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 Affiliated with RC false Status 已發表Published An efficient multigrid solver for two-dimensional spatial fractional diffusion equations with variable coefficients: An efficient multigrid solver for two-dimensional SFDEs Pan,Kejia1; Sun,Hai Wei2; Xu,Yuan2; Xu,Yufeng1 2021-08-01 Source Publication Applied Mathematics and Computation ISSN 0096-3003 Volume 402 Abstract Extrapolation cascadic multigrid (EXCMG) method with the conjugate gradient smoother is shown to be an efficient solver for large sparse symmetric positive definite systems resulting from linear finite element discretization of second-order elliptic boundary value problems [Pan et al. J. Comput. Phys. 344 (2017) 499–515]. In this paper, we generalize the EXCMG method to solve a class of spatial fractional diffusion equations (SFDEs) with variable coefficients. Both steady-state and time-dependent problems are considered. First of all, space-fractional derivatives defined in Riemann–Liouville sense are discretized by using the weighted average of shifted Grünwald formula, which results in a fully dense and nonsymmetric linear system for the steady-state problem, or a semi-discretized ODE system for the time-dependent problem. Then, to solve the former problem, we propose the EXCMG method with the biconjugate gradient stabilized smoother to deal with the dense and nonsymmetric linear system. Next, such technique is extended to solve the latter problem since it becomes fully discrete when the Crank-Nicolson scheme is introduced to handle the temporal derivative. Finally, several numerical examples are reported to show that the EXCMG method is an efficient solver for both steady-state and time-dependent SFDEs, and performs much better than the V-cycle multigrid method with banded-splitting smoother for time-dependent SFDEs [Lin et al. J. Comput. Phys. 336 (2017) 69–86]. Keyword Biconjugate Gradient Stabilized Method Cascadic Multigrid Method Fractional Diffusion Equations Richardson Extrapolation Variable Coefficients DOI 10.1016/j.amc.2021.126091 URL View the original Indexed By SCIE Language 英語English WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000634798800011 Publisher ELSEVIER SCIENCE INC, STE 800, 230 PARK AVE, NEW YORK, NY 10169 USA Scopus ID 2-s2.0-85101654026 Fulltext Access Citation statistics Cited Times [WOS]:8   [WOS Record]     [Related Records in WOS] Document Type Journal article Collection DEPARTMENT OF MATHEMATICS Corresponding Author Xu,Yufeng Affiliation 1.School of Mathematics and Statistics,HNP-LAMA,Central South University,Changsha,410083,China2.Department of Mathematics,University of Macau,Macao,China Recommended CitationGB/T 7714 Pan,Kejia,Sun,Hai Wei,Xu,Yuan,et al. An efficient multigrid solver for two-dimensional spatial fractional diffusion equations with variable coefficients: An efficient multigrid solver for two-dimensional SFDEs[J]. Applied Mathematics and Computation,2021,402. APA Pan,Kejia,Sun,Hai Wei,Xu,Yuan,&Xu,Yufeng.(2021).An efficient multigrid solver for two-dimensional spatial fractional diffusion equations with variable coefficients: An efficient multigrid solver for two-dimensional SFDEs.Applied Mathematics and Computation,402. MLA Pan,Kejia,et al."An efficient multigrid solver for two-dimensional spatial fractional diffusion equations with variable coefficients: An efficient multigrid solver for two-dimensional SFDEs".Applied Mathematics and Computation 402(2021).
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