基于CUDA的JPCG并行算法求解三维DDA方程组

doi:10.13722/j.cnki.jrme.2019.0929

摘要
图/表
参考文献
相关文章 (15)

全文: PDF (739 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要非连续变形分析(discontinuous deformation analysis，DDA)方法已被广泛应用于岩土工程领域。不同于二维DDA，三维DDA更具备分析节理岩体变形和稳定性实际问题的能力。三维DDA块体间接触的复杂化，未知数规模的大幅增加，以及程序中数据和内存的管理，对总体平衡方程组的求解提出了更高的稳定性和效率要求。对于原DDA程序中采用的超松弛(successive over-relaxation，SOR)求解算法，当超松弛因子选取不合适时，会造成方程组求解的不收敛。基于GPU，采用compute unified device architecture(CUDA)并行计算架构，实现了三维DDA总体平衡方程组的雅可比预处理共轭梯度法(jacobi-preconditioned conjugate gradient，JPCG)并行求解，通过算例展示了JPCG算法与GPU技术相结合的加速效果。相较于原有串行SOR算法，不仅避免了超松弛因子选取对求解收敛性的影响，而且提高了求解效率，为采用三维DDA求解实际岩石力学与工程问题创造了有利条件。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	王占学1
	杨军1
	倪克松1
	甯尤军2

关键词 ：岩石力学, 三维非连续变形分析方法, compute unified device architecture(CUDA), 雅可比预处理共轭梯度法, 超松弛算法

Abstract：The discontinuous deformation analysis(DDA) method is widely used in geotechnical engineering. Different from the two-dimensional DDA (2D-DDA)，the three-dimensional DDA(3D-DDA) has more remarkable capability to analyze practical deformation and stability problems of jointed rock masses. For 3D-DDA，however，due to the complexity of block contact，the increase of unknowns and the management of data and memory in the program demand a more stable and efficient algorithm for solving global equilibrium equations. For the successive over-relaxation(SOR) algorithm used in the original DDA program，the improper selection of the SOR factor will make the solution of the global equilibrium equations unable to converge. In the present work，based on the compute unified device architecture of GPU，the parallel Jacobi-preconditioned conjugate gradient(JPCG) algorithm is developed to solve the 3D-DDA global equilibrium equations. Simulation examples are given to demonstrate the acceleration effect of the JPCG algorithm combined with the GPU technology. Compared with the original serial SOR algorithm，the parallel JPCG algorithm not only avoids the influence of the SOR factor on the convergence but also improves solution efficiency，which creates favorable conditions for the 3D-DDA to be used in practical rock mechanics and rock engineering problems.

Key words： rock mechanics three-dimensional discontinuous deformation analysis(3D-DDA) compute unified device architecture(CUDA) Jacobi-preconditioned conjugate gradient(JPCG) successive over-relaxation(SOR)

引用本文:

王占学1，杨军1，倪克松1，甯尤军2. 基于CUDA的JPCG并行算法求解三维DDA方程组[J]. 岩石力学与工程学报, 2020, 39(6): 1231-1241.
WANG Zhanxue1，YANG Jun1，NI Kesong1，NING Youjun2. CUDA-based JPCG parallel solution algorithm for 3D-DDA global equations#br#. , 2020, 39(6): 1231-1241.

链接本文:

http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2019.0929 或 http://rockmech.whrsm.ac.cn/CN/Y2020/V39/I6/1231

[27]	江巍，郑宏. 非连续变形分析方法中人为参数的影响[J]. 岩土力学，2007，28(12)：2 603-2 606.(JIANG Wei，ZHENG Hong. Influences of artificial parameters in DDA method[J]. Rock and Soil Mechanics，2007，28(12)：2 603-2 606.(in Chinese))
[24]	NVIDIA Corporation. cuBLAS (v10.2.89) [EB/OL]. https://docs. nvidia.com/cuda/cublas/index.html，Nov 17，2019/Dec 4，2019.
[11]	SHI G H. Contact theory[J]. Science China Technological Sciences，2015，58(9)：1 450-1 496.
[3]	NI K S，YANG J，NING Y J，et al. A modified sub-block DDA fracturing modelling method for rock[J]. Engineering Analysis with Boundary Elements，2020，111：154-166.
[12]	ZHENG H，ZHANG P，DU X. Dual form of discontinuous deformation analysis[J]. Computer Methods in Applied Mechanics and Engineering，2016，305：196-216.
[7]	LIU G，LI J. A three-dimensional discontinuous deformation analysis method for investigating the effect of slope geometrical characteristics on rockfall behaviors[J]. International Journal of Computational Methods，2018，16(8)：1850122.
[9]	ZHANG Q B，HE L，ZHU W S. Displacement measurement techniques and numerical verification in 3D geomechanical model tests of an underground cavern group[J]. Tunnelling and Ungerground Space Technology，2016，56：54-64.
[14]	徐栋栋，邬爱清. 基于显式时间积分的非连续变形分析方法[J]. 岩石力学与工程学报，2016，35(增2)：3 526-3 534.(XU Dongdong，WU Aiqing. Discontinuous deformation analysis method based on the explicit time integration scheme[J]. Chinese Journal of Rock Mechanics and Engineering，2016，35(Supp.2)：3 526-3 534.(in Chinese))
[17]	SONG Y，DA H，ZENG B. GPU-based parallel computation for discontinuous deformation analysis (DDA) method and its application to modelling earthquake-induced landslide[J]. Computers and Geotechnics，2017，86：80-94.
[19]	PENG X Y，CHEN G Q，YU P C，et al. Parallel computing of three-dimensional discontinuous deformation analysis based on OpenMP[J]. Computers and Geotechnics，2019，106：304-313.
[22]	HELFENSTEIN R，KOKO J. Parallel preconditioned conjugate gradient algorithm on GPU[J]. Journal of Computational and Applied Mathematics，2012，236(15)：3 584-3 590.
[1]	SHI G H. Discontinuous deformation analysis: a new numerical model for the static and dynamics of block systems[J]. Engineering Computations，1992，9(2)：157-168.
[10]	刘泉声，蒋亚龙，何军. 非连续变形分析的精度改进方法及研究趋势[J]. 岩土力学，2017，38(6)：1 746-1 761.(LIU Quansheng，JIANG Yalong，HE Jun. Precision improvement methods and research trends of discontinuous deformation analysis[J]. Rock and Soil Mechanics，2017，38(6)：1 746-1 761.(in Chinese))
[20]	BELL N，GARLAND M. Efficient sparse matrix-vector multiplication on CUDA[R]. Santa Clara：NVIDIA Corporation，Dec，2008.
[25]	NIVIDIA Corporation. cuSPARSE (v10.2.89) [EB/OL]. https://docs. nvidia.com/cuda/cusparse/index.html，Nov 17，2019/Dec 4，2019.
[6]	WANG W，ZHANG H，ZHENG L，et al. A new approach for modeling landslide movement over 3D topography using 3D discontinuous deformation analysis[J]. Computers and Geotechnics，2017，81：87-97.
[8]	TAN B H，REN F Y，NING Y J，et al. A new mining scheme for hanging-wall ore-body during the transition from open pit to underground mining: a numerical study[J]. Advances in Civil Engineering，2018，2018：1465672.
[16]	张洪，张迎宾，郑路，等. 基于中心差分方案的显式三维非连续变形分析法[J]. 岩石力学与工程学报，2018，37(7)：1 649-1 658. (ZHANG Hong，ZHANG Yingbin，ZHENG Lu，et al. Explicit three-dimensional discontinuous deformation analysis based on a central difference scheme[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(7)：1 649-1 658.(in Chinese))
[18]	肖云帆，肖俊，缪青海，等. 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，et al. The parallel methods of simultaneous equations in discontinuous deformation analysis[J]. Journal of University of Chinese Academy of Sciences，2018，35(1)：118-125.(in Chinese))
[26]	张杨，邬爱清，林绍忠. 三维高阶DDA方法的静力分析研究[J]. 岩石力学与工程学报，2010，29(3)：558-564.(ZHANG Yang，WU Aiqing，LIN Shaozhong. Study of static analysis of 3D high-order DDA[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29(3)：558-564.(in Chinese))
[28]	邬爱清，冯细霞，卢波. 非连续变形分析中时间步及弹簧刚度取值研究[J]. 岩土力学，2015，36(3)：891-897.(WU Aiqing，FENG Xixia，LU Bo. Parametric research on time step and spring stiffness in DDA[J]. Rock and Soil Mechanics，2015，36(3)：891-897.(in Chinese))
[2]	徐栋栋，邬爱清，李聪，等. 破裂全过程模拟的改进非连续变形分析方法[J]. 岩土力学，2019，40(3)：1 170-1 178.(XU Dongdong，WU Aiqing，LI Cong，et al. An improved discontinuous deformation analysis method for simulation of whole fracturing process[J]. Rock and Soil Mechanics，2019，40(3)：1 170-1 178.(in Chinese))
[5]	NING Y J，YANG Z，WEI B，et al. Advances in two-dimensional discontinuous deformation analysis for rock-mass dynamics[J]. International Journal of Geomechanics，2017，17(5)：E6016001.
[15]	付晓东，盛谦，张勇慧，等. 非连续变形分析(DDA)线性方程组的高效求解算法[J]. 岩土力学，2016，37(4)：1 171-1 178.(FU Xiaodong，SHENG Qian，ZHANG Yonghui，et al. High efficient algorithms for solving linear equations in discontinuous deformation analysis[J]. Rock and Soil Mechanics，2016，37(4)：1 171-1 178.(in Chinese))
[4]	甯尤军，江成，康歌. 爆炸应力波作用下的凿岩爆破破岩模拟[J]. 北京理工大学学报，2015，35(增2)：33-36.(NING Youjun，JIANG Cheng，KANG Ge. Numerical modeling of rock failure in drilling blasting under the effect of explosion-induced stress waves[J]. Transactions of Beijing of Technology，2015，35(Supp.2)：33-36.(in Chinese))
[13]	JIANG W，ZHENG H，SUN G，et al. 3D DDA based on variational inequality theory and its solution scheme[J]. International Journal of Computational Methods，2018，15(11)：1850081.
[23]	程润伟，格罗斯曼，麦克切尔. CUDA C编程权威指南[M]. 颜成钢，殷建，李亮译. 北京：机械工业出版社，2017：281-283.(CHEN J，GROSSMAN M，MCKERCHER T. Professional CUDA C Programming[M]. Translated by YAN Chenggang，YIN Jian，LI Liang. Beijing：China Machine Press，2017：281-283.(in Chinese))
[21]	戈卢布，范洛恩. 矩阵计算[M]. 第4版. 北京：人民邮电出版社，2014：597-670.(GOLUB G H，VANLOAN C F. Matrix computatipons[M]. 4th ed. Beijing：Post and Telecom Press，2014：597-670.(in Chinese))