Positive Definiteness of the Blended Force-Based Quasicontinuum Method
Positive Definiteness of the Blended Force-Based Quasicontinuum Method
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DOI：
10.1137/110859270
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发表时间：
2011-12
期刊：
影响因子：
--
通讯作者：
X. Li;M. Luskin;C. Ortner
中科院分区：
文献类型：
--
作者：
X. Li;M. Luskin;C. Ortner
发展一致和稳定的多维结晶固体准连续体模型仍然是一个挑战。例如，证明基于力的准连续体（QCF）模型的稳定性[M]。多布森和M.鲁斯金，M2AN数学。模型。号码。分析的。， 42 (2008), pp. 113—139]仍然是一个悬而未决的问题。在一维和二维中，我们表明，通过混合原子力和柯西-玻恩连续统力（而不是像QCF方法中那样的急剧过渡），可以得到正定混合力的准连续统（B-QCF）模型。我们对所需的混合宽度建立了严格的条件。
The development of consistent and stable quasicontinuum models for multidimensional crystalline solids remains a challenge. For example, proving the stability of the force-based quasicontinuum (QCF) model [M. Dobson and M. Luskin, M2AN Math. Model. Numer. Anal., 42 (2008), pp. 113--139] remains an open problem. In one and two dimensions, we show that by blending atomistic and Cauchy--Born continuum forces (instead of a sharp transition as in the QCF method) one obtains positive-definite blended force-based quasicontinuum (B-QCF) models. We establish sharp conditions on the required blending width.