拟连续体平衡方程的延续迭代解法
Iterative Solution of the Quasicontinuum Equilibrium Equations with Continuation
AI总结：
本文分析了一种延续算法用于求解基于力的拟连续体方程，通过能量基拟连续体近似作为预处理器的迭代方法，并确定了参数步长和迭代次数的有效策略，以Lennard-Jones链的拉伸变形为例展示了延续方法的重要性。
摘要：
我们分析了用于数值求解基于力的拟连续体方程的延续算法。通过使用基于能量的拟连续体近似作为预处理器的迭代方法，计算了基于力的拟连续体方程的近似解。本文提出的分析用于确定参数步长和每个参数值处迭代次数的有效策略，以达到所需容差的解。我们展示了Lennard-Jones链在拉伸下的变形计算结果，以证明仔细应用延续方法的必要性，确保随着参数增加，计算解保持在迭代方法的收敛域内。如果参数步长过大，这些结果会在实际载荷极限之前出现断裂。
英文摘要：
We give an analysis of a continuation algorithm for the numerical solution of the force-based quasicontinuum equations. The approximate solution of the force-based quasicontinuum equations is computed by an iterative method using an energy-based quasicontinuum approximation as the preconditioner. The analysis presented in this paper is used to determine an efficient strategy for the parameter step size and number of iterations at each parameter value to achieve a solution to a required tolerance. We present computational results for the deformation of a Lennard-Jones chain under tension to demonstrate the necessity of carefully applying continuation to ensure that the computed solution remains in the domain of convergence of the iterative method as the parameter is increased. These results exhibit fracture before the actual load limit if the parameter step size is too large.
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