[petsc-users] Hypre - AMS / CG

[Vincent Huber]

Hello all,

I want to solve the following system [1]
∇ × 1/μ ∇ × u + ∇ P = f
∇ ⋅ u = 0
with μ​ = cst.

This produce, in the preconditioner, two systems to solve. The first one is
related to AMS (with a non null β​), the second one is a laplacian.

I use *Hypre/Ams*
<http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCHYPRE.html>
as a preconditioner to solve the first system.

I have verified my implementation to solve the full problem in sequential,
using the default parameters, on 3D academic test cases. I obtain the
second order accuracy as expected.

On *some* parallel cases, the solver related to the first system (after few
iterations) does not converge (Indefinite matrix or Indefinite
preconditioner). If I generate [2] - from the same mesh - a new
partitionning, I can obtain convergence (but that is not always true)
I have implemented my own version of the ams preconditioner following [1]
and the system (slowly) converge.
I use {Hypre-AMS OR my own implementation}/CG to solve the corresponding
system.
If I switch from hypre-ams/CG to hypre-ams/gmres, then I obtain - at least
for that case - convergence.
If I use my own implementation/CG, then I obtain - at least for that case -
convergence (but that is very slow !)

My questions are:

   - why does the hypre-ams preconditioner loose the SDP property ?
   - Do I miss anything else ?

I have tried various cycle-type and smoothing options in the hypre-ams
preconditioner with CG without success.

Vincent H

[1]For more details, see *Parallel numerical solution of the time-harmonic
Maxwell equations in mixed form*
[2] gmsh my.msh -3 -part n -o new.msh

–
Docteur Ingénieur de rechercheCeMoSiS <http://www.cemosis.fr> -
vincent.huber at cemosis.fr
Tel: +33 (0)3 68 85 02 06
IRMA - 7, rue René Descartes
67 000 Strasbourg

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