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程宏达教授基本解无网格数值计算方法的综述

已有 2459 次阅读 2020-8-13 15:44 |系统分类:教学心得

程宏达教授基本解无网格数值计算方法的综述

岳中琦

为抗击新冠肺炎疫情(COVID-19)等天灾人祸,港大土木工程系主办系列网络线上公开杰出学术讲座,邀请国际相关知名专家介绍、主讲他们最新研究成果。

昨晚(2020年8月12日)7点到8点半,密西西比大学(University of Mississippi)程宏达教授(Professor Alexander H.-D. Cheng)应邀用英文做了一场精彩的数学物理方程求解方法的学术讲座。讲座题目是“An Overview of Method of Fundamental Solutions: Solvability, Convergence, and Applications”(基本解无网格数值计算方法的综述:可解性、收敛与应用)。

程教授首先回顾了从牛顿(1643-1727)万有引力公式、经拉格郎日(1736-1813)场和势概念、拉普拉斯(1749-1827)公式、到格林(1793-1841)函数的基本解形成历史,再介绍了无网格数值方法求解线性数学物理偏微分方程边值问题解的发展历史。他认为航空工程力学专家冯×卡门(Theodore Von Karman, 1881-1963)当年在飞机空气动力学计算中提出的方法是最早的相关工作。 

F03.jpg

基本解无网格数值计算方法如下图所示。

F01.jpg

F02.jpg

现在,这类方法已经应用于弹性静力学、热弹性力学、多孔介质弹性力学、声学、弹性动力学、多孔介质弹性动力学、电磁学、脑磁描记法、斯托克斯流、和不适定和逆问题。程教授探讨了可解性、退化范围、寄生频率等问题与它们的解决方法,还阐明了调和与非调和边值问题之间误差收敛的区别,建议了一种最优化方法,使得无需采用网格加密就可以获得最优解。

详细内容请参看程教授的这次讲座视频http://www.civil.hku.hk/video/seminar20200812.html和题目为《An Overview of the Method of Fundamental Solutions—Solvability, Uniqueness, Convergence, and Stability》的最新论著。

大约有180国内外相关科技人员网上参加了这场学术讲座会。感谢程教授的精彩详细讲解和敏捷聪慧思维,让我重新找回了在北京大学上数学、物理和力学课时的感受。这种精准精确的数学求解和论证过程充满了学识和智慧,增长了我相关研究进展知识,拓展了我相关研究思路,收益良多!

程教授的讲学使得我心情倍好,给我增加了正能量,有利我抗击新冠肺炎疫情和任何天灾人祸。再次感谢程教授和参加讲座的近200位国内外科技研究人员。

2020年8月13日15:40写成于香港大学602办公室

附件:程宏达教授英文介绍

Alexander Cheng is Dean Emeritus of School of Engineering, and previously served as Chair of Department of Civil Engineering, at the University of Mississippi. He also taught at Cornell University, Columbia University, and University of Delaware, prior to joining UM. He obtained his Ph.D. from Cornell University, M.S. from University of Missouri, and B.S. from National Taiwan University. His research covers groundwater flow and transport, saltwater intrusion, boundary element method, radial basis function collocation method, poromechanics, and nanomechanics. He has authored and coauthored 5 books, including Modeling Groundwater Flow and Contaminant Transport, 2010, and Poroelasticity, 2016, both by Springer, and more than 180 journal articles. He previously served as President of Engineering Mechanics Institute, American Society of Civil Engineers, and Vice President of Academic Affairs, American Institute of Hydrology. He is the Editor-in-Chief of Engineering Analysis with Boundary Elements (Elsevier), Associate Editor of Transport in Porous Media (Springer), International Associate Editor of Journal of Mechanics (Cambridge), and was formerly Associate Editor of Journal of Engineering Mechanics (ASCE) and Journal of Nanomechanics and Micromechanics (ASCE). He was the recipient of the George Green Medal, the Maurice A. Biot Medal, the Walter L. Huber Civil Engineering Research Prize of ASCE, and the Basic Research Award of U.S. National Committee for Rock Mechanics.



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