<div dir="ltr"><div class="gmail_quote">On Mon, Apr 4, 2011 at 11:21, Kontsantinos Kontzialis <span dir="ltr"><<a href="mailto:ckontzialis@lycos.com">ckontzialis@lycos.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
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.
</blockquote></div><br><div>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?</div>
<div><br></div><div>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.</div><div><br></div><div>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 <a href="http://epubs.siam.org/sisc/resource/1/sjoce3/v32/i6/p3394_s1">http://epubs.siam.org/sisc/resource/1/sjoce3/v32/i6/p3394_s1</a> for several examples defining the operator for use with semi-implicit integration). An alternative is to build a custom multigrid, see e.g. <a href="http://aero-comlab.stanford.edu/Papers/jameson.aiaa.01-2673.pdf">http://aero-comlab.stanford.edu/Papers/jameson.aiaa.01-2673.pdf</a>. 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.</div>
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