A New Coarse Grid Correction for RAS/AS

Abstract

Domain decomposition methods for elliptic problems need a coarse space in order to be scalable, and good coarse spaces are currently an active area of research. We propose here a new coarse space for the restricted additive Schwarz method (RAS). The coarse space is adapted to the discontinuous nature of the iterates of RAS, by specific placement of the coarse grid nodes. We explain the idea first for a one dimensional model problem, and then generalize the approach to two dimensional decompositions into rectangular subdomains. We show with numerical experiments that the new coarse grid is much more effective than classical ones, also for the more classical additive Schwarz (AS) method.