报告题目:Immersed Finite Element Methods for Three-Dimensional Interface Problems
报 告 人:张旭教授 美国俄克拉荷马州立大学
报告摘要:Interface problems arise in many applications in science and engineering. Partial differential equations (PDEs) are often used to model interface problems. Solutions to these PDE interface problems often involve kinks, singularities, discontinuities, and other non-smooth behaviors. The immersed finite element method (IFEM) is a class of numerical methods for solving PDE interface problems with unfitted meshes. In this talk, I will introduce recent advances in developing and analyzing several IFEMs for solving 3D interface problems. The proposed method can be utilized on interface-unfitted meshes even if the interface possesses an arbitrary shape. The new IFE space is isomorphic to the standard finite element space, and the isomorphism is stable with respect to the interface location. The IFE method is proven to maintain optimal convergence in both the energy norm and the L2 norm. Numerical examples will be provided to verify our theoretical results and demonstrate the applicability of this method in tackling some real-world 3D interface models.
报告人简介:张旭,美国俄克拉荷马州立大学副教授。2005年和2008年在四川大学数学学院分别获得学士和硕士学位,2013年在美国弗吉尼亚理工大学获得博士学位。2013-2016年在美国普渡大学做博士后。2016年入职密西西比州立大学担任助理教授。2019年起就职俄克拉荷马州立大学,2022年晋升副教授并获终身教职。研究领域是数值偏微分方程,研究问题包括界面问题的有限元方法,自适应算法,超收敛分析等。自2017年起他主持多项美国自然科学基金的科研项目。他的研究成果在SIAM Journal on Numerical Analysis, SIAM Journal Scientific Computing, Journal of Computational Physics, Journal of Scientific Computing 等期刊发表论文30多篇,并有超过1200次的同行引用。他现担任SIAM美国中部分会主席。
报告时间:2024年7月5日 15:00-16:30
报告地点:文渊楼 B536
主办单位:红足1世66814