Robin Transmission Conditions for Overlapping Additive Schwarz Method Applied to Linear Elliptic Problems

Abstract

We consider overlapping Additive Schwarz Method (ASM) with Robin conditions as the transmission conditions (interior boundary conditions). The main difficulty left in this field is how to select the parameters for Robin conditions — these parameters have strong effect on the convergence rate of ASM. In this paper, we proposed the parameters for linear elliptic problems which seemed to be near optimal.