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:

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Collaboration diagram for timestepping::Newmark:

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List of all members.

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

Detailed Description

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

$[ D_2 \partial_t^2 + D_0 ] y(x,t) = f(x,t)$

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 37 of file newmark.hh.

Constructor & Destructor Documentation

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