修正相场晶体模型的带松弛技术的ESAV方法
ESAV Method with Relaxation Technique for the Modified Phase-Field Crystal Model
摘要: 本文首先提出了修正相场晶体(MPFC)模型的一个有效的松弛指数标量辅助变量方法(R-ESAV)。该方法通过引入松弛机制，使离散能量更接近原始自由能，同时保持线性化与无条件能量稳定性的优势。本文构造了一阶向后欧拉格式，严格证明了其无条件能量稳定性，并给出了一阶误差估计的理论分析。数值算例验证了方法的准确性与有效性。
Abstract: This paper first proposes an efficient relaxed exponential scalar auxiliary variable (R-ESAV) method for the modified phase field crystal (MPFC) model. By introducing a relaxation mechanism, the proposed method enables the discrete energy to more closely approximate the original free energy, while preserving the advantages of linearization and unconditional energy stability. A first-order backward Euler scheme is constructed, and its unconditional energy stability is rigorously proved. Furthermore, a theoretical analysis of the first-order error estimate is provided. Numerical examples validate the accuracy and effectiveness of the proposed method.
文章引用：刘苗, 贾宏恩. 修正相场晶体模型的带松弛技术的ESAV方法[J]. 应用数学进展, 2026, 15(4): 538-555. https://doi.org/10.12677/aam.2026.154181

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