On the effect of ghost force in the quasicontinuum method: dynamic problems in one dimension

2012/08/07 by Xiantao Li, Li, Xiantao, Pingbing Ming +1
Engineering · Materials Science · #65N15 #70E55 #74G15 #Elasticity and Material Modeling #FOS: Mathematics #Microstructure and mechanical properties #Nonlocal and gradient elasticity in micro/nano structures #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1208.1321

openalex publication_date 2012/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Numerical error induced by the "ghost forces" in the quasicontinuum method is studied in the context of dynamic problems. The error in the (W^1,∞) norm is analyzed for the time scale (\mcO(\eps)) and the time scale (\mcO(1)) with \eps being the lattice spacing.

Citations

• Convergence of a force-based hybrid method for atomistic and continuum models in three dimension
• Dynamical Theory of Crystal Lattices
• Ghost Force Influence of a Quasicontinuum Method in Two Dimension
• Analysis of an Energy-based Atomistic/Continuum Coupling Approximation of a Vacancy in the 2D Triangular Lattice

Related

• Ghost Force Influence of a Quasicontinuum Method in Two Dimension
• Justification of Leading Order Quasicontinuum Approximations of Strongly Nonlinear Lattices
• Energy-based ghost force removing techniques for the quasicontinuum method
• There is no pointwise consistent quasicontinuum energy
• A study on the quasiconinuum approximations of a one-dimensional fracture model