On the rate of convergence of Schwarz waveform relaxation methods for the time-dependent Schrödinger equation

Abstract

This paper is dedicated to the analysis of the rate of convergence of the classical and quasi-optimal Schwarz waveform relaxation (SWR) method for solving the linear Schrödinger equation with space-dependent potential. The strategy is based on i) the rewriting of the SWR algorithm as a fixed point algorithm in frequency space, and ii) the explicit construction of contraction factors thanks to pseudo-differential calculus. Some numerical experiments illustrating the analysis are also provided.