Dune::ACFem::ParabolicFemScheme< DiscreteFunction, TimeProvider, ImplicitModel, ExplicitModel, InitialValue, QuadratureTraits > Class Template Reference

Basic parabolic fem-scheme class. More...

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

Collaboration diagram for Dune::ACFem::ParabolicFemScheme< DiscreteFunction, TimeProvider, ImplicitModel, ExplicitModel, InitialValue, QuadratureTraits >:

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 TimeProvider	TimeProviderType
	access to the simulation time and time-step
typedef ImplicitModel	ImplicitModelImplementationType
	type of the mathematical model
typedef InitialValue	InitialValueType
	Initial value.
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 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, ImplicitOperatorPartsType, ConstraintsOperatorType, QuadratureTraits >	ImplicitOperatorType
	define differential operator, implicit part
typedef EllipticOperator< ExplicitOperatorPartsType, DiscreteFunctionType, DiscreteFunctionType, EmptyConstraintsType, QuadratureTraits >	ExplicitOperatorType
	explicit part of differential operator. More...
typedef ParabolicEulerEstimator< DiscreteFunctionType, TimeProviderType, ImplicitModelImplementationType, ExplicitModelImplementationType >	EstimatorType
	type of error estimator
typedef MarkingStrategy< EstimatorType >	MarkingStrategyType
	type of marking strategy for space adaptivity
typedef TrueErrorEstimator< InitialValueFunctionType, Dune::Fem::L2Norm< GridPartType > >	InitialEstimatorType
	intial estimator
typedef MarkingStrategy< InitialEstimatorType >	InitialMarkingStrategyType
	Initial marking.
typedef InitialValueFunctionType	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
	ParabolicFemScheme (DiscreteFunctionType &solution, const TimeProviderType &timeProvider, const ImplicitModelType &implicitModel, const ExplicitModelType &explicitModel, const InitialValueType &initialValue, const std::string name="heat")
	Constructor. More...
virtual void	initialize ()
	initialize the solution
virtual void	next ()
	Close the current time-step. More...
virtual void	solve (bool forceMatrixAssembling=true)
	solve the system
virtual bool	mark (const double tolerance)
	mark elements for adaptation
virtual double	estimate ()
	calculate error estimator
virtual double	timeEstimate ()
	return the most recent time estimate
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. More...
virtual size_t	size () const
	return some measure about the number of DOFs in use

Public Attributes
decltype(std::declval< DirichletBoundaryFunctionType >()/std::declval< typename DirichletWeightFunctionType::GridFunctionType >()) typedef	EffectiveDirichletFunctionType
	type of effective Dirichlet values

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 TimeProvider, class ImplicitModel, class ExplicitModel, class InitialValue, template< class > class QuadratureTraits = DefaultQuadratureTraits>
class Dune::ACFem::ParabolicFemScheme< DiscreteFunction, TimeProvider, ImplicitModel, ExplicitModel, InitialValue, QuadratureTraits >

Basic parabolic fem-scheme class.

Parameters

[in]	DiscreteFunction	The type of the discrete solution.
[in]	TimeProvider	The type of the Dune::Fem::TimeProvider.
[in]	ImplicitModel	The type of the implicit model.
[in]	ExplicitModel	The type of the explicit model.
[in]	InitialValue	The type of the initial value. Additionally, this can also be the exact solution in order to perform experimental convergence tests. ParabolicFemScheme::error() will compute the distance to this function; it will also be dumped to the VTK-files for visualization.
[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 TimeProvider , class ImplicitModel , class ExplicitModel , class InitialValue , template< class > class QuadratureTraits = DefaultQuadratureTraits>

typedef EllipticOperator<ExplicitOperatorPartsType, DiscreteFunctionType, DiscreteFunctionType, EmptyConstraintsType, QuadratureTraits> Dune::ACFem::ParabolicFemScheme< DiscreteFunction, TimeProvider, ImplicitModel, ExplicitModel, InitialValue, QuadratureTraits >::ExplicitOperatorType

explicit part of differential operator.

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

RestrictionProlongationType

template<class DiscreteFunction , class TimeProvider , class ImplicitModel , class ExplicitModel , class InitialValue , template< class > class QuadratureTraits = DefaultQuadratureTraits>

typedef Dune::Fem::RestrictProlongDefault<DiscreteFunctionType> Dune::ACFem::ParabolicFemScheme< DiscreteFunction, TimeProvider, ImplicitModel, ExplicitModel, InitialValue, QuadratureTraits >::RestrictionProlongationType

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

LagrangeInterpolation)

Constructor & Destructor Documentation

ParabolicFemScheme()

template<class DiscreteFunction , class TimeProvider , class ImplicitModel , class ExplicitModel , class InitialValue , template< class > class QuadratureTraits = DefaultQuadratureTraits>

Dune::ACFem::ParabolicFemScheme< DiscreteFunction, TimeProvider, ImplicitModel, ExplicitModel, InitialValue, QuadratureTraits >::ParabolicFemScheme ( DiscreteFunctionType &  solution, const TimeProviderType &  timeProvider, const ImplicitModelType &  implicitModel, const ExplicitModelType &  explicitModel, const InitialValueType &  initialValue, const std::string  name = "heat"  )

inline

Constructor.

Parameters

[in,out]	solution	Storage for the discrete solution.
[in]	timeProvider	A Dune::Fem time-provider to communicate time and step-size all over the place.
[in]	implicitModel	The part of the operator to be applied at the end of the time interval.
[in]	explicitModel	The part of the operator to be applied to the old values.
[in]	initialValue	Guess what. This can either be a non-discrete function or something which already has a LocalFunction-property. This can also used to pass an "exact" "solution" for experimental convergence tests. If so the function still has to evaluate at the start of the current time-step, in order to be suitable as an initial value.
[in]	name	Name used for parameters and output.

Member Function Documentation

error()

template<class DiscreteFunction , class TimeProvider , class ImplicitModel , class ExplicitModel , class InitialValue , template< class > class QuadratureTraits = DefaultQuadratureTraits>

virtual double Dune::ACFem::ParabolicFemScheme< DiscreteFunction, TimeProvider, ImplicitModel, ExplicitModel, InitialValue, QuadratureTraits >::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 initialValue 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 TimeProvider , class ImplicitModel , class ExplicitModel , class InitialValue , template< class > class QuadratureTraits = DefaultQuadratureTraits>

virtual void Dune::ACFem::ParabolicFemScheme< DiscreteFunction, TimeProvider, ImplicitModel, ExplicitModel, InitialValue, QuadratureTraits >::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::ParabolicFemScheme< DiscreteFunction, TimeProvider, ImplicitModel, ExplicitModel, InitialValue, QuadratureTraits >::solve().

next()

template<class DiscreteFunction , class TimeProvider , class ImplicitModel , class ExplicitModel , class InitialValue , template< class > class QuadratureTraits = DefaultQuadratureTraits>

virtual void Dune::ACFem::ParabolicFemScheme< DiscreteFunction, TimeProvider, ImplicitModel, ExplicitModel, InitialValue, QuadratureTraits >::next ( )

inlinevirtual

Close the current time-step.

Here: copy new solution to oldSolution. Note that this does not move the timeProvider to the new time-step.

---

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

• dune/acfem/algorithms/parabolicfemscheme.hh