timestepping::Newmark Class Reference

Timestep strategy for the Newmark algorithm to solve second order problems in time with no first order time derivative. More...

#include <newmark.hh>

Inheritance diagram for timestepping::Newmark:

Public Member Functions
	Newmark (concepts::SolverFabric< Real > &fabric, concepts::Operator< Real > &D2, concepts::Operator< Real > &D0, timestepping::TimeVector &trhs, const concepts::Vector< Real > &Y0, const concepts::Vector< Real > &Z0, Real dt, Real beta=0.25, Real gamma=0.5)
	Constructor. More...

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
Real	beta_
	Parameters of the scheme. More...
concepts::Operator< Real > &	D0_
concepts::Operator< Real > &	D2_
	Space operator. More...
Real	gamma_
std::unique_ptr< concepts::Operator< Real > >	lhs_
	Left hand side of the scheme. More...
timestepping::TimeVector &	trhs_
	External driver function. More...
concepts::Vector< Real >	Yn1_
	Store the two latest timesteps. More...
concepts::Vector< Real >	Yn2_

Detailed Description

Timestep strategy for the Newmark algorithm to solve second order problems in time with no first order time derivative.

The scheme has two parameters beta and gamma. The scheme is implicit as soon as beta!=0 and it has convergence order 2 as soon as gamma=1/2. The algorithm is absolutely stable with the predefined parameters.

See also

P.A. Raviart and J.M. Thomas Introduction a l'Analyse Numerique des Equations aux Derivees Partielles, Masson, Paris, 1983.

Author

Manuel Walser, 2002

Definition at line 40 of file newmark.hh.

Constructor & Destructor Documentation

Newmark()

timestepping::Newmark::Newmark	(	concepts::SolverFabric< Real > &	fabric,
		concepts::Operator< Real > &	D2,
		concepts::Operator< Real > &	D0,
		timestepping::TimeVector &	trhs,
		const concepts::Vector< Real > &	Y0,
		const concepts::Vector< Real > &	Z0,
		Real	dt,
		Real	beta = 0.25,
		Real	gamma = 0.5
	)

Constructor.

Parameters

fabric	Solver fabric for solving the occuring systems
D2	Space opeartor D2
D0	Space opeartor D0
trhs	Timedependent external driver f(x,t)
Y0	Initial condition y(x,0)
Z0	Initial condition d/dt y(x,0)
dt	Time step size
beta,gamma	Parameters of the Newmark scheme

Member Function Documentation

info()

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

protectedvirtual

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

next()

virtual void timestepping::Newmark::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

beta_

Real timestepping::Newmark::beta_

private

Parameters of the scheme.

Definition at line 71 of file newmark.hh.

D0_

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

private

Definition at line 65 of file newmark.hh.

D2_

concepts::Operator<Real>& timestepping::Newmark::D2_

private

Space operator.

Definition at line 65 of file newmark.hh.

dt_

Real timestepping::TimeStepStrategy::dt_

protectedinherited

Time step size.

Definition at line 77 of file strategy.hh.

gamma_

Real timestepping::Newmark::gamma_

private

Definition at line 71 of file newmark.hh.

lhs_

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

private

Left hand side of the scheme.

Definition at line 73 of file newmark.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.

trhs_

timestepping::TimeVector& timestepping::Newmark::trhs_

private

External driver function.

Definition at line 67 of file newmark.hh.

Yn1_

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

private

Store the two latest timesteps.

Definition at line 69 of file newmark.hh.

Yn2_

concepts::Vector<Real> timestepping::Newmark::Yn2_

private

Definition at line 69 of file newmark.hh.

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

• timestepping/newmark.hh