Title: Numerical experiments with an overlapping additive Schwarz solver
for 3-D parallel reservoir simulation

Authors' names: Luca F. Pavarino and Marcelo Rame'

Revision information: accepted for publication in the 
International Journal of Supercomputer Applications

Author information: both are research scientists at the 
Department of Computational and Applied Mathematics, Rice University.

Abstract:
Domain decomposition methods are a major area of contemporary research 
in numerical analysis of partial differential equations.
They provide robust, parallel and scalable preconditioned iterative methods 
for the
large linear systems arising when continuous problems are
discretized by finite elements, finite differences or spectral methods.
This paper presents some numerical experiments on a distributed memory
parallel computer, the 512 processor Caltech Touchstone Delta. 
An overlapping additive 
Schwarz method is implemented for the mixed finite element discretization 
of second order elliptic problems in three dimensions, arising from 
flow models in reservoir simulation.
These problems are characterized by large variations in the
coefficients of the elliptic operator, often associated with short 
correlation lengths, which make the problems very ill-conditioned.
The results confirm the theoretical bound on the condition number of 
the iteration operator and show the advantage of domain decomposition
preconditioning as opposed to a simpler but less robust diagonal
preconditioner.