### Electronic Research Archive

2020, Issue 1: 405-421. doi: 10.3934/era.2020023
Special Issues

# Energy minimization and preconditioning in the simulation of athermal granular materials in two dimensions

• Received: 01 November 2019 Revised: 01 January 2020
• Primary: 74G65, 65F08; Secondary: 82B26, 68U20

• Granular materials are heterogenous grains in contact, which are ubiquitous in many scientific and engineering applications such as chemical engineering, fluid mechanics, geomechanics, pharmaceutics, and so on. Granular materials pose a great challenge to predictability, due to the presence of critical phenomena and large fluctuation of local forces. In this paper, we consider the quasi-static simulation of the dense granular media, and investigate the performances of typical minimization algorithms such as conjugate gradient methods and quasi-Newton methods. Furthermore, we develop preconditioning techniques to enhance the performance. Those methods are validated with numerical experiments for typical physically interested scenarios such as the jamming transition, the scaling law behavior close to the jamming state, and shear deformation of over jammed states.

Citation: Haolei Wang, Lei Zhang. Energy minimization and preconditioning in the simulation of athermal granular materials in two dimensions[J]. Electronic Research Archive, 2020, 28(1): 405-421. doi: 10.3934/era.2020023

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• Granular materials are heterogenous grains in contact, which are ubiquitous in many scientific and engineering applications such as chemical engineering, fluid mechanics, geomechanics, pharmaceutics, and so on. Granular materials pose a great challenge to predictability, due to the presence of critical phenomena and large fluctuation of local forces. In this paper, we consider the quasi-static simulation of the dense granular media, and investigate the performances of typical minimization algorithms such as conjugate gradient methods and quasi-Newton methods. Furthermore, we develop preconditioning techniques to enhance the performance. Those methods are validated with numerical experiments for typical physically interested scenarios such as the jamming transition, the scaling law behavior close to the jamming state, and shear deformation of over jammed states.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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