UM
Preconditioning for symmetric positive definite systems in balanced fractional diffusion equations
Fang,Zhi Wei1; Lin,Xue Lei2,3; Ng,Michael K.4; Sun,Hai Wei5
2021
Source PublicationNumerische Mathematik
ISSN0029-599X
AbstractIn this paper, we study the finite volume discretization method for balanced fractional diffusion equations where the fractional differential operators are comprised of both Riemann-Liouville and Caputo fractional derivatives. The main advantage of this approach is that new symmetric positive definite Toeplitz-like linear systems can be constructed for solving balanced fractional diffusion equations when diffusion functions are non-constant. It is different from non-symmetric Toeplitz-like linear systems usually obtained by existing numerical methods for fractional diffusion equations. The preconditioned conjugate gradient method with circulant and banded preconditioners can be applied to solve the proposed symmetric positive definite Toeplitz-like linear systems. Numerical examples, for both of one- and two- dimensional cases, are given to demonstrate the good accuracy of the finite volume discretization method and the fast convergence of the preconditioned conjugate gradient method.
DOI10.1007/s00211-021-01175-x
URLView the original
Language英语
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Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorNg,Michael K.
Affiliation1.School of Mathematics and Big Data,Foshan University,Foshan,China
2.Shenzhen JL Computational Science and Applied Research Institute,Shenzhen,China
3.Beijing Computational Science Research Center,Beijing,100193,China
4.Department of Mathematics,The University of Hong Kong,Pokfulam,Hong Kong
5.Department of Mathematics,University of Macau,Macao
Recommended Citation
GB/T 7714
Fang,Zhi Wei,Lin,Xue Lei,Ng,Michael K.,et al. Preconditioning for symmetric positive definite systems in balanced fractional diffusion equations[J]. Numerische Mathematik,2021.
APA Fang,Zhi Wei,Lin,Xue Lei,Ng,Michael K.,&Sun,Hai Wei.(2021).Preconditioning for symmetric positive definite systems in balanced fractional diffusion equations.Numerische Mathematik.
MLA Fang,Zhi Wei,et al."Preconditioning for symmetric positive definite systems in balanced fractional diffusion equations".Numerische Mathematik (2021).
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