标题:A Preconditioned Fast Finite Volume Method for Distributed-Order Diffusion Equation and Applications
作者:Fu, Hongfei; Liu, Huan; Zheng, Xiangcheng
作者机构:[Fu, Hongfei] China Univ Petr East China, Coll Sci, Qingdao 266580, Shandong, Peoples R China.; [Liu, Huan] Shandong Univ, Sch Math, Jinan 250100, S 更多
通讯作者:Fu, HF
通讯作者地址:[Fu, HF]China Univ Petr East China, Coll Sci, Qingdao 266580, Shandong, Peoples R China.
来源:EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
出版年:2019
卷:9
期:1
页码:28-44
DOI:10.4208/eajam.160418.190518
关键词:Distributed-order diffusion equation; finite volume method; fast; conjugate gradient method; circulant preconditioner; parameter; identification
摘要: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 O(NK) 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 O(MN3 + NK) to O(l(A) MN logN + NK), where l(A) is 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.
收录类别:SCOPUS;SCIE
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85074306965&doi=10.4208%2feajam.160418.190518&partnerID=40&md5=244e9fc377ced7a2a2558b051e0e5367
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