[petsc-users] Can I use TS routines for operator split formulation
Shriram Srinivasan
shriram at ualberta.ca
Mon Jun 9 12:55:59 CDT 2014
/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.
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