学术报告

题      目：Recent developments of SGFEM on 3D problem and high order approximation

报  告  人：张庆辉  教授  (邀请人：钟柳强 )

                                  哈尔滨工业大学（深圳）

时      间：8月14日  16：30-17：30

地     点：数科院西楼二楼会议室

报告人简介:

        张庆辉，哈尔滨工业大学（深圳）教授，博士生导师。中山大学博士毕业，美国雪城大学博士联合培养，曾在香港大学工学院从事博士后研究工作。研究方向为广义有限元法，无网格方法，机器学习等。在Numerische mathematik,CMAME等杂志发表多项研究成果。主持国家基金面上、青年项目、广东省自然科学杰出青年基金项目、国家基金重大研究计划项目集成项目子课题，联合主持国家基金海外与港澳学者合作研究项目等。

摘      要：

       Generalized finite element methods (GFEM) use fix and uniform mesh and augment the FE space with special functions to achieve high precision. These special functions are pasted using a partition of unity technique. Stable GFEM (SGFEM) is a stable version of GFEM, which has optimal convergence rates and good conditioning. We report two recent developments of SGFEM on 3D planar crack problem and high order approximation of interface problem. For 3D crack problem, we prove that the SGFEM enriched with conventional branch functions in 2D problem can attain the optimal convergence rate. For the interface problem, we design a set of novel enrichments, based on which the optimal convergence rates of high order are obtained both numerically and theoretically. using a simple principal component analysis technique, the optimal conditioning of these methods is restored, which is of same order as that of standard FEM.