Blended Ghost Force Correction Method for 3D Crystalline Defects

Abstract

Atomistic/continuum coupling method is a class of multiscale computational method for the efficient simulation of crystalline defects. The recently developed blended ghost force correction (BGFC) method combines the efficiency of blending methods and the accuracy of QNL type methods. BGFC method can be applied to multi-body interaction potentials and general interfaces. In this paper, we present the formulation, implementation and analysis of the BGFC method in three dimensions. In particular, we focus on the difference and connection with other blending variants, such as energy based blended quasi-continuum method (BQCE) and force based blended quasi-continuum method (BQCF). The theoretical results are justified by a few benchmark numerical experiments with point defects and microcrack in the three dimensional FCC lattice.

Adaptive Multigrid Strategy for Large-scale Molecular Mechanics Optimization

“…In this section, we first introduce the continuum approximation and then present the blended ghost force correction (BGFC) method. Though they have already been discussed rigorously in many multiscale modeling literatures [14,21,36], we adapt them to the setting of our paper for the sake of completeness.…”

“…Its mesh generator originally comes from Tetgen [38], which is a C++ program for generating good quality tetrahedral meshes. Compared with the triangulation used in [14] which was only available for FCC crystal, our triangulation can handle more general case. See Figure 1 for an illustration of the triangulation.…”

Efficient flexible boundary conditions for long dislocations

“…An obvious approach to further accelerate the FBC method is to replace the domain decomposition algorithm with a monolithic Newton-Krylov solver as proposed in [19]. However, a non-symmetric force-based coupling limits the realm of suitable linear solvers to generalized minimal residual methods, although switching to one of the state-of-the-art energybased schemes (e.g., [13]) could bypass this requirement. Moreover, the solver proposed in [19] requires an efficient representation of the inverse of L c|c h .…”

“…This implies that the PAD method scales cubically with the number of atoms which is very inefficient. To reduce this computational burden, conventional atomistic/continuum coupling methods (e.g., [23,42,21,11,47,35,48,22,29,13]) can be used to restrict atomistic resolution to some small part around the dislocation core, but scaling the side lengths of the computational domain with the periodic length is still required.…”