题目1：Implicit Gradient for Numerical Solution of PDEs

报告人1：J. S. Chen教授（University of California, San Diego）

时间1：2018年8月23日（周四）上午9:30—10:30

题目2：结构超收敛振动分析

报告人2：王东东教授（厦门大学）

时间2：2018年8月23日（周四）上午10:30—11:30

地点：明故宫校区A18-511会议室

主办单位：机械结构力学及控制国家重点实验室、国际合作处、科协、航空宇航学院

报告摘要1：

Implicit gradient (IG) is expressed in an integral equation with embedded gradient consistency without explicit derivatives. It offers a paradigm for constructing approximation of function derivatives for the numerical solution of PDEs, either by using strong forms or weak forms.  A straightforward application of IG is for the gradient typed regularization of ill-posed problems, such as the strain localization problems. GI can also be used to construct stabilization of convection dominated problems and as the stabilization of nodally integrated Galerkin equation. Without the need of taking directives of approximation functions, GI also offers computational efficiency for Meshfree based numerical solution of PDEs. This talk will introduce continuous and discrete GI for approximation of derivatives, discuss the gradient consistency of GI and its convergence properties in solving PDEs, and demonstrate its applications to strain localization, convection dominated problems, and modeling of damage and fracture processes in solids subjected to extreme loadings.

报告人简介1：

J. S. Chen is currently the Inaugural William Prager Chair Professor of Structural Engineering Department and the Director of Center for Extreme Events Research at UC San Diego. Before joining UCSD in October 2013, he was the Chancellor’s Professor of UCLA Civil & Environmental Engineering Department where he served as the Department Chair during 2007-2012. J. S. Chen’s research is in computational mechanics and multiscale materials modeling with specialization in the development of meshfree methods. He is the Past President of US Association for Computational Mechanics (USACM) and the Past President of ASCE Engineering Mechanics Institute (EMI). He has received numerous awards, including the Computational Mechanics Award from International Association for Computational Mechanics (IACM), ICACM Award from International Chinese Association for Computational Mechanics (ICACM), the Ted Belytschko Applied Mechanics Award from ASME Applied Mechanics Division, the Belytschko Medal, US Association for Computational Mechanics (USACM), among others. He is the Fellow of USACM, IACM, ASME, EMI, ICACM, and ICCEES.

报告摘要：

结构振动分析有着非常广泛的工程应用。报告中首先针对一维杆件结构振动分析，探讨了任意阶有限元高阶质量矩阵的构造方法。与传统一致和集中质量矩阵相比，采用高阶质量矩阵可以将自振频率的收敛阶次提升2次，具有超收敛特性，能够显著地提高计算精度和效率。随后，提出了一维高阶质量矩阵的积分点型广义构造方法，通过张量积形式可以非常方便地将一维超收敛分析推广到多维问题。此外，为了进一步提高计算精度，提出了结构振动问题的超收敛等几何分析方法。在等几何分析方法中，分别针对杆和膜结构及梁板结构，提出了缩减带宽矩阵的概念，并发展了对应的高阶质量矩阵。同时，利用等几何基函数高阶光滑的特点，建立了高效跨单元积分超收敛振动分析方法。最后，简要讨论了无网格法的高阶质量矩阵构造方法。

报告人简介：

王东东，2003年获加州大学洛杉矶分校博士学位，现为厦门大学土木工程系教授。主要研究领域为计算力学和结构高性能静动力数值仿真分析，已发表期刊论文八十余篇。目前主要研究方向有：高效无网格法和等几何分析方法；结构非线性静动力数值仿真与灾变模拟；岩土类材料与结构的大变形非线性损伤破坏模拟。曾获加州大学洛杉矶分校土木工程系杰出博士毕业生奖(2004)、亚太计算力学学会青年学者奖(2007)、国际华人计算力学学会青年学者奖(2011)、钱令希计算力学青年奖(2012)、国际华人计算力学学会Fellow奖(2013)、国际华人计算力学学会计算力学奖(2016)。2009年入选教育部新世纪优秀人才计划，2012年获国家自然科学基金优秀青年科学基金项目资助，2016年被评为厦门市优秀教师。