非连续变形分析中方程组的并行化求解方法

doi:10.7523/j.issn.2095-6134.2018.01.016

中国科学院大学学报 ›› 2018, Vol. 35 ›› Issue (1): 118-125.DOI: 10.7523/j.issn.2095-6134.2018.01.016

非连续变形分析中方程组的并行化求解方法

肖云帆, 肖俊, 缪青海, 王颖

中国科学院大学工程科学学院, 北京 100049

收稿日期:2017-01-09 修回日期:2017-02-24 发布日期:2018-01-15
通讯作者: 肖俊
基金资助:
国家自然科学基金（61471338）、中国科学院青年促进会（2015361）、中国科学院前沿科学重点研究项目（QYZDY-SSW-SYS004）和北京市科技新星计划（Z171100001117048）资助

The parallel methods of simultaneous equations in discontinuous deformation analysis

XIAO Yunfan, XIAO Jun, MIAO Qinghai, WANG Ying

School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2017-01-09 Revised:2017-02-24 Published:2018-01-15

摘要/Abstract

摘要： 非连续变形分析是针对非连续介质的数值计算方法。该方法存在计算效率较低的问题，而方程组求解是瓶颈。研究非连续变形分析在不同的计算条件下，选择不同的方程组求解方法可获得的计算效率。基于OpenMP与CUDA分别并行实现Jacobi迭代法与Jacobi预处理共轭梯度法，分析问题规模、计算时步长、块体接触关系对方程组求解效率的影响。通过算例测试，获得不同条件下选择方程组求解方法的经验公式，可有效指导非连续变形分析的并行方案设计。

关键词: 非连续变形分析, 并行计算, 方程组求解

Abstract: As an advanced numerical analysis method, discontinuous deformation analysis (DDA) shows relatively low efficiency. Simultaneous equations solusion is the bottleneck. This work focuses on how to choose an optimal solver in DDA. Jacobi and Jacobi preconditioned conjugate gradient methods are paralleled with OpenMP and CUDA. Three factors affecting the efficiency, computational scale, time step size, and block contact, are analyzed. Based on the tests, an empirical formula for choosing optimal solver in different computing conditions is obtained.

Key words: discontinuous deformation analysis(DDA), parallel computing, simultaneous equations solution

中图分类号:

O241.6
TU452

肖云帆, 肖俊, 缪青海, 王颖. 非连续变形分析中方程组的并行化求解方法[J]. 中国科学院大学学报, 2018, 35(1): 118-125.

XIAO Yunfan, XIAO Jun, MIAO Qinghai, WANG Ying. The parallel methods of simultaneous equations in discontinuous deformation analysis[J]. , 2018, 35(1): 118-125.

参考文献

[1] Shi G H. Discontinuous deformation analysis:a new numerical model for the statics and dynamics of block systems[J]. Engineering Computations, 1992, 9(2):157-168.
[2] 石根华.数值流形方法与非连续变形分析[M]. 北京:清华大学出版社, 1997:92-93.
[3] Bobet A, Fakhimi A, Johnson S, et al. Numerical models in discontinuous media:review of advances for rock mechanics applications[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2009, 135(11):1547-1561.
[4] Zheng H, Jiang W. Discontinuous deformation analysis based on complementary theory[J]. Science in China Series E:Technological Sciences, 2009, 52(9):2547-2554.
[5] Shi G H. Applications of discontinuous deformation analysis (DDA) to rock engineering[M]. Computational Mechanics. Springer Berlin Heidelberg, 2007:136-147.
[6] 刘婷婷, 王颖. 基于数值流形法的计算机动画建模[J]. 中国科学院研究生院学报, 2008, 25(6):843-848.
[7] 付晓东, 盛谦, 张勇慧. 基于OpenMP的非连续变形分析并行计算方法[J]. 岩土力学, 2014, 35(8):2401-2407.
[8] Yousef S. Iterative methods for sparse linear systems[M]. Philadelphia, Pennsylvania, United States:Society for Industrial and Applied Mathematics, 2003:95-102.
[9] Mikola R G, Sitar N. Explicit three dimensional discontinuous deformation analysis for blocky system[C]//47th US Rock Mechanics. Geomechanics Symposium. American Rock Mechanics Association, 2013.
[10] Miao Q, Huang M, Wei Q. Parallel computing of numerical manifold method with openMP[C]//Information, Computing and Telecommunication. Yc-Ict'09. IEEE Youth Conference on. IEEE, 2009:174-177.
[11] Xiao Y, Miao Q, Huang M, et al. Parallel computing of discontinuous deformation analysis based on graphics processing unit[J]. International Journal of Geomechanics, 2016:E4016010.
[12] Ning Y, Yang Z, Wei B, et al. Advances in two-dimensional discontinuous deformation analysis for rock-mass dynamics[J]. International Journal of Geomechanics, 2016:E6016001.

非连续变形分析中方程组的并行化求解方法

The parallel methods of simultaneous equations in discontinuous deformation analysis

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