[petsc-users] [SPAM] user experience with PCNN

[Jakub Sistek]

Dear PETSc developers and users,

we are using PETSc to solve systems arising from mixed-hybrid FEM 
applied to Darcy flow. First, the saddle point system is reduced to the 
Schur complement problem for Lagrange multipliers on element interfaces, 
which is then symmetric positive definite. Currently, we are using the 
PCASM preconditioner to solve it. We have very positive experience (also 
from other projects) with PCASM, but we have observed some worsening of 
convergence and scalability with going to larger number of processors 
(up to 64) here. As far as we understand, the increasing number of 
iterations may be caused by the lack of coarse correction in the 
implementation of the preconditioner. On the other hand, PCNN should 
contain such a coarse solve. I have modified our FEM code to support 
MATIS matrices besides MPIAIJ, but so far have a mixed experience with 
PCNN. It seems to work on 2 CPUs, but complains about singular local 
problems (solved by MUMPS) on more. After some time spent by debugging ( 
though there are probably still many bugs left in my code ) and 
unsuccessful playing with some of the related options ( 
-pc_is_damp_fixed,  -pc_is_set_damping_factor_floating, etc.) I have 
decided to ask couple of questions before I will continue in further 
investigation why PCNN does not work for me for general case:

1) Am I right that PCNN is the only domain decomposition method 
exploiting coarse correction readily available in PETSc?
2) As PCNN seems much less documented (I have found no example or so) 
than other preconditioners, I would simply like to know if someone else 
uses it and have positive experience with this implementation?
3) What may be proper options for stabilizing solutions of the local 
problems?
4) Are there limitations to the method with respect to nullspace type of 
subdomain problems, i.e. equation?
5) Do these answers depend on version of PETSc? (I have played with 3.0, 
would things be different with 3.2 ?)

In the long run, I would like to connect the FEM code to an own solver 
based on BDDC domain decomposition, for which the MATIS matrix seems as 
a natural format and connection should be straightforward. However, I 
would like to make it work with PCNN as well.

Thank you very much for your help and suggestions.

Best regards,

Jakub

-- 
Jakub Sistek, Ph.D.
postdoctoral researcher
Institute of Mathematics of the AS CR
http://www.math.cas.cz/~sistek/
tel: (+420) 222 090 710