文章基本信息

标题：On TDS-PCG Iteration Method with Circulant Preconditioners for Solving the Space Fractional Coupled Nonlinear Schrodinger Equations
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作者：Mu-Zheng Zhu ; Min-Li Zeng ; Ya-E Qi 等
期刊名称：Engineering Letters
印刷版ISSN：1816-093X
电子版ISSN：1816-0948
出版年度：2021
卷号：29
期号：3
页码：1072-1077
语种：English
出版社：Newswood Ltd
摘要：The goal of this paper is to solve the complexsymmetric linear systems generated from the discretizationof the space fractional coupled nonlinear Schrödinger (CNLS)equations, whose coefficient matrix is equal to the sum of asymmetric positive definite Toeplitz matrix and a Hermitianpositive definite complex diagonal matrix. In order to make thebest use of the full Toeplitz structure of the coefficient matrix,a new Toeplitz and diagonal splitting (TDS) is given and thecorresponding TDS iteration method is proposed to solve thediscretized linear systems, then two circulant preconditionersbased on Strang’s and T. Chan’s circulant approximation, areproposed to accelerate the convergence of the preconditionedconjugated gradient (PCG) method for solving the first linearsub-system in the TDS method. Theoretical analysis andnumerical experiments demonstrate that the TDS methodis unconditional convergence and the TDS-PCG inner-outeriteration method with two circulant preconditioners to solvethe discretization linear systems of the space fractional CNLSequations is feasible and efficient.
关键词：space fractional coupled nonlinear Schrödinger equations; Toeplitz matrix; Toeplitz and diagonal splitting (TDS) iteration method; circulant preconditioner; PCG method