[petsc-users] Can I use TS routines for operator split formulation

[Matthew Knepley]

On Mon, Jun 9, 2014 at 12:55 PM, Shriram Srinivasan <shriram at ualberta.ca>
wrote:

>  *It seems like above you have already chosen a time discretization, in
> that you have time steps appearing. The*
>  *idea with TS is to begin with the continuum form, in the simplest case*
>
>  *   u_t = G(u, t)*
>
>  *and in the implicit form*
>
>  *  F(u_t, u, t) = 0*
>
>  *and let PETSc choose the time discretization (since there are many
> multistep methods). It is likely that*
> *you could reproduce the method you have above by choosing one of the
> existing TS methods. Does this*
>  *make sense?*
>
>
> Yes, I have tried that. I have perhaps not been clear with my question.
> The discretization employed is simply Backward Euler. The problem I see
> with trying to use TS is that my scheme  uses u* as a kind of predictor.
>
> I can write rewrite (u* - u_prev) + (tau )A u* = f1 as
>  u*_t + A u* = f1; I  apply backward Euler on this to find u*  after one
> time step.
>
> But the problem is the next part (u - u*) + (tau)B u = f2.
> This I can rewrite as u_t + B u = f2; But when I apply backward euler, I
> want  u_t = (u - u*)/tau.
>
> This breaks the pattern for use of the TS module, it seems to me. I would
> like to know if I am correct in my assesment.
> Can I still use TS profitably, or do I need to  implement my own time
> stepper---that was my question.
>

I am not sure if you are using something like this,
http://mathworld.wolfram.com/Predictor-CorrectorMethods.html, but TS
does not have an implementation of that. As noted on the page, these have
been largely supplanted by RK methods, which
we do support. If you want to go back to the original continuum
formulation, I think TS is usable. However, for the method as
formulated above, I think you are right that TS is not suitable.

  Thanks,

     Matt

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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