• 论文 •

### 三维颗粒物质的能量最小化模拟方法

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.

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

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.

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