[Trilinos-Users] Slow AztecOO solve time

[Hoekstra, Robert J]

As Mike mentioned, KLU (by Tim Davis, also the originator of the
aforementioned UMFPack)
which is the default solver in the Trilinos/Amesos package has specific
optimizations for
circuit problems and should outperform the more generic tools (UMFPack
and SuperLU) for
sparse direct solves.  As mentioned by both Mike and Randy, it is very
difficult to get
iterative sparse methods to perform well on this class of problems.  For
the Xyce simulator,
(Sandia's in house tool) we use GMRES with ILU(k) preconditioning only
for very large scale
problems (approaching a million or more devices).  If you are bent on
demonstrating an
iterative method rather than performance our default usage is along the
lines of:

AztecOO GMRES
EpetraExt Singleton Filtering
Ifpack ILU(k) w/ RCM Reordering 

Just using AztecOO's ILU(t) may do the trick but I am not sure if you
will get the RCM
reordering by default and it's bandwidth minimization is critical to the
performance of
the preconditioner.  You can probably neglect the singleton filter
unless you have a very
large distributed problem but not the bandwidth minimizing reorder
(approx. minimum degree
works even better than RCM and is what Tim Davis uses in KLU but it is
not available in Ifpack
or AztecOO).

Robert Hoekstra
____________________________ 
Electrical & Microsystems Modeling
Sandia National Laboratories
P.O. Box 5800 / MS 0316
Albuquerque, NM 87185
phone: 505-844-7627
fax:      505-284-5451
e-mail: rjhoeks at sandia.gov 
web: http://www.cs.sandia.gov
 



-----Original Message-----
From: trilinos-users-bounces at software.sandia.gov
[mailto:trilinos-users-bounces at software.sandia.gov] On Behalf Of Randall
Bramley
Sent: Thursday, July 12, 2007 12:37 PM
To: Heroux, Michael A
Cc: trilinos-users at software.sandia.gov
Subject: Re: [Trilinos-Users] Slow AztecOO solve time


>> I'm a student, and a beginner with Trilinos trying to use the AztecOO
>> solver in a SPICE package.   I am getting relatively slow results,

Circuit simulation problems are notoriously difficult for iterative
solvers with non-specialized preconditioners like ILUt, etc. It's not
just a matter of a bad condition number, but the overall eigenvalue
distributions tend to give worst-case properties for Krylov solvers.
That would explain having a large number of iterations, but not
necessarily the time spent in memory management - unless it is used on
every iteration, or you have an lax dropping parameter set in the
preconditioner (and hence many fill-in locations). So this may not be of
help on your problem but be aware that just about any iterative solver
package (e.g., Hypre, PETsC, ...) will in general perform slowly for
SPICE.

There may be some specialized application-specific preconditioners
available now for circuit simulation, but I've been out of the game for
too long to know. Still, that is something I'd recommend hunting for -
it would well repay a couple of hours on Google if such a magic
preconditioner has been developed. And if you do find such a thing,
please post it back to this mail list - a lot of us would be interested
and grateful.

Way back when *I* was a student (shortly after the War of 1812) we
typically had to bite the bullet and use a direct sparse solver rather
than iterative methods. Or more accurately, a complete LU decomposition
followed by a few steps of iterative refinement. Ain't no such thing as
purely direct or purely iterative solvers nowadays and all practical
solvers like Trilinos are essentially hybrids.

Mike's recommendation is good, but I'd go further. You can get a quick
estimate of the number of nonzeros (and sparsity pattern) of the LU
factors when using SuperLU or UMFPACK. Take that number, multiply by 8
to get the number of bytes, and see if that fits inside the amount of
memory you have on the target machine. For parallel solves like
SuperLUdist you'd want to do the same on a per process basis.  Using
memory size can also be used to determine how much fill-in would be
optimal for a solver, modulo adding in 3-10 vectors for the iterative
solver.

_______________________________________________
Trilinos-Users mailing list
Trilinos-Users at software.sandia.gov
http://software.sandia.gov/mailman/listinfo/trilinos-users