Domain Decomposition Preconditioners for Non-selfconjugate Second Order Elliptic Problems

Abstract

A non-symmetric interface Schur complement arises from non- selfcon-jugate second order elliptic problems with domain decomposition methods. The usual numerical methods for solving it are GMRES, OR-THOMIN, and BICGSTAB, but they take a large amount of computer time and memory. The authors find in this paper that the nonsymmetric Schur complement can in fact be changed into a symmetric one by scaling. Then an efficient preconditioner can be provided by which the preconditioned system can be solved iteratively by a modified PCG method. When the problem is imposed on a rectangular region, the condition number is estimated and is nearly one. Numerical experiments are also presented. Non-selfconjugate problems arise in mathematical modeling and numerical simulation of fluid flows and transport in porous media.