题目：Strang's splitting method for spatial fractional Allen-Cahn equations

时间：2022年4月26日（星期二）14:00-17:00

Tencent Room：307-305-558 Password：220426

摘要: In this talk, we study the numerical solutions of the spatial fractional Allen-Cahn equations. After semi-discretization for the spatial fractional Riesz derivative, a system of nonlinear ordinary differential equations with Toeplitz structure is obtained. For the sake of reducing the computational complexity, Strang splitting methods are proposed where the Toeplitz matrix in the system is split into the sum of a circulant matrix and a skew circulant matrix. Therefore, the proposed method can be quickly implemented by the fast Fourier transform, substituting to calculate the expensive Toeplitz matrix exponential. Theoretically, the discrete maximum principle of our method is unconditionally preserved. Moreover, the analysis of error in norms in Banach space with second-order accuracy is conducted in both time and space. Finally, numerical tests are given to corroborate our theoretical conclusions and the efficiency of the proposed method. It is a joint work with Yaoyuan Cai, Zhiwei Fang, and Hao Chen.

报告人简介：Hai-Wei Sun教授是澳门大学全职教授、博士生导师、数学系主任。长期从事计算数学，特别是数值线性代数及其应用、分数阶偏微分方程快速计算方法和计算金融学的研究，曾获得澳门政府科学技术奖励。孙教授分别于1983年和1989年在中山大学获得本科与硕士学位，1996年于香港中文大学获得博士学位，师从著名计算数学专家Raymond Chan教授（香港中文大学）。近年来，孙教授指导了三十余名硕士研究生与博士研究生以及博士后访问学者，在微分方程快速计算领域做出了极具特色的研究工作，得到了广泛的引用。孙教授在计算数学众多权威刊物上共发表七十多篇高水平研究论文，目前担任International Journal Computers Mathematics杂志的编委。