On the rate of convergence of Schwarz waveform relaxation methods for the time-dependent Schrodinger equation

被引：6

作者：

Antoine, X. ^{[1
]}

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

机构：

[1] Univ Lorraine, UMR CNRS 7502, Inst Elie Cartan Lorraine, Inria Nancy Grand Est,SPHINX Team, F-54506 Vandoeuvre Les 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：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 354卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Schrodinger equation; Domain decomposition method; Pseudo-differential operator calculus; ABSORBING BOUNDARY-CONDITIONS; DOMAIN DECOMPOSITION METHODS; LINEAR SCHRODINGER; NUMERICAL-SIMULATION; DIRICHLET-NEUMANN;

D O I：

10.1016/j.cam.2018.12.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is dedicated to the analysis of the rate of convergence of the classical and quasi-optimal Schwarz waveform relaxation (SWR) method for solving the linear Schrodinger equation with space-dependent potential. The strategy is based on i) the rewriting of the SWR algorithm as a fixed point algorithm in frequency space, and ii) the explicit construction of contraction factors thanks to pseudo-differential calculus. Some numerical experiments illustrating the analysis are also provided. (C) 2018 Published by Elsevier B.V.

引用

页码：15 / 30

页数：16

共 50 条

[41] Solution of the time-dependent Schrodinger equation using time-dependent basis functions
Varga, Kalman
PHYSICAL REVIEW E, 2012, 85 (01):
[42] Time Domain Maxwell Equations Solved with Schwarz Waveform Relaxation Methods
Section de mathématiques, University of Geneva, Case Postale 64, 1211 Genève 4, Switzerland
Lect. Notes Comput. Sci. Eng., 2013, (263-270):
[43] Adaptive numerical methods for time-dependent Schrodinger equation in atomic and laser physics
Derbov, VL
Kaschiev, MS
Serov, VV
Gusev, AA
Vinitsky, SI
SARATOV FALL MEETING 2002: LASER PHYSICS AND PHOTONICS, SPECTROSCOPY, AND MOLECULAR MODELING III; COHERENT OPTICS OF ORDERED AND RANDOM MEDIA III, 2003, 5067 : 218 - 226
[44] Optimal stability polynomials for splitting methods, with application to the time-dependent Schrodinger equation
McLachlan, RI
Gray, SK
APPLIED NUMERICAL MATHEMATICS, 1997, 25 (2-3) : 275 - 286
[45] Efficient methods for linear Schrodinger equation in the semiclassical regime with time-dependent potential
Bader, Philipp
Iserles, Arieh
Kropielnicka, Karolina
Singh, Pranav
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2016, 472 (2193):
[46] A note on the H1-convergence of the overlapping Schwarz waveform relaxation method for the heat equation
Hui Zhang
Yao-Lin Jiang
Numerical Algorithms, 2014, 66 : 299 - 307
[47] A note on the H1-convergence of the overlapping Schwarz waveform relaxation method for the heat equation
Zhang, Hui
Jiang, Yao-Lin
NUMERICAL ALGORITHMS, 2014, 66 (02) : 299 - 307
[48] A method of generating exact solutions of the time-dependent Schrodinger equation with time-dependent mass
Schulze-Halberg, A
MODERN PHYSICS LETTERS A, 2002, 17 (24) : 1567 - 1573
[49] Solution of the time-dependent Schrodinger equation using a basis in time
Weatherford, CA
Red, E
Wynn, A
JOURNAL OF MOLECULAR STRUCTURE-THEOCHEM, 2002, 592 : 47 - 51
[50] Exact time dependence of solutions to the time-dependent Schrodinger equation
Lohe, M. A.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (03)

← 1 2 3 4 5 →