Toeplitz-like preconditioner for linear systems from spatial fractional diffusion equations

Iranian Journal of Numerical Analysis and Optimization

مقاله 5، دوره 11، شماره 1 - شماره پیاپی 19، خرداد 2021، صفحه 95-106   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2021.11325.0

نویسنده

N. Akhoundi^*

School of mathematics and computer science, Damghan university, Damghan, Iran.

چکیده

‎The article deals with constructing Toeplitz-like preconditioner for linear systems arising from finite difference discretization of the spatial fractional diffusion equations‎. ‎The coefficient matrices of these linear systems have an $S+L$ structure‎, ‎where $S$ is a symmetric positive definite (SPD) matrix and $L$ satisfies $\mbox{rank}(L)\leq 2$‎. ‎We introduce an approximation for the SPD part $S$‎, ‎which is called $P_S$‎, ‎and then we show that the preconditioner $P=P_S+L$ has the Toeplitz-like structure and its displacement rank is 6‎.  ‎The analysis shows that the eigenvalues of the corresponding preconditioned matrix are clustered around 1. Numerical experiments exhibit that the Toeplitz-like preconditioner can significantly improve the convergence properties of the applied iteration method.

کلیدواژه‌ها

Fractional diffusion equation؛ Toeplitz-like matrix؛ Krylov subspace methods؛ PGMRES

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