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Domain decomposition algorithms for the two dimensional nonlinear Schrödinger equation and simulation of Bose-Einstein condensates. (English) Zbl 1416.65328
Summary: 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.

MSC:
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
65Y05 Parallel numerical computation
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
Software:
GPELab; PETSc
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References:
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