基于能量多体作用的原子/连续耦合方法的后验误差估计

A posteriori error estimates for energy-based atomistic/continuum method for multi-body interaction systems

摘要:

本文研究了一维情形下基于能量多体作用的原子/连续耦合方法的后验误差估计，得到基于能量的后验误差估计子.基于理论结果，我们还设计了一个不依赖于原子节点自适应网格加密算法。实验结果显示本文的算法是有效的。

Abstract:

We derive the a posterior error estimate for an energy-based atomistic/continuum method for a one-dimensional periodic chain with multi-body interactions. The current extends previous results by eliminating the requirement that the computational nodes in the continuum region coincide with the lattice sites and providing a thorough stability analysis. Based on the estimator, we design an adaptive refinement algorithm which produces the optimal convergence rate. We also show numerically that error estimator is efficient.