4月8日 乔中华教授学术报告(数学与统计学院)

来源:数学科研研究生作者:时间:2022-03-29浏览:278设置

报告人:乔中华教授 香港理工大学

报告题目:Maximum bound principle preserving integrating factor Runge–Kutta methods for semilinear parabolic equations 

报告时间:2022年4月8日 下午3:00-4:00

报告地点:腾讯会议 ID:728 670 484

主办单位:数学与统计学院、科研院

报告人简介:

乔中华,香港理工大学教授。2006年在香港浸会大学获得博士学位,2006年7月到2008年7月在美国北卡莱罗纳州立大学科学工程计算研究中心从事博士后研究。主要从事数值微分方程方面算法设计及分析,特别是相场方程的数值模拟及计算流体力学的高效算法。至今在 SIAM Rev.、SIAM J. Numer. Anal.、SIAM J. Sci. Comp.、Numer. Math.、Math. Comp、 J. Comp. Phys.等计算数学顶级期刊上发表学术论文60余篇, 合计被引用1800余次。2013年获香港研究资助局颁发的杰出青年学者奖,2018年获得香港数学会青年学者奖,2020年获得香港研究资助局研究学者奖。

报告摘要:

A large class of semilinear parabolic equations satisfy the maximum bound principle (MBP) in the sense that the time-dependent solution preserves for any time a uniform pointwise bound imposed by its initial and boundary conditions. The MBP plays a crucial role in understanding the physical meaning and the wellposedness of the mathematical model. Investigation on numerical algorithms with preservation of the MBP has attracted increasingly attentions in recent years, especially for the temporal discretizations, since the violation of MBP may lead to nonphysical solutions or even blow-ups of the algorithms. In this work, we study high-order MBP-preserving time integration schemes by means of the integrating factor Runge–Kutta (IFRK) method. Beginning with the space-discrete system of semilinear parabolic equations, we present the IFRK method in general form and derive the sufficient conditions for the method to preserve the MBP. In particular, we show that the classic four-stage, fourth-order IFRK scheme is MBP preserving for some typical semilinear systems although not strong stability preserving, which can be instantly applied to the Allen–Cahn type of equations.


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