基于CUDA的二维泊松方程快速直接求解

计算机科学 ›› 2013, Vol. 40 ›› Issue (10): 21-23.

基于CUDA的二维泊松方程快速直接求解

岳小宁,肖炳甲,罗正平

中国科学技术大学核科学技术学院合肥230027;中国科学院等离子体物理研究所计算机应用研究室合肥230031;中国科学院等离子体物理研究所计算机应用研究室合肥230031

出版日期:2018-11-16 发布日期:2018-11-16
基金资助:
本文受国家科技部“973”项目ITER计划专项(国内配套研究)(2012GB105000),国家自然科学基金(10835009)资助

Fast 2-dimension Poisson Direct Solver Based on CUDA

YUE Xiao-ning,XIAO Bing-jia and LUO Zheng-ping

Online:2018-11-16 Published:2018-11-16

摘要/Abstract

摘要： 二维泊松方程离散化之后可以转化为一个具有特殊格式的块三对角方程的求解问题,通过对这一结构化线性方程组的研究,提出了一个适用于统一计算架构(CUDA)的泊松方程并行算法。该算法通过离散正弦变化,可以将计算任务划分为若干相互独立的部分进行求解,各部分求解完成后再通过一次离散正弦变换即可获得最终解,整个求解过程只需要两次全局通信。结合GPU的硬件特征进行优化之后,该算法相比CPU上的串行算法可以获得10倍以上的加速比。

关键词: 泊松方程,统一计算架构,并行计算,块三对角方程

Abstract: The finite difference approximation of two-dimension poisson equation would create a block-tridiagonal equation system．An algorithm which is suitable with the Compute Unified Device Architecture(CUDA)was proposed．Through a discrete sine transform,the computation task could be divided into several completely independent parts,after solving these parts in parallel,the final result could be obtained through another discrete sine transform．Only two global synchronizing is needed during the computation．After carefully optimized,an acceleration rate of more than 10times is obtained.

Key words: Poisson equation,Compute unified device architecture,Parallel computing,Block-tridiagonal equation

岳小宁,肖炳甲,罗正平. 基于CUDA的二维泊松方程快速直接求解[J]. 计算机科学, 2013, 40(10): 21-23. https://doi.org/

YUE Xiao-ning,XIAO Bing-jia and LUO Zheng-ping. Fast 2-dimension Poisson Direct Solver Based on CUDA[J]. Computer Science, 2013, 40(10): 21-23. https://doi.org/

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