无公度相场晶体模型的高阶能量稳定格式
High-order energy stable schemes of incommensurate phase-field crystal model
摘要：
本文主要研究了多尺度无公度相场晶体模型的高阶能量稳定格式，该模型能够研究非周期结构的相行为。这些基于标量辅助变量（SAV）和谱延迟校正（SDC）方法的高阶格式适用于L2梯度流方程，即，Allen-Cahn动力学方程具体地，我们提出了SAV系统的二阶Crank-Nicolson（CN）格式，证明了能量耗散律，并给出了殆周期函数意义下的误差估计。此外，我们使用SDC方法来提高SAV/CN格式的计算精度。数值结果表明了高阶数值方法在数值计算中的优势，并显示了长度尺度对有序结构形成的影响。
英文摘要：
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.
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