A fast finite volume method for conservative space-fractional diffusion equations in convex domains

We develop a fast finite volume method for variable-coefficient, conservative space-fractional diffusion equations in convex domains via a volume-penalization approach. The method has an optimal storage and an almost linear computational complexity. The method retains second-order accuracy without r...

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Bibliographic Details
Published in:Journal of computational physics 2016-04, Vol.310, p.63-84
Main Authors: Jia, Jinhong, Wang, Hong
Format: Article
Language:English
Subjects:
Anomalous diffusion
Circulant matrix
Computation
Conjugate gradient squared method
Diffusion
Diffusion rate
Extrapolation
Fast Fourier transform
Finite volume method
Mathematical analysis
Mathematical models
Optimization
Space-fractional diffusion equation
Toeplitz matrix
Volume penalization
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Summary:We develop a fast finite volume method for variable-coefficient, conservative space-fractional diffusion equations in convex domains via a volume-penalization approach. The method has an optimal storage and an almost linear computational complexity. The method retains second-order accuracy without requiring a Richardson extrapolation. Numerical results are presented to show the utility of the method.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2016.01.015