Research Article A Parallel Algorithm for the Two-Dimensional Time Fractional Diffusion Equation with Implicit Difference Method Chunye Gong, 1,2,3 Weimin Bao, 1,2 Guojian Tang, 1 Yuewen Jiang, 4 and Jie Liu 3 1 College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China 2 Science and Technology on Space Physics Laboratory, Beijing 100076, China 3 School of Computer Science, National University of Defense Technology, Changsha 410073, China 4 Department of Engineering Science, University of Oxford, Oxford OX2 0ES, UK Correspondence should be addressed to Chunye Gong; gongchunye@gmail.com Received 9 January 2014; Accepted 6 February 2014; Published 12 March 2014 Academic Editors: F. Liu, A. Sikorskii, and S. B. Yuste Copyright © 2014 Chunye Gong et al. his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. It is very time consuming to solve fractional diferential equations. he computational complexity of two-dimensional fractional diferential equation (2D-TFDE) with iterative implicit inite diference method is (     2 ). In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. he experimental results show that the parallel algorithm compares well with the exact solution. he parallel algorithm on single Intel Xeon X5540 CPU runs 3.16–4.17 times faster than the serial algorithm on single CPU core. he parallel eiciency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future. 1. Introduction Building fractional mathematical models for speciic phe- nomenon and developing numerical or analytical solutions for these fractional mathematical models are very hot in recent years. Fractional difusion equations have been used to represent diferent kinds of dynamical systems [1]. But the fractional applications are rare. One reason for rare fractional applications is that the computational cost of approximating for fractional equations is too much heavy. he idea of fractional derivatives dates back to the 17th century. A fractional diferential equation is a kind of equation which uses fractional derivatives. Fractional equations provide a powerful instrument for the description of memory and hereditary properties of diferent substances. here has been a wide variety of numerical methods proposed for fractional equations [2, 3], for example, inite diference method [4–7], inite element method [8, 9], spec- tral method [10, 11], and meshless techniques [12]. Zhuang and Liu [4] presented an implicit diference approximation for two-dimensional time fractional difusion equation (2D- TFDE) on a inite domain and discussed the stability and convergence of the method. he numerical result of an example agrees well with their theoretical analysis. Tadjeran and Meerschaert presented a numerical method, which combines the alternating directions implicit (ADI) approach with a Crank-Nicolson discretization and a Richardson extrapolation to obtain an unconditionally stable second- order accurate inite diference method, to approximate a two-dimensional fractional difusion equation [13]. Two ADI schemes based on the  1 approximation and backward Euler method are considered for the two-dimensional fractional subdifusion equation [14]. It is very time consuming to numerically solve fractional diferential equations for high spatial dimension or big time integration. Short memory principle [15] and parallel computing [16, 17] can be used to overcome this diiculty. Parallel computing is used to solve computation intensive applications simultaneously [18–21]. Large scale applications in science and engineering such as particle transport [22–24], Hindawi Publishing Corporation e Scientific World Journal Volume 2014, Article ID 219580, 8 pages http://dx.doi.org/10.1155/2014/219580