A Schwarz waveform relaxation method for time-dependent space fractional Schrodinger/heat equations

被引：3
作者：
Antoine, Xavier [1 ]
Lorin, Emmanuel [2 ,3 ]
机构：
[1] Univ Lorraine, CNRS, Inria, IECL, F-54000 Nancy, France
[2] Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada
[3] Univ Montreal, Ctr Rech Math, Montreal, PQ H3T 1J4, Canada
来源：
APPLIED NUMERICAL MATHEMATICS | 2022年 / 182卷
关键词：
Space fractional Schr?dinger equation; Space fractional heat equation; Fractional Laplacian; Domain decomposition method; Schwarz relaxation waveform algorithm; DOMAIN DECOMPOSITION METHODS; LINEAR SCHRODINGER; DIFFERENCE SCHEME; NUMERICAL-METHODS; GROUND-STATES; DYNAMICS; APPROXIMATION; COLLOCATION; DIFFUSION; BEAMS;
D O I：
10.1016/j.apnum.2022.07.012
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 and analysis of a Schwarz waveform relaxation domain decomposition method for solving time-dependent linear/nonlinear space fractional Schrodinger and heat equations. Along with the details of the derivation of the method and some mathematical properties, we also propose some illustrating numerical experiments and conjectures on the rate of convergence of the method. (C) 2022 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：248 / 264
页数：17
相关论文
共 71 条
[1]   Time Fractional Schrodinger Equation Revisited [J].
Achar, B. N. Narahari ;
Yale, Bradley T. ;
Hanneken, John W. .
ADVANCES IN MATHEMATICAL PHYSICS, 2013, 2013
[2]   ANALYSIS AND APPROXIMATION OF A FRACTIONAL CAHN-HILLIARD EQUATION [J].
Ainsworth, Mark ;
Mao, Zhiping .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2017, 55 (04) :1689-1718
[3]  
[Anonymous], 2002, PHYS FRACTAL OPERATO
[4]  
[Anonymous], 1990, The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis
[5]   Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layers [J].
Antoine, X. ;
Lorin, E. ;
Zhang, Y. .
NUMERICAL ALGORITHMS, 2021, 87 (01) :409-444
[6]   On the rate of convergence of Schwarz waveform relaxation methods for the time-dependent Schrodinger equation [J].
Antoine, X. ;
Lorin, E. .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 354 :15-30
[7]   Multilevel preconditioning technique for Schwarz waveform relaxation domain decomposition method for real- and imaginary-time nonlinear Schrodinger equation [J].
Antoine, X. ;
Lorin, E. .
APPLIED MATHEMATICS AND COMPUTATION, 2018, 336 :403-417
[8]   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
[9]  
Antoine X., NUMER LINEAR ALGEBRA, V28, pe2399
[10]  
Antoine X., 2019, MULTISCALE SCI ENG, V1, P34
12345678