Fast Preconditioned Iterative Method for the Space Fractional Complex Ginzburg-Landau Equation

Lu Zhang; Lei Chen; Wenyu Zhou

Simulation Tools and Techniques. 12th EAI International Conference, SIMUtools 2020, Guiyang, China, August 28-29, 2020, Proceedings, Part I

Research Article

Fast Preconditioned Iterative Method for the Space Fractional Complex Ginzburg-Landau Equation

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@INPROCEEDINGS{10.1007/978-3-030-72792-5_8,
    author={Lu Zhang and Lei Chen and Wenyu Zhou},
    title={Fast Preconditioned Iterative Method for the Space Fractional Complex Ginzburg-Landau Equation},
    proceedings={Simulation Tools and Techniques. 12th EAI International Conference, SIMUtools 2020, Guiyang, China, August 28-29, 2020, Proceedings, Part I},
    proceedings_a={SIMUTOOLS},
    year={2021},
    month={4},
    keywords={Space fractional Ginzburg-Landau equation Toeplitz matrix Preconditioned numerical method},
    doi={10.1007/978-3-030-72792-5_8}
}

Lu Zhang
Lei Chen
Wenyu Zhou
Year: 2021
Fast Preconditioned Iterative Method for the Space Fractional Complex Ginzburg-Landau Equation
SIMUTOOLS
Springer
DOI: 10.1007/978-3-030-72792-5_8

Lu Zhang¹^,*, Lei Chen², Wenyu Zhou¹

1: School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou
2: School of Information Engineering, Xuzhou University of Technology, Xuzhou

*Contact email: yulu7517@126.com

Abstract

In this work, we give an effective preconditioned numerical method to solve the discreted linear system, which is obtained from the space fractional complex Ginzburg-Landau equation. The coefficient matrix of the linear system is the sum of a symmetric tridiagonal matrix and a complex Toeplitz matrix. The preconditioned iteration method has computational superiority since we can use the fast Fourier transform (FFT) and the circulant preconditioner to solve the discreted linear system. Numerical examples are tested to illustrate the advantage of the proposed preconditioned numerical method.

Keywords: Space fractional Ginzburg-Landau equation Toeplitz matrix Preconditioned numerical method

Published: 2021-04-27
Appears in: SpringerLink

: http://dx.doi.org/10.1007/978-3-030-72792-5_8

Fast Preconditioned Iterative Method for the Space Fractional Complex Ginzburg-Landau Equation

Abstract

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