标题:A FAST FINITE ELEMENT METHOD FOR SPACE-FRACTIONAL DISPERSION EQUATIONS ON BOUNDED DOMAINS IN R-2
作者:Du, Ning;Wang, Hong
作者机构:[Du, N] School of Mathematics, Shandong University, Jinan, Shandong, 250100, China;[ Wang, H] Department of Mathematics, University of South Carolina, 更多
通讯作者地址:[Du, N]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
来源:SIAM Journal on Scientific Computing
出版年:2015
卷:37
期:3
页码:A1614-A1635
DOI:10.1137/15M1007458
关键词:anomalous dispersion;fast Fourier transform;finite element method;integral-differential equations;space-fractional partial differential equations;Toeplitz matrix
摘要:We develop a fast and accurate finite element method for space-fractional dispersion equations in two space dimensions, which are expressed in terms of fractional directional derivatives in all the directions that are integrated with respect to a probability measure on the unit circle. The fast method significantly reduces the computational work of solving the discrete linear algebraic systems from O(N-3) by a direct solver to O(N logN) per iteration and a memory requirement from O(N-2) to O(N). Furthermore, the fast method reduces the evaluation of the stiffness matrix, which often constitutes a large portion of the CPU time, from O(N-2) to O(N). The developed preconditioned fast Krylov subspace iterative solver significantly reduces the number of iterations in a Krylov subspace iterative method and may improve the convergence behavior of the solver. Numerical results show the utility of the method.
收录类别:EI;SCOPUS;SCIE
WOS核心被引频次:9
Scopus被引频次:10
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-84940118596&doi=10.1137%2f15M1007458&partnerID=40&md5=a9abc7a3d361ac9a1311a6d212841835
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