发表机构
School of Mathematical Sciences, Beijing Normal University（北京师范大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为近晶A液晶修正模型提出二阶GSAV-ETD2格式，证明其无条件能量耗散并建立无耦合条件的误差估计，实现最优收敛阶，数值实验验证并模拟自组装。
AI 中文摘要
本文针对近晶A（SmA）液晶的修正Landau-de Gennes模型，开发了一种二阶、线性、解耦且保结构的数值格式。主要贡献有三方面。首先，据我们所知，我们首次将广义标量辅助变量（GSAV）方法与二阶指数时间差分Runge-Kutta（ETDRK2）离散相结合，提出了二阶GSAV-ETD2格式。其次，我们证明了所提格式满足无条件能量耗散律，从而填补了该类二阶GSAV指数积分器能量稳定性分析的理论空白。第三，通过推导一个强制离散重构，我们在不施加τ与h之间任何耦合条件的情况下建立了全离散误差估计，实现了最优收敛阶O(τ²+h²)。数值实验验证了我们的理论结果，并模拟了SmA相的自组装动力学。
英文摘要
In this work, we develop a second-order, linear, decoupled, and structure-preserving numerical scheme for the modified Landau--de Gennes model of smectic-A (SmA) liquid crystals. The main contributions are threefold. First, to the best of our knowledge, we propose the first integration of the generalized scalar auxiliary variable (GSAV) approach with a second-order exponential time-differencing Runge--Kutta (ETDRK2) discretization, leading to a second-order GSAV--ETD2 scheme. Second, we prove that the proposed scheme satisfies an unconditional energy-dissipation law, thereby closing the theoretical gap in the energy-stability analysis of second-order GSAV exponential integrators of this class. Third, by deriving a coercive discrete reformulation, we establish a fully discrete error estimate without imposing any coupling condition between $τ$ and $h$, achieving the optimal convergence rate $\mathcal{O}(τ^2+h^2)$. Numerical experiments are presented to verify our theoretical results and to simulate the self-assembly dynamics of the SmA phase.
Comments37 pages,10 figures
