报告题目：Fundamental Solutions  as Basis Function for Solution of Partial Differential Equations: Global vs.  Local Interpolation, Strong vs. Weak Formulation, Mesh vs. Meshless

报告人：程宏达（Alexander H. –D. Cheng）教授

时间：2021年2月28日（周日）上午10:00

ZOOM：会议ID：955 8800 5907   密码：123456

腾讯会议：会议ID：463 523 625

主办单位：河海大学力学与材料学院固体力学研究所

报告摘要：Fundamental solutions and T-complete general solutions can be used as  basis functions to interpolate the solutions of partial differential equations.  The interpolation can be global or local. The solution convergence can be  enforced using the strong or the weak formulation. If global interpolation and  collocation (strong formulation) are used, it leads to the method of fundamental  solutions (MFS) and Trefftz collocation method (TCM). If local interpolation and  weak formulation are utilized, it becomes the Trefftz finite  element method. The local FEM has elements, and the global MFS and TCM are  element-free, or meshless. In the localized MFS (LMFS), fundamental solutions  are used for local interpolation and collocation, and is meshless. The meshless  local Petrov-Galerkin (MLPG) method is a local weak formulation. Various basis  functions have been used as trial and test functions, and the fundamental and  T-complete functions can be strong candidates. This talk gives an overview of  these methods, with an emphasis on the strength of the fundamental  solutions.

报告人简介：

程宏达（Alexander H. –D. Cheng）教授为美国密西西比大学工程学院荣誉院长，并曾受聘为海岸带资源开发与安全学科创新引智基地（111重大国际合作计划）海外专家。程教授1974年本科毕业于台湾大学土木工程专业，1979年获得Missouri—Columbia 大学土木工程硕士学位，1981年获得Cornell University土木工程博士学位。程教授研究领域包括多孔材料力学、地下水、海水侵蚀、边界元法、无网格配置法、纳米力学等，学术成就丰硕，出版了5本专著和180余篇杂志论文。他曾担任美国土木工程师学会工程力学分会会长，美国水文学学会学术事务副主席，目前担任Engineering Analysis with Boundary Elements杂志主编。他曾获得George Green奖章, Maurice A. Biot奖章以及ASCE Walter L. Huber土木工程研究奖。程教授还受聘为力学与材料学院兼职教授，迄今已合作培养4名博士研究生。