论文标题
使用凸形分裂技术的Landau-Brazovskii模型的光谱递延校正方法
Spectral Deferred Correction Method for Landau-Brazovskii Model with Convex Splitting Technique
论文作者
论文摘要
Landau-Brazovskii模型是一种著名的Landau模型，用于在麦克相分离的系统中找到从块共聚物到液晶的复杂相结构。对于具有能量耗散和质量保护特性的Landau-Brazovskii模型设计有效的数值方案至关重要。在这里，我们通过将光谱递延校正（SDC）方法与凸出技术相结合，以有效地解决Landau-Brazovskii模型，从而提出了一种质量保守和能量稳定的方案。实施了SDC方法的自适应校正策略，以减少成本时间并保持能量稳定性。介绍了数值实验，包括Landau-Brazovskii模型中的二维周期晶体，以显示提出的数值方法的效率。
The Landau-Brazovskii model is a well-known Landau model for finding the complex phase structures in microphase-separating systems ranging from block copolymers to liquid crystals. It is critical to design efficient numerical schemes for the Landau-Brazovskii model with energy dissipation and mass conservation properties. Here, we propose a mass conservative and energy stable scheme by combining the spectral deferred correction (SDC) method with the convex splitting technique to solve the Landau-Brazovskii model efficiently. An adaptive correction strategy for the SDC method is implemented to reduce the cost time and preserve energy stability. Numerical experiments, including two- and three-dimensional periodic crystals in the Landau-Brazovskii model, are presented to show the efficiency of the proposed numerical method.
