[petsc-users] help with snes

[Jed Brown]

On Mon, Apr 4, 2011 at 11:21, Kontsantinos Kontzialis <ckontzialis at lycos.com
> wrote:

>  I am using a Discontinuous Galerkin method for the Euler equations of gas
> dynamics. I noticed that snes iterations do not drop the function norm and i
> need to set ksp_rtol to very low values in order to get converged solution.
> But this takes time. I use a matrix-free method with coloring for computing
> the jacobian as a preconditioner.


I don't see SNES convergence here because it's still in the linear solve.
The restart is apparently too small for use with this preconditioner because
you are losing a lot of ground in each restart. For reference, how does
-pc_type asm -sub_pc_type lu work?

For globalization at moderate to high Mach numbers, I would recommend grid
sequencing if possible, otherwise you may be forced to take smaller time
steps.

For the linear solve, especially at low Mach number, you can precondition
using the Schur complement of momentum applied in the pressure space (this
contains the fast acoustic waves, see
http://epubs.siam.org/sisc/resource/1/sjoce3/v32/i6/p3394_s1 for several
examples defining the operator for use with semi-implicit integration). An
alternative is to build a custom multigrid, see e.g.
http://aero-comlab.stanford.edu/Papers/jameson.aiaa.01-2673.pdf. Both of
these options require some work on your part. You should recognize that
scalable solvers for implicit Euler at large time steps is still a hard
enough problem that "black box" approaches will not give the best
performance.
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