Domain decomposition and parallel processing of a finite element model of the shallow water equations

We present nonoverlapping domain decomposition techniques applied to a two-stage NumerovGalerkin finite element model of the shallow water equations over a limited-area domain. The Schur complement matrix formulation is employed and a modified interface matrix approach is proposed to handle the coupling between subdomains. The resulting nonsymmetric Schur complement matrices, modified interface matrices as well as the subdomain coefficient matrices are solved using Preconditioned Conjugate Gradient Squared (PCGS) non-symmetric iterative solvers. Various stages of the finite element solution are parallelized and the code is implemented on a four processor CRAY Y-MP supercomputer applying multitasking techniques in a dedicated environment.