论文标题
不一致相位场晶体模型的高阶能量稳定方案
High-order energy stable schemes of incommensurate phase-field crystal model
论文作者
论文摘要
本文着重于为多长度尺度不一致的相位场晶体模型的高阶能量稳定方案的开发，该模型能够研究上的植物结构的相行为。这些基于标量辅助变量（SAV）和光谱递延校正（SDC）方法的高阶方案适用于L 2梯度流动方程，即allen-cahn动态方程。具体而言，我们提出了SAV系统的二阶曲柄 - 尼科尔森（CN）方案，证明了能量耗散定律，并在几乎是周期性的函数意义上给出了误差估计。此外，我们使用SDC方法来提高SAV/CN方案的计算准确性。数值结果证明了数值计算中高阶数值方法的优势，并显示了长度尺度对有序结构形成的影响。
This article focuses on the development of high-order energy stable schemes for the multi-length-scale incommensurate phase-field crystal model which is able to study the phase behavior of aperiodic structures. These high-order schemes based on the scalar auxiliary variable (SAV) and spectral deferred correction (SDC) approaches are suitable for the L 2 gradient flow equation, i.e., the Allen-Cahn dynamic equation. Concretely, we propose a second-order Crank-Nicolson (CN) scheme of the SAV system, prove the energy dissipation law, and give the error estimate in the almost periodic function sense. Moreover, we use the SDC method to improve the computational accuracy of the SAV/CN scheme. Numerical results demonstrate the advantages of high-order numerical methods in numerical computations and show the influence of length-scales on the formation of ordered structures.
