A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes

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	A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes
	Fang, Z. W.; Zhang, J.L.; Sun, H. W.
	2022-02-01
Source Publication	Computers and Mathematics with Applications
ISSN	0898-1221
Pages	175-184
Abstract	In this paper, a fast finite volume method is proposed for the initial and boundary value problems of spatial fractional diffusion equations on nonuniform meshes. The discretizations of the Riemann-Liouville fractional derivatives lead to unstructured dense coefficient matrices, differing from the Toeplitz-like structure under the uniform mesh. The fast algorithm is proposed by using the sum-of-exponentials (SOE) technique to the spatial kernel 𝑥𝛼−1,𝛼∈(0, 1). Then, the matrix-vector multiplications of the resulting coefficient matrices could be implemented in (𝑚 log2𝑚)operations, where 𝑚 denotes the size of matrices. Iterative solvers are preferably applied to obtain the numerical solution. The proposed fast scheme is proved to be unconditionally stable for sufficiently accurate SOE approximation. Meanwhile, a banded preconditioner is exploited to accelerate the Krylov subspace method. Numerical experiments are provided to demonstrate the efficiency of the proposed fast algorithm.
Keyword	Spatial fractional diffusion equations Finite volume method Sum-of-exponentials technique Fast algorithm Banded preconditioner
Language	英語English
The Source to Article	PB_Publication
PUB ID	62905
Document Type	Journal article
Collection	University of Macau
Corresponding Author	Sun, H. W.
Recommended Citation GB/T 7714	Fang, Z. W.,Zhang, J.L.,Sun, H. W.. A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes[J]. Computers and Mathematics with Applications, 2022, 175-184.
APA	Fang, Z. W.., Zhang, J.L.., & Sun, H. W. (2022). A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes. Computers and Mathematics with Applications, 175-184.
MLA	Fang, Z. W.,et al."A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes".Computers and Mathematics with Applications (2022):175-184.

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