Numerical Experiments With an Overlapping Additive Schwarz Solver for 3-d pArallel Reservoir Simulation

Abstract

Domain decomposition methods are a major area of contemporary research in the numerical analysis of partial differential equations. They provide robust, par allel, and scalable preconditioned iterative methods for the large linear systems arising when continuous prob lems are discretized by finite elements, finite differ ences, or spectral methods. This paper presents nu merical experiments on a distributed-memory parallel computer, the 512-processor Touchstone Delta at the California Institute of Technology. An overlapping ad ditive Schwarz method is implemented for the mixed finite-element discretization of second-order elliptic problems in three dimensions arising from flow mod els in reservoir simulation. These problems are charac terized 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 con dition number of the iteration operator and show the advantage of domain decomposition preconditioning as opposed to the simpler but less robust diagonal preconditioner.