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

Domain decomposition methods are a major area of contemporary research in numerical analysis of partial diierential equations. They provide robust, parallel and scalable preconditioned iterative methods for the large linear systems arising when continuous problems are discretized by nite elements, nite diierences 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 nite element discretization of second order elliptic problems in three dimensions, arising from ow models in reservoir simulation. These problems are characterized by large variations in the coeecients of the elliptic operator, often associated with short correlation lengths, which make the problems very ill-conditioned. The results connrm 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.