Dune::ACFem::SplittingFemSchemeBase< DiscreteFunction, ImplicitModel, ExplicitDataFunction, ExplicitModel, InitialGuessFunction > Class Template Reference

Basic fem-scheme class. More...

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

Collaboration diagram for Dune::ACFem::SplittingFemSchemeBase< DiscreteFunction, ImplicitModel, ExplicitDataFunction, ExplicitModel, InitialGuessFunction >:

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 ImplicitModel	ImplicitModelType
	type of the mathematical model
typedef ExplicitDataFunction	ExplicitDataType
	Data for explicit model.
typedef InitialGuessFunction	InitialGuessType
	Initial Guess.
typedef ImplicitModelType::FunctionSpaceType	FunctionSpaceType
	type of function space (scalar functions, \(f: \Omega -> R\))
typedef Fem::NewtonInverseOperator< LinearOperatorType, LinearInverseOperatorType >	NonLinearInverseOperatorType
	Non-linear solver.
typedef Dune::Fem::RestrictProlongDefault< DiscreteFunctionType >	RestrictionProlongationType
	type of restriction/prolongation projection for adaptive simulations (use default here, i.e. More...
typedef Dune::Fem::AdaptationManager< GridType, RestrictionProlongationType >	AdaptationManagerType
	type of adaptation manager handling adapation and DoF compression
typedef ImplicitModelType::DirichletIndicatorType	DirichletIndicatorType
	types for various data
typedef ImplicitModelType::DirichletBoundaryFunctionType	DirichletBoundaryFunctionType
	type of Dirichlet boundary values
typedef ImplicitModelType::DirichletWeightFunctionType	DirichletWeightFunctionType
	type of Dirichlet weight function
typedef decltype(std::declval< DirichletBoundaryFunctionType >()/std::declval< typename DirichletWeightFunctionType::GridFunctionType >())	EffectiveDirichletFunctionType
	type of effective Dirichlet values
typedef DirichletConstraints< LinearOperatorType, EffectiveDirichletFunctionType, DirichletIndicatorType >	ConstraintsOperatorType
	type of Dirichlet constraints
typedef DifferentiableEmptyBlockConstraints< LinearOperatorType >	EmptyConstraintsType
	empty constraints for the explicit operator (old solution is already constrained)
typedef DifferentiableEllipticOperator< LinearOperatorType, ImplicitModelType, ConstraintsOperatorType >	ImplicitOperatorType
	define differential operator, implicit part
typedef EllipticOperator< ExplicitModelType, ExplicitDataFunctionType, DiscreteFunctionType, EmptyConstraintsType >	ExplicitOperatorType
	explicit part of differential operator. More...
typedef InitialGuessFunctionType	ExactSolutionFunctionType
	adapter to turn exact solution into a grid function (for visualization)
typedef std::tuple< DiscreteFunctionType *, const ExactSolutionFunctionType * >	IOTupleType
	type of input/output tuple
typedef DataOutput< GridType, IOTupleType >	DataOutputType
	type of data writer (produces VTK data)
typedef Dune::Fem::CheckPointer< GridType >	CheckPointerType
	type of check-pointer (dumps unaltered simulation data)
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 SumModelType::BulkForcesFunctionType	BulkForcesFunctionType
typedef L2InnerProductFunctional< DiscreteFunctionSpaceType, BulkForcesFunctionType >	BulkForcesFunctional
typedef SumModelType::NeumannBoundaryFunctionType	BoundaryFluxFunctionType
typedef L2BoundaryFunctional< DiscreteFunctionSpaceType, BoundaryFluxFunctionType, typename ImplicitModelType::NeumannIndicatorType >	BoundaryFluxFunctional

Public Member Functions
	SplittingFemSchemeBase (DiscreteFunctionType &solution, const ModelInterface< ImplicitModelType > &implicitModel, const ExplicitDataType &explicitData, const ModelInterface< ExplicitModelType > &explicitModel, const InitialGuessType &initialGuess, const std::string name="femscheme")
	Constructor. More...
virtual void	initialize ()
	initialize the solution
virtual void	solve (bool forceMatrixAssembling=true)
	solve the system
virtual int	output ()
	data I/O
virtual double	residual () const
	calculate residual (in small l^2)
virtual double	error () const
	Calculate L2/H1 error. More...
virtual size_t	size () const
	return some measure about the number of DOFs in use

Protected Member Functions
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 ImplicitModel, class ExplicitDataFunction, class ExplicitModel, class InitialGuessFunction>
class Dune::ACFem::SplittingFemSchemeBase< DiscreteFunction, ImplicitModel, ExplicitDataFunction, ExplicitModel, InitialGuessFunction >

Basic fem-scheme class.

The scheme takes an implicit model and explicit model, the unknown and a grid-function (s.t. with HasLocalFunction property) for the explicit model (which becomes part of the right-hand-side) and provides the method prescribed by the BasicFemScheme interface class, most promiently the solve() method.

Parameters

[in]	DiscreteFunction	The type of the discrete solution.
[in]	ImplicitModel	The type of the implicit model.
[in]	ExplicitDataFunction	The point of evaluation for the operator defined by ExplicitModel
[in]	ExplicitModel	The type of the explicit model.
[in]	InitialGuess	Possibly provide an initial guess for the solver. Also, the error() method will compute the distance to the initial guess.
[in]	QuadratureTraits	Special quadrature rules, for instance to implement mass-lumping. Defaults to DefaultQuadratureTraits. The template argument of the template template-parameter is the GridPartType.

Member Typedef Documentation

ExplicitOperatorType

template<class DiscreteFunction , class ImplicitModel , class ExplicitDataFunction , class ExplicitModel , class InitialGuessFunction >

typedef EllipticOperator<ExplicitModelType, ExplicitDataFunctionType, DiscreteFunctionType, EmptyConstraintsType> Dune::ACFem::SplittingFemSchemeBase< DiscreteFunction, ImplicitModel, ExplicitDataFunction, ExplicitModel, InitialGuessFunction >::ExplicitOperatorType

explicit part of differential operator.

Need not be differentiable as it is only needed for the RHS.

RestrictionProlongationType

template<class DiscreteFunction , class ImplicitModel , class ExplicitDataFunction , class ExplicitModel , class InitialGuessFunction >

typedef Dune::Fem::RestrictProlongDefault<DiscreteFunctionType> Dune::ACFem::SplittingFemSchemeBase< DiscreteFunction, ImplicitModel, ExplicitDataFunction, ExplicitModel, InitialGuessFunction >::RestrictionProlongationType

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

LagrangeInterpolation)

Constructor & Destructor Documentation

SplittingFemSchemeBase()

template<class DiscreteFunction , class ImplicitModel , class ExplicitDataFunction , class ExplicitModel , class InitialGuessFunction >

Dune::ACFem::SplittingFemSchemeBase< DiscreteFunction, ImplicitModel, ExplicitDataFunction, ExplicitModel, InitialGuessFunction >::SplittingFemSchemeBase ( DiscreteFunctionType &  solution, const ModelInterface< ImplicitModelType > &  implicitModel, const ExplicitDataType &  explicitData, const ModelInterface< ExplicitModelType > &  explicitModel, const InitialGuessType &  initialGuess, const std::string  name = "femscheme"  )

inline

Constructor.

Parameters

[in,out]	solution	Storage for the discrete solution.
[in]	implicitModel	The part of the operator to be applied at the end of the time interval.
[in]	explicitData	The grid-function the operator defined by explicitModel is applied to. This defaults to the ZeroGridFunction.
[in]	explicitModel	The part of the operator to be applied to the old values. This defaults to the ZeroModel.
[in]	initialGuess	Initial guess. If present, initialize() will call the natural interpolation routine for the given discrete function space.
[in]	name	Name used for parameters and output.

Member Function Documentation

error()

template<class DiscreteFunction , class ImplicitModel , class ExplicitDataFunction , class ExplicitModel , class InitialGuessFunction >

virtual double Dune::ACFem::SplittingFemSchemeBase< DiscreteFunction, ImplicitModel, ExplicitDataFunction, ExplicitModel, InitialGuessFunction >::error ( ) const

inlinevirtual

Calculate L2/H1 error.

This actually computes the distance to the initial value which optionally may be used for experimental convergence tests in order to pass an exact "solution". In this case initialGuess may be time-dependent and has to give the correct value at the start of the time-step.

Implements Dune::ACFem::BasicFemScheme.

linearSolve()

template<class DiscreteFunction , class ImplicitModel , class ExplicitDataFunction , class ExplicitModel , class InitialGuessFunction >

virtual void Dune::ACFem::SplittingFemSchemeBase< DiscreteFunction, ImplicitModel, ExplicitDataFunction, ExplicitModel, InitialGuessFunction >::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::SplittingFemSchemeBase< DiscreteFunction, ImplicitModel, ExplicitDataFunction, ExplicitModel, InitialGuessFunction >::solve().

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

• dune/acfem/algorithms/splittingfemscheme.hh