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arXiv · 1308.3894

(In-)Stability and Stabilisation of QNL-Type Atomistic-to-Continuum Coupling Methods

Christoph Ortner·Alexander Shapeev·Lei Zhang
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Abstract

We study the stability of ghost force-free energy-based atomistic-to-continuum coupling methods. In 1D we essentially complete the theory by introducing a universally stable a/c coupling as well as a stabilisation mechanism for unstable coupling schemes. We then present a comprehensive study of a two-dimensional scalar planar interface setting, as a step towards a general 2D/3D vectorial analysis. Our results point out various new challenges. For example, we find that none of the ghost force-free methods known to us are universally stable (i.e., stable under general interaction and general loads). We then explore to what extent our 1D stabilisation mechanism can be extended.

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Christoph Ortner, Alexander Shapeev, Lei Zhang. 2013-08-18. (In-)Stability and Stabilisation of QNL-Type Atomistic-to-Continuum Coupling Methods. https://arxiv.org/abs/1308.3894

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