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:

Collaboration diagram for timestepping::Theta:

List of all members.

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.
virtual	~Theta ()
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
virtual void	next ()
	The overloaded member function next() has to calculate the new right hand side and to release the solution vector.
Protected Attributes
Real	dt_
	Time step size.
concepts::Operator< Real > *	liCo_
	Operator of the linear equation system which is solved by the friend class TimeStepping.
concepts::Vector< Real >	rhs_
	The right hand side vector of the linear equation system which is solved by the friend class TimeStepping.
concepts::Vector< Real >	sol_
	The solution vector of the linear equation system which is solved by the friend class TimeStepping.
std::auto_ptr < concepts::Operator< Real > >	solver_
	Solver for the linear system.
Real	t_
	Time of the actual solution.
Private Attributes
concepts::Operator< Real > &	D0_
concepts::Operator< Real > &	D1_
	Space operator.
std::auto_ptr < concepts::Operator< Real > >	lhs_
	Left hand side of the scheme.
Real	theta_
	Parameter of the scheme.
timestepping::TimeVector &	trhs_
	External driver function.
concepts::Vector< Real >	Yn1_
	Store the latest timestep.
Friends
class	TimeStepping

---

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 35 of file theta.hh.

---

Constructor & Destructor Documentation

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

virtual timestepping::Theta::~Theta

(

)

[virtual]

---

Member Function Documentation

virtual std::ostream& timestepping::Theta::info

(

std::ostream &

os

)

const [protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

virtual void timestepping::Theta::next

(

)

[protected, virtual]

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.

---

Friends And Related Function Documentation

friend class TimeStepping [friend, inherited]

Definition at line 48 of file strategy.hh.

---

Member Data Documentation

concepts::Operator<Real> & timestepping::Theta::D0_ [private]

Definition at line 59 of file theta.hh.

concepts::Operator<Real>& timestepping::Theta::D1_ [private]

Space operator.

Definition at line 59 of file theta.hh.

Real timestepping::TimeStepStrategy::dt_ [protected, inherited]

Time step size.

Definition at line 73 of file strategy.hh.

std::auto_ptr<concepts::Operator<Real> > timestepping::Theta::lhs_ [private]

Left hand side of the scheme.

Definition at line 67 of file theta.hh.

concepts::Operator<Real>* timestepping::TimeStepStrategy::liCo_ [protected, inherited]

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 61 of file strategy.hh.

concepts::Vector<Real> timestepping::TimeStepStrategy::rhs_ [protected, inherited]

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

See also:

TimeStepping

Definition at line 71 of file strategy.hh.

concepts::Vector<Real> timestepping::TimeStepStrategy::sol_ [protected, inherited]

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

See also:

TimeStepping

Definition at line 66 of file strategy.hh.

std::auto_ptr<concepts::Operator<Real> > timestepping::TimeStepStrategy::solver_ [protected, inherited]

Solver for the linear system.

Definition at line 55 of file strategy.hh.

Real timestepping::TimeStepStrategy::t_ [protected, inherited]

Time of the actual solution.

Definition at line 75 of file strategy.hh.

Real timestepping::Theta::theta_ [private]

Parameter of the scheme.

Definition at line 65 of file theta.hh.

timestepping::TimeVector& timestepping::Theta::trhs_ [private]

External driver function.

Definition at line 61 of file theta.hh.

concepts::Vector<Real> timestepping::Theta::Yn1_ [private]

Store the latest timestep.

Definition at line 63 of file theta.hh.

---

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

• timestepping/theta.hh