基于静态双重区域分解的两种接触并行算法
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摘要
CHAP3D是北京应用物理与计算数学研究所自主研发的Lagrange通用弹塑性流体力学分析程序.文章介绍了在CHAP3D程序中使用的、针对多处理器集群的、基于静态双重区域分解的两种接触并行算法.第一种是分配单个完整接触面的接触并行算法,此算法将一对完整的接触面分配到一个处理器上,并建立计算域与接触域的通信关系.此接触并行算法的优点是简单,在具有接触面的处理器上可以直接使用串行的接触搜索算法和接触力耦合计算算法.另一种是主面剖分区域分解的接触并行算法,此算法将所有接触面的主面区域分解到所有处理器上.须建立计算域与接触域以及接触域内各处理器间的两种通信关系.该接触并行算法是一个负载平衡的并行算法,具有很好的并行效率和可扩展性.数值算例显示,这两种接触并行算法都能够很好地模拟多种不同类型的接触问题.
CHAP3 D code is a three-dimensional elastic-plastic Lagrangian program developed by IAPCM. The contact parallel algorithms used in CHAP3 D code for the clusters of multi-processors were introduced in this paper. The dual domain decomposition method and two strategies of contact domain decomposition were adopted in these parallel contact algorithms. One is to distribute a pair of whole contact surfaces to a processor, and a communication between the computational domain and the contact domain was established. The serial contact search algorithm and the contact forces algorithm can be applied directly. The other is to divide the master surface mesh into every processor. Two types of communications, the communication between the computational domain and the contact domain and the communication among all the processors in the contact domain, should be constructed in this contact parallel algorithm. The contact parallel algorithm is a scalable parallel algorithm with load-balance. The numerical examples illustrate that these two types of contact parallel algorithms have the abilities to simulate different types of contact problems.
CHAP3 D code is a three-dimensional elastic-plastic Lagrangian program developed by IAPCM. The contact parallel algorithms used in CHAP3 D code for the clusters of multi-processors were introduced in this paper. The dual domain decomposition method and two strategies of contact domain decomposition were adopted in these parallel contact algorithms. One is to distribute a pair of whole contact surfaces to a processor, and a communication between the computational domain and the contact domain was established. The serial contact search algorithm and the contact forces algorithm can be applied directly. The other is to divide the master surface mesh into every processor. Two types of communications, the communication between the computational domain and the contact domain and the communication among all the processors in the contact domain, should be constructed in this contact parallel algorithm. The contact parallel algorithm is a scalable parallel algorithm with load-balance. The numerical examples illustrate that these two types of contact parallel algorithms have the abilities to simulate different types of contact problems.
引文
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[28] Wang F J,Feng Y T,Owen D R.Parallelisation for finite-discrete element analysis in a distributed-memory environment[J].International Journal of Computational Engineering Science,2004,5(1):1-23.
[29] Zheng J W,An X H,Huang M S.GPU-based parallel algorithm for particle contact detection and its application in self-compacting concrete flow simulations[J].Com-puters & Structures,2012,112-113:193-204.
[30] Melanz D,Fang L N,Jayakumar P,et al.A comparison of numerical methods for solving multibody dynamics problems with frictional contact modeled via differential variational inequalities[J].Computer Methods in Applied Mechanics and Engineering,2017,320:668-693.
[31] Cai Y,Cui X Y,Li G Y,et al.A parallel finite element procedure for contact-impact problems using edge-based smooth triangular element and GPU[J].Computer Physics Communications,2018,225:47-58.
[32] 姜玉曦,周海兵,张树道.基于三角剖分局部搜索的三维滑移面算法[J].北京理工大学学报,2010,30(4):501-504.Jiang Y X,Zhou H B,Zhang S D.Three-dimensional contact algorithm for sliding surface based on triangular subdivision local search[J].Transactions of Beijing Institute of Technology,2010,30(4):501-504 (in Chinese).
[33] 姜玉曦,周海兵,熊俊,等.基于双三次曲面片的三维接触面光滑方法[J].工程力学,2016,33(2):11-17.Jiang Y X,Zhou H B,Xiong J,et al.A 3D contact smoothing method based on Bi-cubic parametric pat-ches[J].Engineering Mechanics,2016,33(2):11-17 (in Chinese).
[34] Wriggers P.Computational contact mechanics[M].Ber-lin:Springer,2006.
[35] 姜玉曦,周海兵,熊俊,等.三维光滑接触界面上的分配参数滑移面算法[J].计算物理,2015,32(4):386-394.Jiang Y X,Zhou H B,Xiong J,et al.A distributed parameter contact algorithm for sliding surfaces on a three-dimensional smoothed contact surface[J].Chinese Journal of Computational Physics,2015,32(4):386-394 (in Chinese).
[36] Dawes A S.A three-dimensional contact algorithm for sliding surfaces[J].International Journal for Numerical Methods in Fluids,2003,42(11):1189-1210.
[37] 张世文,华劲松,刘仓理,等.金属圆管内爆轰波相互作用效应的数值模拟研究[J].爆炸与冲击,2004,24(3):219-225.Zhang S W,Hua J S,Liu C L,et al.A numerical simulation of the metallic tube expansion induced by inside head-on hitting two detonation waves[J].Explosion and Shock Waves,2004,24(3):219-225 (in Chinese).
[2] 张树道,熊俊,周海兵,等.拉氏计算方法研究和应用数值模拟软件研制[C].第八届全国爆炸力学学术会议论文集.井冈山:中国力学学会爆炸力学专业委员会,2007.Zhang S D,Xiong J,Zhou H B,et al.The study of the Lagrangian numerical algorithm and the development of the numerical application software[C].The 8th National Conference on Explosion Mechanics,Jinggang Mountain,Jiangxi,2007(in Chinese).
[3] Bauer A L,Burton D E,Caramana E J,et al.The internal consistency,stability,and accuracy of the discrete,compatible formulation of Lagrangian hydrodynamics[J].Journal of Computational Physics,2006,218(2):572-593.
[4] Barlow A J.A compatible finite element multi-material ALE hydrodynamics algorithm[J].International Journal for Numerical Methods in Fluids,2008,56(8):953-964.
[5] Chang C H,Stagg A K.A compatible Lagrangian hydrodynamic scheme for multicomponent flows with mixing[J].Journal of Computational Physics,2012,231(11):4279-4294.
[6] Owen J M,Shashkov M.Arbitrary Lagrangian Eulerian remap treatments consistent with staggered compatible total energy conserving Lagrangian methods[J].Journal of Computational Physics,2014,273:520-547.
[7] Kucharik M,Scovazzi G,Shashkov M,et al.A multi-scale residual-based anti-hourglass control for compatible staggered Lagrangian hydrodynamics[J].Journal of Computational Physics,2018,354:1-25.
[8] Har J,Fulton R E.A parallel finite element procedure for contact-impact problems[J].Engineering with Computers,2003,19(2/3):67-84.
[9] Tezuka A,Matsumoto J,Suzuki T,et al.A platform for parallel CFD FEM computations[J].International Journal of Computational Fluid Dynamics,2005,19(3):235-242.
[10] Kosturski N,Margenov S,Vutov Y.Balancing the communications and computations in parallel FEM simula-tions on unstructured grids[C].Proceedings of the 9th International Conference on Parallel Processing and Applied Mathematics.Torun,Springer,2012:211-220.
[11] Pikle N K,Sathe S R,Vyavhare A Y.GPGPU-based parallel computing applied in the FEM using the conju-gate gradient algorithm:a review[J].Sādhanā,2018,43(7):111.
[12] 莫则尧,袁国兴.消息传递并行编程环境MPI[M].北京:科学出版社,2001.Mo Z Y,Yuan G X.MPI:message passing parallel programming environment[M].Beijing:Science Press,2001(in Chinese).
[13] Mishra B S,Dehuri S.Parallel computing environments:a review[J].IETE Technical Review,2011,28(3):240-247.
[14] Gao W J,Kemao Q.Parallel computing in experimental mechanics and optical measurement:a review[J].Optics and Lasers in Engineering,2012,50(4):608-617.
[15] Wang T Y,Qian K M.Parallel computing in experimen-tal mechanics and optical measurement:a review (II)[J].Optics and Lasers in Engineering,2018,104:181-191.
[16] Karypis G.METIS:a software package for partitioning unstructured graphs,partitioning meshes,and computing fill-reducing orderings of sparse matrices[EB/OL].Version 5.1.0,University of Minnesota,Department of Computer Science.(2013-03-30).https://www.lrz.de/services/software/mathematik/metis/metis_5_0.pdf.
[17] Hallquist J O.LS-DYNA theoretical manual R:9320[EB/OL].Livermore Software Technology Corporation,Livermore.http://ftp.lstc.com/anonymous/outgoing/jday/manuals/.
[18] Malone J G,Johnson N L.A parallel finite element contact/impact algorithm for non-linear explicit transient analysis:part Ⅰ-the search algorithm and contact mecha-nics[J].International Journal for Numerical Methods in Engineer,1994,37(4):559-590.
[19] Malone J G,Johnson N L.A parallel finite element contact/impact algorithm for non-linear explicit transient analysis:part Ⅱ-parallel implementation[J].Interna-tional Journal for Numerical Methods in Engineer,1994,37(4):591-603.
[20] Xu Z,Accorsi M,Leonard J.Parallel contact algorithms for nonlinear implicit transient analysis[J].Computa-tional Mechanics,2004,34(4):247-255.
[21] Dureisseix D,Farhat C.A numerically scalable domain decomposition method for the solution of frictionless contact problems[J].International Journal for Numerical Methods in Engineer,2001,50(12):2643-2666.
[22] Avery P,Rebel G,Lesoinne M,et al.A numerically scalable dual-primal substructuring method for the solution of contact problems-part I:the frictionless case[J].Computer methods in Applied Mechanics and Engineering,2004,193(23/26):2403-2426.
[23] Avery P,Farhat C.The FETI family of domain decomposition methods for inequality-constrained quadratic programming:application to contact problems with confor-ming and nonconforming interfaces[J].Computer Metho-ds in Applied Mechanics and Engineering,2009,198(21/26):1673-1683.
[24] Kozubek T,Vondrak V,Men?ík M,et al.Total FETI domain decomposition method and its massively parallel implementation[J].Advances in Engineering Software,2013,60-61:14-22.
[25] Benson D J,Hallquist J O.A single surface contact algorithm for the post-buckling analysis of shell struc-tures[J].Computer Methods in Applied Mechanics and Engineering,1990,78(2):141-163.
[26] Attaway S W,Hendrickson B A,Plimpton S J,et al.A parallel contact detection algorithm for transient solid dynamics simulations using PRONTO3D[J].Computational Mechanics,1998,22(2):143-159.
[27] Pierce T,Rodrigue G.A parallel two-sided contact algorithm in ALE3D[J].Computer Methods in Applied Mechanics and Engineering,2005,194(27/29):3127-3146.
[28] Wang F J,Feng Y T,Owen D R.Parallelisation for finite-discrete element analysis in a distributed-memory environment[J].International Journal of Computational Engineering Science,2004,5(1):1-23.
[29] Zheng J W,An X H,Huang M S.GPU-based parallel algorithm for particle contact detection and its application in self-compacting concrete flow simulations[J].Com-puters & Structures,2012,112-113:193-204.
[30] Melanz D,Fang L N,Jayakumar P,et al.A comparison of numerical methods for solving multibody dynamics problems with frictional contact modeled via differential variational inequalities[J].Computer Methods in Applied Mechanics and Engineering,2017,320:668-693.
[31] Cai Y,Cui X Y,Li G Y,et al.A parallel finite element procedure for contact-impact problems using edge-based smooth triangular element and GPU[J].Computer Physics Communications,2018,225:47-58.
[32] 姜玉曦,周海兵,张树道.基于三角剖分局部搜索的三维滑移面算法[J].北京理工大学学报,2010,30(4):501-504.Jiang Y X,Zhou H B,Zhang S D.Three-dimensional contact algorithm for sliding surface based on triangular subdivision local search[J].Transactions of Beijing Institute of Technology,2010,30(4):501-504 (in Chinese).
[33] 姜玉曦,周海兵,熊俊,等.基于双三次曲面片的三维接触面光滑方法[J].工程力学,2016,33(2):11-17.Jiang Y X,Zhou H B,Xiong J,et al.A 3D contact smoothing method based on Bi-cubic parametric pat-ches[J].Engineering Mechanics,2016,33(2):11-17 (in Chinese).
[34] Wriggers P.Computational contact mechanics[M].Ber-lin:Springer,2006.
[35] 姜玉曦,周海兵,熊俊,等.三维光滑接触界面上的分配参数滑移面算法[J].计算物理,2015,32(4):386-394.Jiang Y X,Zhou H B,Xiong J,et al.A distributed parameter contact algorithm for sliding surfaces on a three-dimensional smoothed contact surface[J].Chinese Journal of Computational Physics,2015,32(4):386-394 (in Chinese).
[36] Dawes A S.A three-dimensional contact algorithm for sliding surfaces[J].International Journal for Numerical Methods in Fluids,2003,42(11):1189-1210.
[37] 张世文,华劲松,刘仓理,等.金属圆管内爆轰波相互作用效应的数值模拟研究[J].爆炸与冲击,2004,24(3):219-225.Zhang S W,Hua J S,Liu C L,et al.A numerical simulation of the metallic tube expansion induced by inside head-on hitting two detonation waves[J].Explosion and Shock Waves,2004,24(3):219-225 (in Chinese).