[petsc-users] Suggestions for code with dof >> 1 ?

[Jed Brown]

Christophe Ortiz <christophe.ortiz at ciemat.es> writes:
> Before I go on implementing all the coupling between all the dof, I am
> doing some tests with the system described above and I see some strange
> behavior...
> To do some tests, as initial conditions I set two gaussian distributions
> for u and v. When the peak value of the gaussians is in the order of unity,
> no problem, ARKIMEX as well as ROSW work fine. However, when I use peak
> values in the order of 1e15-1e20 (which is of interest for me), then
> troubles arise. I see it takes much more time to do one timestep for
> ARKIMEX. This, even when I switch off the coupling and there is only
> diffusion. It takes too long.
>  I tried KSPCG and KSPGMRES and PCNONE/PCILU.
>
> - is it due to some problem with ARKIMEX and large values ?

Error control should be the same.  Run with -ts_adapt_monitor and send
output if you don't understand it.

> - How do you use ts_adapt_basic_clip in the run command to decrease the
> fastest increase of timestep ? I would like to set 1.5 for the fastest
> increase instead of 10, which is the default. I tried but PETSc complains
> saying:
>
> [0]PETSC ERROR: Argument out of range!
> [0]PETSC ERROR: Must give exactly two values to -ts_adapt_basic_clip!

-ts_adapt_basic_clip 0.1,1.5

The first number is the fastest decrease that will be allowed.

> - ARKIMEX seems to work better if I decrease the number of nodes, ie if I
> increase the dx.

Then you'll be swamped with spatial error.

> - I found out with ts_view that the ARKIMEX type is always ARKIMEX3, even
> when I use
>
>    ierr = TSARKIMEXSetType(ts,TSARKIMEX1BEE);

Maybe you call this before the type has been set, e.g., before
TSSetFromOptions().  Use -ts_arkimex_type 1bee.

> - With TSROSW, much better. Any idea why ?

Default TSROSW method (ra34pw2) has a good error estimate.  It's
probably faster because it only does linear solves.  If your problem is
linear (or weakly nonlinear), TSROSW is usually better than ARKIMEX, at
least unless you tell the SNES to compute the Jacobian only once.

> - Do you recommend a particular KSP/PC for this type of problem ?

Use a direct solver until you understand what is happening in the outer
levels.  Then use multigrid because it is the right way to solve the problem.
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