Domain decomposition algorithms for the two dimensional nonlinear Schrödinger equation and simulation of Bose-Einstein condensates

Christophe Besse (1) , Feng Xing (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 COFFEE - COmplex Flows For Energy and Environment

In this paper, we apply the optimized Schwarz method to the two dimensional nonlinear Schrödinger equation and extend this method to the simulation of Bose-Einstein condensates (Gross-Pitaevskii equation). We propose an extended version of the Schwartz method by introducing a preconditioned algorithm. The two algorithms are studied numerically. The experiments show that the preconditioned algorithm improves the convergence rate and reduces the computation time. In addition, the classical Robin condition and a newly constructed absorbing condition are used as transmission conditions.

Mots clés: nonlinear Schrödinger equation; optimized Schwarz method; rotating Bose–Einstein condensate; preconditioned algorithm; parallel algorithm

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

Christophe Besse, Feng Xing. Domain decomposition algorithms for the two dimensional nonlinear Schrödinger equation and simulation of Bose-Einstein condensates. SMAI Journal of Computational Mathematics, 2016, 2, pp.277-300. ⟨10.5802/smai-jcm.17⟩. ⟨hal-01285359⟩