A Domain Decomposition Method for Parabolic Equations Based on Finite Elements

A domain decomposition procedure for solving parabolic partial differential equations is presented. In this scheme, a Galerkin finite element discretization on a rectangular mesh is used. Boundary values at sub domain interfaces are calculated by an implicit/ explicit procedure. This solution serves as boundary data for fully implicit subdomain problems, which can be solve simultaneously. Thus, the scheme is non-iterative, and requires non-overlapping subdomains. Numerical results are presented for problems in two space dimensions. • Mathematical Sciences Dept., Rice University, Houston, TX 77251. This research was supported by NSF Grant DMS-8807257, and used the CRAY-2 at the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, and the Alliant FX/8 Computer at Argonne National Laboratory, Mathematics and Computer Science Division. t Dept. of Mathematics, Michigan State University, East Lansing, Michigan, 48824.