Title: A Domain Decomposition Discretization of Parabolic Problems

(NYU-CS-TR860)

Author:  Maksymilian Dryja and Xuemin Tu

Abstract:
In recent years, domain decomposition methods have attracted much attention
due to their successful application to many elliptic and parabolic
problems. Domain decomposition methods treat problems based on a domain
substructuring, which is attractive for parallel computation,
due to the independence among the subdomains.   In principle, domain
decomposition methods may be applied to the system resulting from a standard
discretization of the parabolic problems or, directly, be carried out through
a direct discretization of  parabolic problems.   In this paper, a
direct domain decomposition method is introduced to discretize the parabolic
problems. The stability and convergence of this algorithm are analyzed,
and an $O(\tau+h)$ error bound is provided.