An Interface Strip Preconditioner For Domain Decomposition Methods: Application To The Coupled Surface And Groundwater Flow.

Abstract

In this paper, the efficiency of a parallelizable preconditioner for Domain
Decomposition Methods in the context of the solution of non-symmetric linear equations
arising from the discretization of the conservation laws in hydrology (e.g., the coupled
surface and sub-surface flow over a freatic acuifer) is investigated. The Interface Strip
Preconditioner (IS) proposed is based on solving a problem in a narrow strip around the
interface. It requires much less memory and computing time than classical Neumann-
Neumann preconditioner, and handles correctly the flux splitting among subdomains that
share the interface. The performance of this preconditioner is assessed with an analytical
study of Schur complement matrix eigenvalues and numerical experiments conducted in a
parallel computational environment (consisting of a Beowulf cluster of twenty-nodes).