timestepping::Alpha Class Reference

Timestep strategy for the Alpha algorithm of Hilber, Hughes and Taylor to solve second order problems in time with no first order time derivative. More...

#include <alpha.hh>

Inheritance diagram for timestepping::Alpha:

Public Member Functions
	Alpha (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 alpha=0.)
	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
concepts::Vector< Real >	A_
Real	alpha_
	Parameters of the scheme. More...
Real	beta_
concepts::Operator< Real > &	D0_
	Space operator. More...
Real	gamma_
timestepping::TimeVector &	trhs_
	External driver function. More...
concepts::Vector< Real >	Z_
	Store velocity Z and acceleration A. More...

Detailed Description

Timestep strategy for the Alpha algorithm of Hilber, Hughes and Taylor to solve second order problems in time with no first order time derivative.

The scheme has one parameter alpha. The scheme is implicit, has convergence order 2 and is unconditionally stable. The parameter alpha controls dissipation. For alpha = 0, there is no dissipation, and the scheme is equivalent to the Newmark scheme with default parameters. For -1/3 <= alpha < 0, the scheme is dissipative. The damping of higher eigenmodes is stronger.

See also

T.J.R. Hughes The Finite Element Method, Dover, Mineola, 2000

Author

Christoph Winkelmann, 2004

Definition at line 42 of file alpha.hh.

Constructor & Destructor Documentation

Alpha()

timestepping::Alpha::Alpha	(	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	alpha = 0.
	)

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
alpha	Parameter of the Alpha scheme

Member Function Documentation

info()

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

protectedvirtual

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

next()

virtual void timestepping::Alpha::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

A_

concepts::Vector<Real> timestepping::Alpha::A_

private

Definition at line 70 of file alpha.hh.

alpha_

Real timestepping::Alpha::alpha_

private

Parameters of the scheme.

Definition at line 72 of file alpha.hh.

beta_

Real timestepping::Alpha::beta_

private

Definition at line 72 of file alpha.hh.

D0_

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

private

Space operator.

Definition at line 66 of file alpha.hh.

dt_

Real timestepping::TimeStepStrategy::dt_

protectedinherited

Time step size.

Definition at line 77 of file strategy.hh.

gamma_

Real timestepping::Alpha::gamma_

private

Definition at line 72 of file alpha.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::Alpha::trhs_

private

External driver function.

Definition at line 68 of file alpha.hh.

Z_

concepts::Vector<Real> timestepping::Alpha::Z_

private

Store velocity Z and acceleration A.

Definition at line 70 of file alpha.hh.

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

• timestepping/alpha.hh