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
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.