Multilevel preconditioning technique for Schwarz waveform relaxation domain decomposition method for real- and imaginary-time nonlinear Schrodinger equation

被引：3

作者：

Antoine, X. ^{[1
]}

Lorin, E. ^{[2
,3
]}

机构：

[1] Univ Lorraine, CNRS, Inria, IECL, F-54000 Nancy, France

[2] Univ Montreal, Ctr Rech Math, Montreal, PQ H3T 1J4, Canada

[3] Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 336卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Domain decomposition method; Schwarz waveform relaxation algorithm; Multilevel preconditioning; Nonlinear Schrodinger equation; Dynamics; Stationary states; ARTIFICIAL BOUNDARY-CONDITIONS; GROSS-PITAEVSKII EQUATIONS; LINEAR SCHRODINGER;

D O I：

10.1016/j.amc.2018.04.075

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is dedicated to the derivation of multilevel Schwarz Waveform Relaxation (SWR) Domain Decomposition Methods (DDM) in real- and imaginary-time for the NonLinear Schrodinger Equation (NLSE). In imaginary-time, it is shown that the multilevel SWR-DDM accelerates the convergence compared to the one-level SWR-DDM, resulting in an important reduction of the computational time and memory storage. In real-time, the method requires in addition the storage of the solution in overlapping zones at any time, but on coarser discretization levels. The method is numerically validated on the Classical SWR and Robin-based SWR methods, but can however be applied to any SWR-DDM approach. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：403 / 417

页数：15

共 28 条

[1]

[Anonymous], 1999, P 11 INT C DOM DEC M

[2] Artificial boundary conditions for one-dimensional cubic nonlinear Schrodinger equations [J].

Antoine, X ;

Besse, C ;

Descombes, S .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 43 (06) :2272-2293

[3] An analysis of Schwarz waveform relaxation domain decomposition methods for the imaginary-time linear Schrodinger and Gross-Pitaevskii equations [J].

Antoine, X. ;

Lorin, E. .

NUMERISCHE MATHEMATIK, 2017, 137 (04) :923-958

[4] Lagrange-Schwarz Waveform Relaxation domain decomposition methods for linear and nonlinear quantum wave problems [J].

Antoine, X. ;

Lorin, E. .

APPLIED MATHEMATICS LETTERS, 2016, 57 :38-45

[5] Domain Decomposition Method and High-Order Absorbing Boundary Conditions for the Numerical Simulation of the Time Dependent Schrodinger Equation with Ionization and Recombination by Intense Electric Field [J].

Antoine, X. ;

Lorin, E. ;

Bandrauk, A. D. .

JOURNAL OF SCIENTIFIC COMPUTING, 2015, 64 (03) :620-646

[6]

Antoine X., 2015, LECT NOTES MATH, V1

[7]

Antoine X, 2008, COMMUN COMPUT PHYS, V4, P729

[8] ASYMPTOTIC ESTIMATES OF THE CONVERGENCE OF CLASSICAL SCHWARZ WAVEFORM RELAXATION DOMAIN DECOMPOSITION METHODS FOR TWO-DIMENSIONAL STATIONARY QUANTUM WAVES [J].

Antoine, Xavier ;

Hou, Fengji ;

Lorin, Emmanuel .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2018, 52 (04) :1569-1596

[9] GPELab, a Matlab toolbox to solve Gross-Pitaevskii equations I: Computation of stationary solutions [J].

Antoine, Xavier ;

Duboscq, Romain .

COMPUTER PHYSICS COMMUNICATIONS, 2014, 185 (11) :2969-2991

[10] Robust and efficient preconditioned Krylov spectral solvers for computing the ground states of fast rotating and strongly interacting Bose-Einstein condensates [J].

Antoine, Xavier ;

Duboscq, Romain .

JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 258 :509-523

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