论文标题
高效的指数标量辅助变量方法与梯度流的松弛（RE-SAV）
Highly efficient exponential scalar auxiliary variable approaches with relaxation (RE-SAV) for gradient flows
论文作者
论文摘要
在过去的几年中，标量辅助变量（SAV）和SAV型方法成为模拟各种梯度流的非常热和有效的方法。受\ cite {huang2020highly}的新SAV方法的启发，我们提出了一种新型技术，以构建一种新的指数标量辅助变量（E-SAV）方法，以构建梯度流的高阶数值稳定方案。为了明显提高其准确性和一致性，我们提出了一种带有放松的E-SAV方法，我们将其命名为梯度流的放松E-SAV（RE-SAV）方法。 Re-SAV方法保留了传统SAV方法的所有优势。此外，我们不需要任何自由能潜力或非线性项的界限假设。此外，一阶，二阶和高阶无条件能量稳定的时间稳定方案易于构建。提供了几个数值示例，以证明该方法的提高效率和准确性。
For the past few years, scalar auxiliary variable (SAV) and SAV-type approaches became very hot and efficient methods to simulate various gradient flows. Inspired by the new SAV approach in \cite{huang2020highly}, we propose a novel technique to construct a new exponential scalar auxiliary variable (E-SAV) approach to construct high-order numerical energy stable schemes for gradient flows. To improve its accuracy and consistency noticeably, we propose an E-SAV approach with relaxation, which we named the relaxed E-SAV (RE-SAV) method for gradient flows. The RE-SAV approach preserves all the advantages of the traditional SAV approach. In addition, we do not need any the bounded-from-below assumptions for the free energy potential or nonlinear term. Besides, the first-order, second-order and higher-order unconditionally energy stable time-stepping schemes are easy to construct. Several numerical examples are provided to demonstrate the improved efficiency and accuracy of the proposed method.
