基于力的准连续近似迭代方法
Iterative Methods for the Force-based Quasicontinuum Approximation
AI总结：
针对力耦合准连续近似线性化方程的不定性，提出用GMRES方法求解，并通过预条件实现高效可靠。
摘要：
基于力的原子-连续混合方法是已知的唯一能够将一般原子模型与有限元连续模型耦合的点态一致方法。因此，并且由于其算法简单性，基于力的耦合方法已成为一类流行的原子-连续混合模型以及其他类型的多物理场模型。然而，最近发现的线性化力基准连续（QCF）近似的不寻常稳定性性质，特别是其不定性，对开发高效可靠的迭代方法提出了挑战。我们给出了线性化QCF平衡方程的广义最小残差（GMRES）解的分析和计算结果。我们表明，GMRES方法准确地再现了基于力近似的稳定性，并得出结论，适当预条件的GMRES方法产生了一个可靠且高效的求解方法。
英文摘要：
Force-based atomistic-continuum hybrid methods are the only known pointwise consistent methods for coupling a general atomistic model to a finite element continuum model. For this reason, and due to their algorithmic simplicity, force-based coupling methods have become a popular class of atomistic-continuum hybrid models as well as other types of multiphysics models. However, the recently discovered unusual stability properties of the linearized force-based quasicontinuum (QCF) approximation, especially its indefiniteness, present a challenge to the development of efficient and reliable iterative methods. We present analytic and computational results for the generalized minimal residual (GMRES) solution of the linearized QCF equilibrium equations. We show that the GMRES method accurately reproduces the stability of the force-based approximation and conclude that an appropriately preconditioned GMRES method results in a reliable and efficient solution method.
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