual void	linearSolve (DiscreteFunctionType &rhs, bool forceMatrixAssembling)
	Perform only one step of the Newton scheme for the affine-linear case. More...

Detailed Description

template<class DiscreteFunction, class Model, class InitialGuess>
class Dune::ACFem::EllipticFemSchemeBase< DiscreteFunction, Model, InitialGuess >

Adaptive fem-scheme for "elliptic" problems.

The quotes are due to the fact, that neither the EllipticFemScheme nor the EllipticOperator used in the scheme make any assumptions on the ellipticity except for the solvers which are used inside. But even here in principle the EllipticOperator has the possibility to flag that it is indefinite.

This scheme provides the necessary modules

ESTIMATE - MARK - ADAPT - SOLVE - DATA I/O

which then can be used by an adaptive algorithm for stationary problems, see the exeternal Dune module ellipt-dot-c for an example.

Parameters

[in]	DiscreteFunction	Type of the discrte function for solution and test functions.
[in]	Model	A model satisfying the ModelInterface which describes the operator at a local basis by providing "operator germs", i.e. half of the integrants which constitute the discrete bilinear forms.
[in]	InitialGuess	An initial guess in order to start an iterative solver. This can be used in order to pass an "exact solution" for experimental convergence tests.

Member Typedef Documentation

RestrictionProlongationType

template<class DiscreteFunction , class Model , class InitialGuess >

typedef Fem::RestrictProlongDefault<DiscreteFunctionType> Dune::ACFem::EllipticFemSchemeBase< DiscreteFunction, Model, InitialGuess >::RestrictionProlongationType

type of restriction/prolongation projection for adaptive simulations (use default here, i.e.

LagrangeInterpolation)

Constructor & Destructor Documentation

EllipticFemSchemeBase()

template<class DiscreteFunction , class Model , class InitialGuess >

Dune::ACFem::EllipticFemSchemeBase< DiscreteFunction, Model, InitialGuess >::EllipticFemSchemeBase ( DiscreteFunctionType &  solution, const ModelType &  model, const InitialGuessType &  initialGuess, const std::string &  name = "ellipt"  )

inlineprotected

Constructor for the elliptic fem-scheme.

Parameters

[in]	solution	Mutable reference to an existing discrete function in order to store the solution.
[in]	model	A const reference to something satisfying the ModelInterface.
[in]	initialGuess	An initial guess for an iterative solver or an exact solution for experimental convergence tests. EllipticFemScheme::error() will compute the H1-distance from thise function.
[in]	name	Fancy prefix name for parameters and debugging.

Member Function Documentation

linearSolve()

template<class DiscreteFunction , class Model , class InitialGuess >

virtual void Dune::ACFem::EllipticFemSchemeBase< DiscreteFunction, Model, InitialGuess >::linearSolve ( DiscreteFunctionType &  rhs, bool  forceMatrixAssembling  )

inlineprotectedvirtual

Perform only one step of the Newton scheme for the affine-linear case.

This implies that an affine linear case is really allowed.

Referenced by Dune::ACFem::EllipticFemSchemeBase< DiscreteFunction, Model, InitialGuess >::solve().

solve()

template<class DiscreteFunction , class Model , class InitialGuess >

virtual void Dune::ACFem::EllipticFemSchemeBase< DiscreteFunction, Model, InitialGuess >::solve ( bool  forceMatrixAssembling = true )

inlinevirtual

Solve the system.

Parameters

[in]

forceMatrixAssembling

If the solve step requires assembling of matrices, then by default the application may give a hint to the FemScheme that this might not be necessary. The actual implementation can then decide if it caches the assembled matrix from the last solve() invocation and reuses it. If forceAssemble is true then the implementation has to discard and cached assembled matrices and recompute them.

Implements Dune::ACFem::BasicFemScheme.

References Dune::ACFem::DirichletConstraints< JacobianOperator, BoundaryValues, Indicator >::constrain(), Dune::ACFem::isZero(), Dune::ACFem::EllipticFemSchemeBase< DiscreteFunction, Model, InitialGuess >::linearSolve(), Dune::ACFem::EllipticFemSchemeBase< DiscreteFunction, Model, InitialGuess >::nonLinearSolve(), and Dune::ACFem::DirichletConstraints< JacobianOperator, BoundaryValues, Indicator >::zeroConstrain().

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

• dune/acfem/algorithms/ellipticfemscheme.hh