报告题目： Multipoint Stress Approximation-Based Finite Difference Methods as Mixed Finite Element Methods for Linear Viscoelasticity

报 告 人：孙树瑜 教授  同济大学

报告时间：2025年11月21日 14：15—15：15

报告地点：正新楼209

校内联系人： 吕俊良 [email protected]

报告摘要：When a body of material is subjected to mechanical loads, very often, materials do not merely display elastic behavior. In many materials, previous behavior may impact the mechanical response. In particular, viscoelastic materials possess both elastic characteristic of solid and viscous characteristic of fluid, which is devoting an increasing attention, particularly to the applications of synthetic polymers or biological materials.  In this talk, we propose a family of Multipoint Stress Mixed Finite Element (MSMFE) methods for linear viscoelasticity with weak symmetry on quadrilateral grids, which can be implemented like a family of finite difference methods. The methods are constructed based on the lowest order Brezzi-Douglas-Marini mixed finite element spaces for elastic and viscous stress, piecewise constant velocity and piecewise constant (linear) vorticity. A special quadrature rule is applied for local stress and vorticity elimination. This results in a positive definite cell centered velocity-vorticity or only velocity system at each time step. Unconditional energy-dissipation of the MSMFE methods is proved rigorously. The accuracy of all the numerical solutions in their nature norms are established to be first order space convergence, both for the semi-discrete and fully-discrete formulations. Numerical results validate the theory results of the proposed methods. This is a joint work with Prof. Yang Wang in Hubei Normal University.

报告人简介：孙树瑜，同济大学数学科学金沙娱乐城 院长，教育部长江学者讲席教授，上海白玉兰创新人才，曾任教育部长江学者讲座教授。他先后于1991年和1994年毕业于天津大学获学士和硕士学位，随后继续就读于天津大学化工研究所获化学工程专业博士 (1997年，师从中国科金沙娱乐城 院士余国琮)；之后就读美国德克萨斯大学奥斯丁分校并获计算与应用数学专业博士 (2003年，师从美国国家工程院院士Mary Wheeler)。他于2003年至2009年间先后在美国德克萨斯大学奥斯丁分校任博士后和副研究员及在美国克莱姆森大学任助理教授兼博士生导师。2009年8月，他作为百位创校教授之一加盟阿卜杜拉国王科技大学 (KAUST)，任该校计算传质现象实验室(CTPL)主任，地球科学系教授，石油工程系教授和数学系教授。2024年12月他全职回国加入同济大学。他已发表SCI期刊论文400余篇，总计被引超过15000余次，H指数63。先后指导硕博研究生共50余名(已毕业博士20名)，博士后研究人员20余位。目前兼任 Journal of Computational Physics (JCP) 和 Computational Geoscience 等国际知名期刊的编委或者编辑，以及 Applied Energy，Applied Thermal Engineering，Fuel，Computer Methods in Applied Mechanics and Engineering (CMAME), Journal of Computational Physics (JCP) 等国际知名期刊客座主编。他从2020年起至今，连续五年入选了“工程学科全球顶尖科学家” (斯坦福大学发布的全球前2%顶尖科学家榜单)。