Speaker: Prof. Zhonghua Qiao (乔中华教授)

Time: 15:30-16:30, 28 September 2022 (Wednesday) 

Venue: CC126

Tencent Meeting ID:947-380-666


Abstract

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.



About Prof.Qiao

乔中华教授于2006年在香港浸会大学获得博士学位,现为香港理工大学应用数学系教授。乔博士主要从事数值微分方程方面算法设计及分析,近年来研究工作集中在相场方程的数值模拟及计算流体力学的高效算法。他至今在SCI期刊上发表论文60余篇,文章被合计引用1300余次。他于2013年获香港研究资助局颁发2013至2014年度杰出青年学者奖,于2018年获得香港数学会青年学者奖,并且于2020年获得香港研究资助局研究学者称号。