An analysis of Schwarz waveform relaxation domain decomposition methods for the imaginary-time linear Schrödinger and Gross-Pitaevskii equations

DOI10.1007/s00211-017-0897-3zbMath1383.65122OpenAlexW2612062628MaRDI QIDQ1681793

Xavier Antoine, Emmanuel Lorin

Publication date: 24 November 2017

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-017-0897-3

zbMATH Keywords

convergencenumerical resultsdomain decompositionGross-Pitaevskii equationnonlinear Schrödinger equationsSchwarz waveform relaxationlinear Schrödinger equationnormalized gradient flow methodsemi-implicit Euler scheme

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items

Domain decomposition method for the \(N\)-body time-independent and time-dependent Schrödinger equations ⋮ On the rate of convergence of Schwarz waveform relaxation methods for the time-dependent Schrödinger equation ⋮ Asymptotic estimates of the convergence of classical Schwarz waveform relaxation domain decomposition methods for two-dimensional stationary quantum waves ⋮ Explicit Computation of Robin Parameters in Optimized Schwarz Waveform Relaxation Methods for Schro¨dinger Equations Based on Pseudodifferential Operators ⋮ A Schwarz waveform relaxation method for time-dependent space fractional Schrödinger/heat equations ⋮ Multilevel preconditioning technique for Schwarz waveform relaxation domain decomposition method for real- and imaginary-time nonlinear Schrödinger equation ⋮ Schwarz waveform relaxation-learning for advection-diffusion-reaction equations ⋮ Lagrange-Schwarz waveform relaxation domain decomposition methods for linear and nonlinear quantum wave problems

Uses Software

• GPELab

Cites Work

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