Ghost force reduction and spectral analysis of the 1D bridging method

Guillaume Anciaux (1, 2) , Olivier Coulaud (2) , Jean Roman (2) , Gilles Zerah (3)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 SCALAPPLIX - Algorithms and high performance computing for grand challenge applications
3 DAM/DIF - DAM Île-de-France

In this paper we study the Bridging Method recently developed by T. Belytschko and S. Xiao to couple continuum mechanics with molecular dynamics. This method uses an overlap zone where both models exist and where degrees of freedom are coupled. We analyze the method in the 1D case. Firstly, we show that the spatial weighting of the potential energy leads to some appreciable numerical artifacts. Then, after presenting a modification of the time integration scheme that removes such spurious effects, we introduce the method employed to numerically measure the wave reflection rates. The limitation of these reflections constitute a major issue in all existing coupling methods for dynamics simulations. After discussing some first results achieved from numerical measurements, we present a spectral analysis that attempts to explain the behavior of the coupling zone by treating it as an independent material. The predictions of this spectral analysis are finally compared to some parametric studies issued from 1D coupling simulations.

Mots clés: multiscale method; atomistic-to-continuum coupling; coupling method

Domaines: Modélisation et simulation

Guillaume Anciaux, Olivier Coulaud, Jean Roman, Gilles Zerah. Ghost force reduction and spectral analysis of the 1D bridging method. [Research Report] RR-6582, INRIA. 2008. ⟨inria-00300603⟩