137 citations · 235 across the 26 of their papers we have counts for
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math.NA2012★ 1 cited
Stability of a force-based hybrid method with planar sharp interface
Jianfeng Lu, Pingbing Ming
We study a force-based hybrid method that couples atomistic model with Cauchy-Born elasticity model with sharp transition interface. We identify stability conditions that guarantee…
math.NA2012★ 2 cited
On the effect of ghost force in the quasicontinuum method: dynamic problems in one dimension
Xiantao Li, Pingbing Ming
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,\infty}) norm is analyzed for the…
math.NA2012
Ghost Force Influence of a Quasicontinuum Method in Two Dimension
Jingrun Chen, Pingbing Ming
We derive an analytical expression for the solution of a two-dimensional quasicontinuum method with a planar interface. The expression is used to prove that the ghost force may lea…