讲座主题：Two modified SAV schemes with unconditional energy stability for phase field models

主讲人：刘争光

工作单位：山东师范大学

讲座时间：2019年12月7日（周六）下午16:50--17:30

讲座地点：数学院341

主办单位：烟台大学数学与信息科学学院

内容摘要：

we consider two novel auxiliary variable methods to obtain energy stable schemes for phase field models. The auxiliary variable based on energy bounded above does not limited to the hypothetical conditions adopted in previous approaches. We proved the unconditional energy stability for all the semi-discrete schemes carefully and rigorously. The novelty of the proposed schemes is that the computed values for the functional in square root are guaranteed to be positive. This method, termed novel auxiliary energy variable (NAEV) method does not consider any bounded below restrictions any longer. However, these restrictions are necessary in invariant energy quadratization (IEQ) and scalar auxiliary variable (SAV) approaches which are very popular methods recently. This property of guaranteed positivity is not available in previous approaches. A comparative study of classical SAV and NAEV approaches is considered to show the accuracy and efficiency. Finally, we present various 2D numerical simulations to demonstrate the stability and accuracy.

主讲人介绍：

刘争光，山东师范大学副教授，2018年12月山东大学博士毕业，主要研究领域为非局部模型快速计算及相场模型的能量稳定算法研究，已在Comput. Methods Appl. Mech. Engrg., Appl. Math. Lett., J Sci Comput.等计算数学知名期刊发表学术论文17篇。博士期间，参与国家科技重大专项两项，2019年以博士第一层次引进山东师范大学。