This paper introduces the MeshAC package, which generates three-dimensional adaptive meshes tailored for the efficient and robust implementation of multiscale coupling methods. While Delaunay triangulation is commonly used for mesh generation across the entire computational domain, generating meshes for multiscale coupling methods is more challenging due to intrinsic discrete structures such as defects, and the need to match these structures to the continuum domain at the interface. The MeshAC package tackles these challenges by generating meshes that align with fine-level discrete structures. It also incorporates localized modification and reconstruction operations specifically designed for interfaces. These enhancements improve both the implementation efficiency and the quality of the coupled mesh. Furthermore, MeshAC introduces a novel adaptive feature that utilizes gradient-based a posteriori error estimation, which automatically adjusts the atomistic region and continuum mesh, ensuring an optimal balance between accuracy and efficiency. This package can be directly applied to the geometry optimization problems of a/c coupling in static mechanics, with potential extensions to many other scenarios. Its capabilities are demonstrated for complex material defects, including straight edge dislocation in BCC W and double voids in FCC Cu. These results suggest that MeshAC can be a valuable tool for researchers and practitioners in computational mechanics.

翻译：本文介绍MeshAC软件包，该软件包能够生成面向多尺度耦合方法高效稳健实现的三维自适应网格。尽管Delaunay三角剖分常被用于整个计算域内的网格生成，但由于缺陷等内禀离散结构的存在，以及需在界面处将这些结构与连续介质域进行匹配，为多尺度耦合方法生成网格更具挑战性。MeshAC软件包通过生成与精细尺度离散结构对齐的网格来解决这些挑战，并针对界面引入了局部修改与重构操作，从而提高了耦合网格的实现效率与质量。此外，MeshAC引入了一项新颖的自适应功能，该功能利用基于梯度的后验误差估计，自动调整原子区与连续介质网格，确保精度与效率之间的最优平衡。该软件包可直接应用于静态力学中原子/连续耦合的几何优化问题，并具有扩展至其他多种场景的潜力。通过对复杂材料缺陷（包括BCC钨中的直刃型位错与FCC铜中的双空洞）的数值模拟展示了其能力。结果表明，MeshAC可成为计算力学研究者与从业者的重要工具。