Second-order maximum principle preserving Strang splitting schemes for fractional Allen-Cahn equations

主讲人：陈浩

摘要：In this talk, we consider the Strang splitting technique for solving the multidimensional Allen-Cahn equations with spatial fractional Riesz derivatives. Fully discrete numerical methods are proposed using exponential Strang splitting schemes for the time integration with finite difference discretization in space. We proved that the proposed methods can preserve the discrete maximum principle unconditionally. Furthermore, the fully discrete methods are theoretically confirmed to be convergent with second-order accuracy in both of time and space. In practical implementation, the proposed algorithms require  to compute the matrix exponential associated with only one dimensional discretized matrices that possess Toeplitz structure. Meanwhile, a fast algorithm is further developed for evaluating the product of the Toeplitz matrix exponential with a vector. Numerical examples are presented to verify the theoretical analysis and demonstrate the efficiency of the proposed methods.

主讲人简介：陈 浩，博士，重庆师范大学数学科学学院教授、 硕士生导师，中国仿真算法专业委员会委员. 主要从事微分方程数值解研究, 主持过国家自然科学基金及多项省级科研项目，在《J. Comput. Phys.》 、 《J. Sci. Comput.》 、 《BIT  Numer. Math.》等计算数学刊物发表科研论文20余篇.。

邀请人：张诚坚

时间：2022年8月31日（星期三）19:00-21:00

地点：腾讯会议室     ID:3182838293