孙海卫教授学术报告通知(2021-32)


发布时间: 2021-12-08     浏览次数: 11

题  An exponential Runge-Kutta method with dimensional splitting technique for multidimensional fractional Allen-Cahn equations

报告人:孙海卫教授,澳门大学数学系

   :江宁校区乐学楼1105

腾讯会议:390-832-760

时间2021129星期四,上午10:00-12:00

主办单位:力学与材料学院水力学与流体力学研究所

欢迎各位老师、同学参加!

报告摘要: In this talk, we study numerical methods for solving the multidimensional Allen-Cahn equations with spatial fractional Riesz derivatives. A fully discrete numerical scheme is proposed using an exponential Runge-Kutta method with the dimensional splitting strategy for the time integration with finite difference discretization in space. Theoretically, we prove that the proposed numerical scheme can unconditionally preserve the discrete maximum principle. The error estimate is also established in the fully discrete sense. In practical computation, the proposed algorithm can be carried out by computing linear systems and the matrix exponential associated with only 1D discretized matrices that possess the Toeplitz structure.  Meanwhile, fast methods for inverting the Toeplitz matrix and computing the Toeplitz exponential multiplying a vector are exploited to reduce the complexity. Numerical examples are given to illustrate the effectiveness and efficiency of the proposed scheme. It is a joint work with Prof. Hao CHEN.

报告人简介:孙海卫,澳门大学数学系主任、教授,1996年于香港中文大学获得博士学位。主要研究领域为数值线性代数、分数阶微分方程快速算法、数值偏微分方程以及计算金融等。在SIAM J. Numer. Anal.SIAM J.Sci. Comut.等计算数学众多权威刊物上共发表80余篇高等水平研究论文,担任国际期刊 “International Journal Computer Mathematics” 编委。于2018年获得澳门自然科学奖二等奖。共主持澳门科学技术发展基金五项。