Asymptotic Convergence Rates of Schwarz Waveform Relaxation Algorithms for Schrödinger Equations with an Arbitrary Number of Subdomains

Abstract

We derive some asymptotic estimates of the rate of convergence of Schwarz Waveform Relaxation domain decomposition methods for the Schrodinger equation when using an arbitrary number of subdomains. Hence, we justify that under certain conditions, the rates of convergence mathematically obtained for two subdomains (Antoine et al. in ESAIM M2AN, https://doi.org/10.1051/m2an/2017048 , 2018; Antoine and Lorin in Numer Math 137(4):923–958, 2017; Antoine et al. in (submitted), 2018) are still asymptotically valid for a larger number of subdomains, as it is usually numerically observed (Halpern and Szeftel in Math Models Methods Appl Sci 20(12):2167–2199, 2010).