An Efficient Multigrid Method for Molecular Mechanics Modeling in Atomic Solids (Communications in Computational Physics, 2011)
We propose a multigrid method to solve the molecular mechanics model(molecular dynamics at zero temperature). The Cauchy-Born elasticity model is employedas the coarse grid operator and the elastically deformed state as the initial guessof the molecular mechanics model. The efficiency of the algorithm is demonstrated bythree examples with homogeneous deformation, namely, one dimensional chain undertensile deformation and aluminum under tension and shear deformations. Themethod exhibits linear-scaling computational complexity, and is insensitive to parametersarising from iterative solvers. In addition, we study two examples with inhomogeneousdeformation: vacancy and nanoindentation of aluminum. The results are stillsatisfactory while the linear-scaling property is lost for the latter example.