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.

Domain decomposition method, Pseudo-differential operator calculus, Schrödinger equation
dx.doi.org/10.1016/j.cam.2018.12.006
Journal of Computational and Applied Mathematics
School of Mathematics and Statistics

Antoine, X. (X.), & Lorin, E. (2019). On the rate of convergence of Schwarz waveform relaxation methods for the time-dependent Schrödinger equation. Journal of Computational and Applied Mathematics, 354, 15–30. doi:10.1016/j.cam.2018.12.006