Asymptotic estimates of the convergence of classical Schwarz waveform relaxation domain decomposition methods for two-dimensional stationary quantum waves

DOI10.1051/m2an/2017048zbMath1407.65152OpenAlexW2612168875MaRDI QIDQ4613923

Fengji Hou, Xavier Antoine, Emmanuel Lorin

Publication date: 25 January 2019

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/m2an/2017048

zbMATH Keywords

stationary statesSchrödinger equationconvergence ratedomain decomposition methodGross-Pitaevskii equationabsorbing boundary conditionsSchwarz waveform relaxationnormalized gradient flowsymbolical asymptotic expansionpseudo-differential operator theoryimaginary-time

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) Asymptotic expansions of solutions to PDEs (35C20) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

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 ⋮ 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

Uses Software

• GPELab

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