基于能量的准连续方法中鬼力去除技术
Energy-based ghost force removing techniques for the quasicontinuum method
AI总结：
针对原子材料准连续近似中局部与非局部区域界面的数值处理，提出基于有限元思想的准连续投影方法，在相同计算成本下有效去除鬼力且误差更低。
摘要：
本文研究在原子材料的准连续近似中，精确处理局部与非局部区域界面的数值方法。仅考虑基于能量的方法。特别地，基于有限元思想的准连续投影方法被证明对该问题准确且高效。我们分析了QCP方法并研究了其与现有方法（如准非局部准连续方法和几何一致重建方法）的关系。分析和数值测试结果证实，投影法在与其他方法相同计算成本下成功去除了鬼力。在所有计算示例中，QCP的误差与其他方法相同或更低。还考察了这些方法在处理局部区域单元界面时的性能。
英文摘要：
This paper studies numerical methods for accurate treatment of the interface between the local and the nonlocal region in a QC approximation of atomistic materials. Only the energy-based methods are considered. Particularly, a quasicontinuum projection (QCP) method based on the idea of finite elements is shown to be accurate and efficient for this problem. We analyse the QCP method and study its relation to the existing methods, such as the quasinonlocal quasicontinuum method and the geometrically consistent reconstruction-based method. The analysis and the results of numerical tests confirm that the projection-based QC method successfully removes the ghost force with the same computational cost as the other methods. In all computed examples the error of QCP is either the same or lower as the error of the other methods. The performance of these methods in treating interfaces of elements in the local region is also examined.
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