Adaptive Multigrid Strategy for Geometry Optimization of Large-Scale Three Dimensional Molecular Mechanics

TL;DR

This paper introduces an adaptive multigrid approach for large-scale 3D molecular mechanics optimization, significantly reducing computational complexity and accelerating simulations of crystalline defects.

Contribution

It develops a novel adaptive multigrid method with atomistic/continuum coupling and error estimation, improving efficiency for large molecular systems.

Findings

Achieves five-fold CPU time acceleration for systems with 10^8 atoms.

Reduces complexity by exploiting low-rank properties and hierarchical multigrid structure.

Effectively handles 3D crystalline defects like vacancies and dislocations.

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 $10^8$ atoms.