Volume 9, Issue 1
A Preconditioned Fast Finite Volume Method for Distributed-Order Diffusion Equation and Applications

Hongfei Fu ,  Huan Liu and Xiangcheng Zheng

10.4208/eajam.160418.190518

East. Asia. J. Appl. Math., 9 (2019), pp. 28-44.

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  • Abstract

A Crank-Nicolson finite volume scheme for the modeling of the Riesz space distributed-order diffusion equation is proposed. The corresponding linear system has a symmetric positive definite Toeplitz matrix. It can be efficiently stored in θ (N K) memory. Moreover, for the finite volume scheme, a fast version of conjugate gradient (FCG) method is developed. Compared with the Gaussian elimination method, the computational complexity is reduced from θ (MN3 + N K) to O (lAMN logN + N K), where lAis the average number of iterations at a time level. Further reduction of the computational cost is achieved due to use of a circulant preconditioner. The preconditioned fast finite volume method is combined with the Levenberg-Marquardt method to identify the free parameters of a distribution function. Numerical experiments show the efficiency of the method.

  • History

Published online: 2019-01

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