An efficient preconditioner for linear systems arising from high-order accurate schemes of time fractional diffusion equations

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Di Gan, Guo-Feng Zhang, Zhao-Zheng Liang
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引用次数: 0

Abstract

In this paper, we study preconditioners for all-at-once systems arising from the discretization of time-fractional sub-diffusion equations. Due to the use of high-order accurate formulas in time fractional derivative, the coefficient matrix does not have a Toeplitz structure. We reconstructed the coefficient matrix so that the all-at-once system has a non-symmetric Toeplitz-like structure. Based on the non-symmetric Toplitz-like structure of the new system, we designed a preconditioner that can be quickly diagonalized by discrete sine transform and fast Fourier transform techniques. we show that the spectrum of the preconditioned matrix are clustered around 1. Also, we verified the effectiveness of the proposed preconditioner by numerical experiments.

Abstract Image

时间分数扩散方程高阶精确方案所产生的线性系统的高效预处理器
本文研究了由时间分数子扩散方程离散化产生的全一次系统的预处理。由于在时间分数导数中使用了高阶精确公式,系数矩阵不具有 Toeplitz 结构。我们对系数矩阵进行了重构,从而使全一次系统具有非对称托普利兹结构。基于新系统的非对称托普利兹结构,我们设计了一种预处理器,它可以通过离散正弦变换和快速傅里叶变换技术快速对角。我们的研究表明,预处理矩阵的频谱集中在 1 附近。
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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