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

[Matthew Knepley]

On Mon, Jun 9, 2014 at 11:51 AM, Shriram Srinivasan <shriram at ualberta.ca>
wrote:

> Hi,
> I am working with the (discretised) PDE:
> (u* - u_prev) + (tau )A u* = f1
> (u - u*) + (tau)B u = f2
> Here A and B are constant matrices which have been assembled, u_prev is
> solution at previous time level, tau is the time step and u is the solution
> at current time level.
>
> It appears to me I cannot rewrite this in a form required by the TS
> module. So my question(s) are:
>
> 1) Am I missing something here, or is there a way to cast this into the
> framework of TS
>

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?

  Thanks,

     Matt


> 2) If there isn’t a way, am I better off doing the time stepping myself ?
>
> Thanks,
> Shriram
>



-- 
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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