timestepping::Theta Class Reference

Timestep strategy for the Theta-Scheme algorithm for first order problems in time. More...

#include <theta.hh>

Inheritance diagram for timestepping::Theta:

Public Member Functions
	Theta (concepts::SolverFabric< Real > &fabric, concepts::Operator< Real > &D1, concepts::Operator< Real > &D0, timestepping::TimeVector &trhs, const concepts::Vector< Real > &Y0, Real dt, Real theta=0.5)
	Constructor. More...
virtual	~Theta ()

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream. More...
virtual void	next ()
	The overloaded member function next() has to calculate the new right hand side and to release the solution vector. More...

Protected Attributes
Real	dt_
	Time step size. More...
concepts::Operator< Real > *	liCo_
	Operator of the linear equation system which is solved by the friend class TimeStepping. More...
concepts::Vector< Real >	rhs_
	The right hand side vector of the linear equation system which is solved by the friend class TimeStepping. More...
concepts::Vector< Real >	sol_
	The solution vector of the linear equation system which is solved by the friend class TimeStepping. More...
std::unique_ptr< concepts::Operator< Real > >	solver_
	Solver for the linear system. More...
Real	t_
	Time of the actual solution. More...

Private Attributes
concepts::Operator< Real > &	D0_
concepts::Operator< Real > &	D1_
	Space operator. More...
std::unique_ptr< concepts::Operator< Real > >	lhs_
	Left hand side of the scheme. More...
Real	theta_
	Parameter of the scheme. More...
timestepping::TimeVector &	trhs_
	External driver function. More...
concepts::Vector< Real >	Yn1_
	Store the latest timestep. More...

Detailed Description

Timestep strategy for the Theta-Scheme algorithm for first order problems in time.

The scheme has one parameter theta. The scheme is implicit if theta!=0 and it has convergence order 2 if theta = 1/2. The algorithm is absolutely stable with the predefined parameters.

See also

C. Schwab Einführung in die Numerik Partieller Differentialgleichungen: Zeitabhängige Probleme, lecture notes 2001.

Author

Manuel Walser, 2002

Definition at line 40 of file theta.hh.

Constructor & Destructor Documentation

Theta()

timestepping::Theta::Theta	(	concepts::SolverFabric< Real > &	fabric,
		concepts::Operator< Real > &	D1,
		concepts::Operator< Real > &	D0,
		timestepping::TimeVector &	trhs,
		const concepts::Vector< Real > &	Y0,
		Real	dt,
		Real	theta = 0.5
	)

Constructor.

Parameters

fabric	Solver fabric to solve the occuring systems
D1	Space operator D1
D0	Space operator D0
trhs	Timedependent external driver f(x,t)
Y0	Initial condition y(x,0)
dt	Time step size
theta	Parameter of the Theta scheme

~Theta()

virtual timestepping::Theta::~Theta ( )

virtual

Member Function Documentation

info()

virtual std::ostream& timestepping::Theta::info ( std::ostream &  os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

next()

virtual void timestepping::Theta::next ( )

protectedvirtual

The overloaded member function next() has to calculate the new right hand side and to release the solution vector.

Then the Timestepping solver can set the new solution.

Implements timestepping::TimeStepStrategy.

Member Data Documentation

D0_

concepts::Operator<Real> & timestepping::Theta::D0_

private

Definition at line 64 of file theta.hh.

D1_

concepts::Operator<Real>& timestepping::Theta::D1_

private

Space operator.

Definition at line 64 of file theta.hh.

dt_

Real timestepping::TimeStepStrategy::dt_

protectedinherited

Time step size.

Definition at line 77 of file strategy.hh.

lhs_

std::unique_ptr<concepts::Operator<Real> > timestepping::Theta::lhs_

private

Left hand side of the scheme.

Definition at line 72 of file theta.hh.

liCo_

concepts::Operator<Real>* timestepping::TimeStepStrategy::liCo_

protectedinherited

Operator of the linear equation system which is solved by the friend class TimeStepping.

It can be stored as a linear combination of two operators. The exact form depends on the specific scheme.

See also

TimeStepping

Definition at line 65 of file strategy.hh.

rhs_

concepts::Vector<Real> timestepping::TimeStepStrategy::rhs_

protectedinherited

The right hand side vector of the linear equation system which is solved by the friend class TimeStepping.

See also

TimeStepping

Definition at line 75 of file strategy.hh.

sol_

concepts::Vector<Real> timestepping::TimeStepStrategy::sol_

protectedinherited

The solution vector of the linear equation system which is solved by the friend class TimeStepping.

See also

TimeStepping

Definition at line 70 of file strategy.hh.

solver_

std::unique_ptr<concepts::Operator<Real> > timestepping::TimeStepStrategy::solver_

protectedinherited

Solver for the linear system.

Definition at line 59 of file strategy.hh.

t_

Real timestepping::TimeStepStrategy::t_

protectedinherited

Time of the actual solution.

Definition at line 79 of file strategy.hh.

theta_

Real timestepping::Theta::theta_

private

Parameter of the scheme.

Definition at line 70 of file theta.hh.

trhs_

timestepping::TimeVector& timestepping::Theta::trhs_

private

External driver function.

Definition at line 66 of file theta.hh.

Yn1_

concepts::Vector<Real> timestepping::Theta::Yn1_

private

Store the latest timestep.

Definition at line 68 of file theta.hh.

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

• timestepping/theta.hh