A Parallel Algorithm for the Two-Dimensional Time Fractional Diffusion Equation with Implicit Difference Method

被引：4

作者：

Gong, Chunye ^{[1
,2
,3
]}

Bao, Weimin ^{[1
,2
]}

Tang, Guojian ^{[1
]}

Jiang, Yuewen ^{[4
]}

Liu, Jie ^{[3
]}

机构：

[1] Natl Univ Def Technol, Coll Aerosp Sci & Engn, Changsha 410073, Hunan, Peoples R China

[2] Sci & Technol Space Phys Lab, Beijing 100076, Peoples R China

[3] Natl Univ Def Technol, Sch Comp Sci, Changsha 410073, Hunan, Peoples R China

[4] Univ Oxford, Dept Engn Sci, Oxford OX2 0ES, England

来源：

SCIENTIFIC WORLD JOURNAL | 2014年

基金：

中国国家自然科学基金;

关键词：

PARTICLE-TRANSPORT; NUMERICAL-SOLUTION; STABILITY;

D O I：

10.1155/2014/219580

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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(MxMyN2). 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.

引用

页数：8

共 50 条

[1] An Implicit Difference-ADI Method for the Two-dimensional Space-time Fractional Diffusion Equation
Nasrollahzadeh, F.
Hosseini, S. M.
[J]. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS, 2016, 11 (02): : 71 - 86
[2] Implicit difference approximation for the two-dimensional space-time fractional diffusion equation
Zhuang P.
Liu F.
[J]. Journal of Applied Mathematics and Computing, 2007, 25 (1-2) : 269 - 282
[3] Compact alternating direction implicit method for two-dimensional time fractional diffusion equation
Cui, Mingrong
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (06) : 2621 - 2633
[4] Additive Difference Scheme for Two-Dimensional Fractional in Time Diffusion Equation
Hodzic-Zivanovic, Sandra
Jovanovic, Bosko S.
[J]. FILOMAT, 2017, 31 (02) : 217 - 226
[5] Finite difference approximation for two-dimensional time fractional diffusion equation
Zhuang, P.
Liu, F.
[J]. JOURNAL OF ALGORITHMS & COMPUTATIONAL TECHNOLOGY, 2007, 1 (01) : 1 - 15
[6] Finite Difference/Element Method for a Two-Dimensional Modified Fractional Diffusion Equation
Zhang, Na
Deng, Weihua
Wu, Yujiang
[J]. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2012, 4 (04) : 496 - 518
[7] Pointwise error estimate of an alternating direction implicit difference scheme for two-dimensional time-fractional diffusion equation
Wang, Yue
Chen, Hu
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2021, 99 : 155 - 161
[8] An implicit nonlinear difference scheme for two-dimensional time-fractional Burgers’ equation with time delay
Mingcong Xiao
Zhibo Wang
Yan Mo
[J]. Journal of Applied Mathematics and Computing, 2023, 69 : 2919 - 2934
[9] An implicit nonlinear difference scheme for two-dimensional time-fractional Burgers' equation with time delay
Xiao, Mingcong
Wang, Zhibo
Mo, Yan
[J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2023, 69 (04) : 2919 - 2934
[10] An implicit numerical method for the two-dimensional fractional percolation equation
Chen, S.
Liu, F.
Turner, I.
Anh, V.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (09) : 4322 - 4331

← 1 2 3 4 5 →