[petsc-dev] [petsc-maint #57017] Hypre

[Jed Brown]

On Wed, Dec 1, 2010 at 15:18, Barry Smith <bsmith at mcs.anl.gov> wrote:

> If your problem is a "Stokes" like problem that just throwing a generic
> preconditioner like Euclid at it without doing something special for the
> fact that it is "Stokes like" problem won't work well. Perhaps Jed has some
> suggestions.


Yes, please describe the problem you are solving, including your choice of
space and time discretization.  If you are fully implicit in time for
incompressible flow, chances are you will have to do some work to make it
scale.

When dealing with indefinite problems (like Stokes), it is extremely
important to check *unpreconditioned* residuals because it is not somewhat
common for preconditioners to be singular when applied to such problems.
 BoomerAMG is often afflicted by this.  The following is pasted from an old
email, but should serve as a warning:

This issue came up when a libmesh dev inquired why -pc_type hypre
appeared to converge, but didn't actually solve the system (BoomerAMG
has massive null space on this system).  Since they use penalty boundary
conditions, working in the unpreconditioned norm is tricky, so it's
necessary to be very careful that the preconditioner is full-rank.  So
unpreconditioned residuals would look like:

 0 KSP Residual norm 9.899494936612e+05
 1 KSP Residual norm 3.460941545811e-02
 2 KSP Residual norm 3.411670842883e-02
 3 KSP Residual norm 3.406431296292e-02
 4 KSP Residual norm 3.376198186394e-02
 5 KSP Residual norm 3.374434209905e-02
 6 KSP Residual norm 3.370086274150e-02
 7 KSP Residual norm 3.334190783058e-02
 8 KSP Residual norm 3.321057363881e-02
 9 KSP Residual norm 3.321055343672e-02
 10 KSP Residual norm 3.318392045928e-02

while preconditioned residuals looked fantastic, despite being nonsense

 0 KSP Residual norm 9.526419214320e+00
 1 KSP Residual norm 9.406988599189e-02
 2 KSP Residual norm 2.767040414824e-03
 3 KSP Residual norm 1.649604812054e-03
 4 KSP Residual norm 1.611023301144e-03
 5 KSP Residual norm 7.073431543229e-04
 6 KSP Residual norm 1.404066303578e-04
 7 KSP Residual norm 1.347821147393e-04
 8 KSP Residual norm 7.713640141302e-05
 9 KSP Residual norm 5.121198361232e-05
 10 KSP Residual norm 4.790100151952e-05
 11 KSP Residual norm 1.769376148248e-05
 12 KSP Residual norm 1.671836687758e-05
 13 KSP Residual norm 9.561298137614e-06
 14 KSP Residual norm 6.509746067580e-07
 15 KSP Residual norm 5.863323408081e-07
 16 KSP Residual norm 5.120192651612e-07
 17 KSP Residual norm 3.403122131501e-07
 18 KSP Residual norm 3.342529361191e-07
 19 KSP Residual norm 9.178974981883e-08

Jed
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