NUMERICAL EXPERIMENTS WITH AN OVERLAPPING ADDITIVE SCHWARZ SOLVER FOR3-D PARALLEL RESERVOIR SIMULATION

Domain decomposition methods are a major area of contemporary research in the numerical analysis of partial differential equations. They pro vide robust, parallel, and scalable preconditioned iterative methods f or the large linear systems arising when continuous problems are discr etized by finite elements, finite differences, or spectral methods. Th is paper presents numerical experiments on a distributed-memory parall el computer, the 512-processor Touchstone Delta at the California Inst itute of Technology. An overlapping additive Schwarz method is impleme nted for the mixed finite-element discretization of second-order ellip tic problems in three dimensions arising from flow models in reservoir simulation. These problems are characterized by large variations in t he 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 prec onditioning as opposed to the simpler but less robust diagonal precond itioner.