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

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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)

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	Articles by authors
	WANG Zhanxue1
	YANG Jun1
	NI Kesong1
	NING Youjun2

Cite this article:

WANG Zhanxue1,YANG Jun1,NI Kesong1, et al. CUDA-based JPCG parallel solution algorithm for 3D-DDA global equations#br#[J]. , 2020, 39(6): 1231-1241.

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https://rockmech.whrsm.ac.cn/EN/10.13722/j.cnki.jrme.2019.0929 OR https://rockmech.whrsm.ac.cn/EN/Y2020/V39/I6/1231

[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.
[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))
[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.
[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))
[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.
[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.
[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.
[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.
[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.
[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))
[11] SHI G H. Contact theory[J]. Science China Technological Sciences，2015，58(9)：1 450–1 496.
[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.
[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.
[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))
[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))
[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))
[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.
[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))
[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.
[20] BELL N，GARLAND M. Efficient sparse matrix-vector multiplication on CUDA[R]. Santa Clara：NVIDIA Corporation，Dec，2008.
[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))
[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.
[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))
[24] NVIDIA Corporation. cuBLAS (v10.2.89) [EB/OL]. https://docs. nvidia.com/cuda/cublas/index.html，Nov 17，2019/Dec 4，2019.
[25] NIVIDIA Corporation. cuSPARSE (v10.2.89) [EB/OL]. https://docs. nvidia.com/cuda/cusparse/index.html，Nov 17，2019/Dec 4，2019.
[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))
[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))
[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))