title: A parallel algorithm for the two-dimensional time fractional diffusion equation with implicit difference method.
abstract: It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE) with iterative implicit finite difference method is O(M(x)M(y)N(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. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16-4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency 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.
authors.affiliation: College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China ; Science and Technology on Space Physics Laboratory, Beijing 100076, China ; School of Computer Science, National University of Defense Technology, Changsha 410073, China.
authors.forename: Chunye
authors.identifier: 0000-0003-0349-1100
authors.initials: C
authors.lastname: Gong
authors.affiliation: College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China ; Science and Technology on Space Physics Laboratory, Beijing 100076, China.
authors.forename: Weimin
authors.initials: W
authors.lastname: Bao
authors.affiliation: College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China.
authors.forename: Guojian
authors.initials: G
authors.lastname: Tang
authors.affiliation: Department of Engineering Science, University of Oxford, Oxford OX2 0ES, UK.
authors.forename: Yuewen
authors.initials: Y
authors.lastname: Jiang
authors.affiliation: School of Computer Science, National University of Defense Technology, Changsha 410073, China.
authors.forename: Jie
authors.initials: J
authors.lastname: Liu
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004058:Diffusion; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted
references.citation: J Math Anal Appl. 2013 Jul 15;403(2):532-546
references.pmid: 23626377