On single-step HSS iterative method with circulant preconditioner for fractional diffusion equations

Autor:	Ya-E Qi, Guo-Feng Zhang, Mu-Zheng Zhu
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	Circulant preconditioner Algebra and Number Theory Partial differential equation Preconditioned conjugate gradient (PCG) method Preconditioner Iterative method Applied Mathematics lcsh:Mathematics 010103 numerical & computational mathematics lcsh:QA1-939 01 natural sciences Hermitian matrix Computer Science::Numerical Analysis Toeplitz 010101 applied mathematics Rate of convergence Conjugate gradient method Fractional diffusion equations Applied mathematics Single-step Hermitian and skew-Hermitian splitting 0101 mathematics Coefficient matrix Circulant matrix Analysis Mathematics
Zdroj:	Advances in Difference Equations, Vol 2019, Iss 1, Pp 1-14 (2019)
ISSN:	1687-1847
Popis:	By exploiting Toeplitz-like structure and non-Hermitian dense property of the discrete coefficient matrix, a new double-layer iterative method called SHSS-PCG method is employed to solve the linear systems originating from the implicit finite difference discretization of fractional diffusion equations (FDEs). The method is a combination of the single-step Hermitian and skew-Hermitian splitting (SHSS) method with the preconditioned conjugate gradient (PCG) method. Further, the new circulant preconditioners are proposed to improve the efficiency of SHSS-PCG method, and the computation cost is further reduced via using the fast Fourier transform (FFT). Theoretical analysis shows that the SHSS-PCG iterative method with circulant preconditioners is convergent. Numerical experiments are given to show that our SHSS-PCG method with circulant preconditioners preforms very well, and the proposed circulant preconditioners are very efficient in accelerating the convergence rate.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::49ac31df97addd03ccc7e3fb6fdea463 http://link.springer.com/article/10.1186/s13662-019-2353-4 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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