Adaptive Multigrid Strategy for Geometry Optimization of Large-Scale Three Dimensional Molecular Mechanics
Abstract
In this paper, we present an efficient adaptive multigrid strategy for the geometry optimization of large-scale three dimensional molecular mechanics. The resulting method can achieve significantly reduced complexity by exploiting the intrinsic low-rank property of the material configurations and by combining the state-of-the-art adaptive techniques with the hierarchical structure of multigrid algorithms. To be more precise, we develop a oneway multigrid method with adaptive atomistic/continuum (a/c) coupling, e.g., blended ghost force correction (BGFC) approximations with gradient-based a posteriori error estimators on the coarse levels. We utilize state-of-the-art 3D mesh generation techniques to effectively implement the method. For 3D crystalline defects, such as vacancies, micro-cracks and dislocations, compared with brute-force optimization, complexity with superior rates can be observed numerically, and the strategy has a five-fold acceleration in terms of CPU time for systems with atoms.
Cite
@article{arxiv.2105.02672,
title = {Adaptive Multigrid Strategy for Geometry Optimization of Large-Scale Three Dimensional Molecular Mechanics},
author = {Kejie Fu and Mingjie Liao and Yangshuai Wang and Jianjun Chen and Lei Zhang},
journal= {arXiv preprint arXiv:2105.02672},
year = {2022}
}