Solving the Caputo Fractional Reaction-Diffusion Equation on GPU

被引：9

作者：

Liu, Jie ^{[1
]}

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

Bao, Weimin ^{[2
,3
]}

Tang, Guojian ^{[3
]}

Jiang, Yuewen ^{[4
]}

机构：

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

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

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

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

来源：

DISCRETE DYNAMICS IN NATURE AND SOCIETY | 2014年 / 2014卷

基金：

中国国家自然科学基金;

关键词：

PARTICLE-TRANSPORT; PARALLEL ALGORITHM; STABILITY;

D O I：

10.1155/2014/820162

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a parallel GPU solution of the Caputo fractional reaction-diffusion equation in one spatial dimension with explicit finite difference approximation. The parallel solution, which is implemented with CUDA programming model, consists of three procedures: preprocessing, parallel solver, and postprocessing. The parallel solver involves the parallel tridiagonal matrix vector multiplication, vector-vector addition, and constant vectormultiplication. Themost time consuming loop of vector-vector addition and constant vector multiplication is optimized and impressive performance improvement is got. The experimental results show that the GPU solution compares well with the exact solution. The optimized GPU solution on NVIDIA Quadro FX 5800 is 2.26 times faster than the optimized parallel CPU solution on multicore Intel Xeon E5540 CPU.

引用

页数：7

共 37 条

[1] Stability of functional equations in single variable
Agarwal, RP
Xu, B
Zhang, WN
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 288 (02) : 852 - 869
[2] On the Numerical Solution of Fractional Parabolic Partial Differential Equations with the Dirichlet Condition
Ashyralyev, Allaberen
Cakir, Zafer
[J]. DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2012, 2012
[3] Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann Condition
Ashyralyev, Allaberen
Dal, Fadime
[J]. DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2012, 2012
[4] On Some Recent Developments in Ulam's Type Stability
Brillouet-Belluot, Nicole
Brzdek, Janusz
Cieplinski, Krzysztof
[J]. ABSTRACT AND APPLIED ANALYSIS, 2012,
[5] Ulam's Type Stability
Brzdek, Janusz
Brillouet-Belluot, Nicole
Cieplinski, Krzysztof
Xu, Bing
[J]. ABSTRACT AND APPLIED ANALYSIS, 2012,
[6] [陈景华 CHEN Jinghua], 2007, [厦门大学学报. 自然科学版, Journal of Xiamen University. Natural Science], V46, P616
[7] Chen SJ, 2012, RECONFIGURABLE NETWORKS-ON-CHIP, P15, DOI 10.1007/978-1-4419-9341-0_2
[8] AN EFFICIENT PARALLEL ALGORITHM FOR THE NUMERICAL SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATIONS
Diethelm, Kai
[J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2011, 14 (03) : 475 - 490
[9] Fosner A., AEQUATIONES MATH, V84
[10] Mathematical modeling of time fractional reaction-diffusion systems
Gafiychuk, V.
Datsko, B.
Meleshko, V.
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 220 (1-2) : 215 - 225

← 1 2 3 4 →