Asymptotic convergence rates of SWR methods for Schrödinger equations with an arbitrary number of subdomains

Xavier Antoine (1, 2) , Emmanuel Lorin (3, 4)

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
2 IECL - Institut Élie Cartan de Lorraine
3 School of Mathematics and Statistics [Ottawa]
4 CRM - Centre de Recherches Mathématiques [Montréal]

We derive some estimates of the rate of convergence of Schwarz Waveform Relaxation (SWR) methods for the Schrödinger equation using an arbitrary number of subdomains. Hence, we justify that under certain conditions, the rates of convergence mathematically obtained for two subdomains [6, 7, 8] are still asymptotically valid for a larger number of subdomains, as it is usually numerically observed [22].

Mots clés: domain decomposition method; Schwarz Waveform Relaxation; Schrödinger equation; asymptotic convergence rate

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Xavier Antoine, Emmanuel Lorin. Asymptotic convergence rates of SWR methods for Schrödinger equations with an arbitrary number of subdomains. Multiscale Science and Engineering, 2019, 1, pp.34-46. ⟨10.1007/s42493-018-00012-y⟩. ⟨hal-02340909⟩