Optimized and quasi-optimal schwarz waveform relaxation for the one dimensional schrödinger equation

Abstract

We design and study Schwarz Waveform relaxation algorithms for the linear Schrödinger equation with a potential in one dimension. We show that the overlapping algorithm with Dirichlet exchanges of informations on the boundary is slowly convergent, and we introduce two new classes of algorithms: the optimized Robin algorithm and the quasi-optimal algorithm. Numerical results illustrate the great improvement of these methods over the classical algorithm.