• 论文 • 上一篇    

三维颗粒物质的能量最小化模拟方法

王浩磊, 张镭   

  1. 上海交通大学数学科学学院, 自然科学研究院, 教育部科学工程计算重点实验室, 上海 200240
  • 收稿日期:2019-12-31 发布日期:2021-03-18
  • 基金资助:
    国家自然科学基金(11871339,11861131004,11571314)资助.

王浩磊, 张镭. 三维颗粒物质的能量最小化模拟方法[J]. 数值计算与计算机应用, 2021, 42(1): 80-90.

Wang Haolei, Zhang Lei. SIMULATING THREE DIMENSIONAL GRANULAR MATERIALS BY ENERGY MINIMIZATION METHODS[J]. Journal on Numerica Methods and Computer Applications, 2021, 42(1): 80-90.

SIMULATING THREE DIMENSIONAL GRANULAR MATERIALS BY ENERGY MINIMIZATION METHODS

Wang Haolei, Zhang Lei   

  1. School of Mathematical Sciences, Institute of Natural Sciences, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2019-12-31 Published:2021-03-18
颗粒物质是大量宏观颗粒的集合,广泛存在于自然界,日常生活和工业生产中.颗粒物质的运动表现出非常复杂的现象,如堵塞(jamming)等.颗粒物质体系的定量研究仍是一个巨大的挑战.本文采用能量最小化方法对颗粒物质进行准静态模拟.对一些典型的非线性优化方法,如共轭梯度法,拟牛顿法等,通过预条件来提高这些方法的效率.这些预条件方法基于颗粒体系的几何结构和能量函数来构建.通过对一些典型的准静态过程,如压缩和剪切试验的数值模拟,观察到对三维颗粒体系,预条件方法可以有40%左右的效率提升.
Granular materials are collections of discrete macroscopic particles, which are ubiquitous in nature, everyday life and industry. Granular materials pose a great challenge to predictability, due to the presence of complicated physical phenomena such as jamming. In this paper, we consider the quasi-static simulation by minimizing the energy of dense granular media, and investigate the performances of typical nonlinear optimization algorithms such as conjugate gradient methods and quasi-Newton methods. Furthermore, we develop preconditioning techniques to enhance the performance of energy minimization. These preconditioning techniques are based on the geometric structures and the energy functional of the granular system. The numerical results for several typical quasi-static evolutions, such as, compression and simple shear deformations, reveal that the preconditioning techniques can yield a speedup by a factor of nearly 40% for three-dimensional granular systems.

MR(2010)主题分类: 

()
[1] Bagi K. Stress and strain in granular assemblies[J]. Mechanics of materials, 1996, 22(3):165-177.
[2] Bezanson J, Edelman A, Karpinski S, et al. Julia:A fresh approach to numerical computing[J]. SIAM review, 2017, 59(1):65-98.
[3] Bitzek E, Koskinen P, G?hler F, et al. Structural relaxation made simple[J]. Physical review letters, 2006, 97(17):170201.
[4] Cundall P A, Strack O D L. A discrete numerical model for granular assemblies[J]. geotechnique, 1979, 29(1):47-65.
[5] Hager W W, Zhang H. A new conjugate gradient method with guaranteed descent and an efficient line search[J]. SIAM Journal on optimization, 2005, 16(1):170-192.
[6] Johnson K L, Johnson K L. Contact mechanics[M]. Cambridge university press, 1987.
[7] Kou B, Cao Y, Li J, et al. Granular materials flow like complex fluids[J]. Nature, 2017, 551(7680):360.
[8] Krijgsman D, Luding S. Simulating granular materials by energy minimization[J]. Computational particle mechanics, 2016, 3(4):463-475.
[9] Majmudar T S, Behringer R P. Contact force measurements and stress-induced anisotropy in granular materials[J]. Nature, 2005, 435(7045):1079.
[10] Mones L, Ortner C, Csányi G. Preconditioners for the geometry optimisation and saddle point search of molecular systems[J]. Scientific reports, 2018, 8(1):13991.
[11] Nocedal J. Updating quasi-Newton matrices with limited storage[J]. Mathematics of computation, 1980, 35(151):773-782.
[12] Nocedal J, Wright S. Numerical optimization[M]. Springer Science & Business Media, 2006.
[13] Ortner C, Kermode J, et al. JuLIP:Julia Library for Interatomic Potentials[CP]. https://github.com/JuliaMolSim/JuLIP.jl.
[14] Packwood D, Kermode J, Mones L, et al. A universal preconditioner for simulating condensed phase materials[J]. The Journal of chemical physics, 2016, 144(16):164109.
[15] Plimpton S. Fast parallel algorithms for short-range molecular dynamics[J]. Journal of computational physics, 1995, 117(1):1-19. http://lammps.sandia.gov.
[16] Stukowski A. Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool[J]. Modelling and Simulation in Materials Science and Engineering, 2009, 18(1):015012.
[17] 孙其诚, 厚美瑛, 金峰. 颗粒物质物理与力学[M]. 科学出版社, 2011.
[18] Wang H, Zhang L. Energy Minimization and Preconditioning in the Simulation of Athermal Granular Materials in Two Dimensions[J]. arXiv preprint arXiv:1911.08305, 2019.
[19] Zhang H P, Makse H A. Jamming transition in emulsions and granular materials[J]. Physical Review E, 2005, 72(1):011301.
[1] 张文生, 张丽娜. 基于有限元方法的频率域弹性波全波形反演[J]. 数值计算与计算机应用, 2020, 41(4): 315-336.
[2] 徐小文. 并行代数多重网格算法:大规模计算应用现状与挑战[J]. 数值计算与计算机应用, 2019, 40(4): 243-260.
[3] 卢晴, 舒适, 彭洁. 一种变系数扩散问题有限体积格式的高效预条件子[J]. 数值计算与计算机应用, 2018, 39(2): 150-160.
[4] 李政, 吴淑红, 李巧云, 张晨松, 王宝华, 许进超, 赵颖. 精细油藏模拟的一种线性求解算法[J]. 数值计算与计算机应用, 2018, 39(1): 1-9.
[5] 张文生, 庄源. 频率域声波方程全波形反演[J]. 数值计算与计算机应用, 2017, 38(3): 167-196.
[6] 张慧荣, 曹建文. 针对对称对角占优线性系统的组合预条件算法[J]. 数值计算与计算机应用, 2015, 36(4): 310-322.
[7] 朱雪芳. 求解鞍点问题的一类广义SSOR预条件子[J]. 数值计算与计算机应用, 2014, 35(2): 117-124.
[8] 纪国良, 冯仰德. 大规模有限元刚度矩阵存储及其并行求解算法[J]. 数值计算与计算机应用, 2012, 33(3): 230-240.
[9] 冯春生, 王俊仙, 舒适. 一种求解 H(curl)型椭圆问题的高效并行预条件子及并行实现[J]. 数值计算与计算机应用, 2012, (1): 48-58.
[10] 潘春平. 一种有效的新预条件Gauss-Seidel迭代法[J]. 数值计算与计算机应用, 2011, 32(4): 267-273.
[11] 汪祥, 李乐波. 对称Toeplitz线性方程组的基于余弦变换的最佳预优矩阵[J]. 数值计算与计算机应用, 2010, 31(3): 223-231.
[12] 沈海龙, 邵新慧, 张铁, 李长军. H-矩阵方程组的预条件迭代法[J]. 数值计算与计算机应用, 2009, 30(4): 266-276.
[13] 王俊仙, 胡齐芽, 舒适. 求解 Maxwell 线性元鞍点系统的基于 HX 预条件子的 Uzawa 算法[J]. 数值计算与计算机应用, 2009, 30(4): 305-314.
[14] 徐小文, 莫则尧, 刘旭. 基于局部松弛和粗化策略的代数多重网格方法[J]. 数值计算与计算机应用, 2009, 30(2): 81-91.
[15] 杨超,孙家昶. 平面三向交错网格上Cauchy-Riemann方程的数值离散及快速解法[J]. 数值计算与计算机应用, 2008, 29(1): 25-38.
阅读次数
全文


摘要