A Recursive Variant of Schwarz Type Domain Decomposition Methods

Abstract

In this paper a slightly different approach to the use of the domain decomposition method of the Schwarz type is proposed. Instead of the standard coarse space construction we propose to use a recursive solution on each domain. Thus we do not need to construct a coarse space but nevertheless we are still keeping O(1) convergence speed. For local problems we use the standard iterative solvers for which the amount of the work for one step is O(N), where N is the number of equations. Due to the fact that the overlapping is under our control we can keep total work in O(N^(1+γ) ) operations with arbitrary positive γ.

Keywords

• Domain Decomposition, Finite Element Method, Linear Systems.