A Class of Preconditioners Based on Positive-Definite Operator Splitting Iteration Methods for Variable-Coefficient Space-Fractional Diffusion Equations  

作　　者：Jun-Feng Yin Yi-Shu Du 

机构地区：[1]School of Mathematical Sciences,Tongji University,Shanghai 200092,China

出　　处：《Communications on Applied Mathematics and Computation》2021年第1期157-176,共20页应用数学与计算数学学报（英文）

基　　金：This work was supported by the National Natural Science Foundation of China(No.11971354);The author Yi-Shu Du acknowledges the financial support from the China Scholarship Council(File No.201906260146).

摘　　要：After discretization by the finite volume method,the numerical solution of fractional diffusion equations leads to a linear system with the Toeplitz-like structure.The theoretical analysis gives sufficient conditions to guarantee the positive-definite property of the discretized matrix.Moreover,we develop a class of positive-definite operator splitting iteration methods for the numerical solution of fractional diffusion equations,which is unconditionally convergent for any positive constant.Meanwhile,the iteration methods introduce a new preconditioner for Krylov subspace methods.Numerical experiments verify the convergence of the positive-definite operator splitting iteration methods and show the efficiency of the proposed preconditioner,compared with the existing approaches.

关 键 词：Fractional diffusion equations Finite volume method Operator splitting Positive-definite 

分 类 号：O17[理学—数学]