报告人: Tao Lin（Department of Mathematics, Virginia Tech）

报告时间：2016年6月23日（星期四）下午4:30-6:30

地点：明理楼B203

报告人简介：林涛，弗吉尼亚理工大学教授、博士生导师。林教授1982年获得四川大学学士学位，1985年在中科院获得硕士学位，随后在美国怀俄明大学师从Richard Ewing攻读博士学位，并于1990年获得博士学位。2001年获得弗吉尼亚理工大学正教授职位。林教授的研究工作集中在有限元方法进行微分方程、微分积分方程大规模数值模拟，是浸入式有限元的提出者和代表人物。浸入式有限元是计算流体领域应用广泛的数值计算方法。目前，他在该领域出版著作1本，发表研究性论文100多篇。

Abstract: Interface problems often appear in numerical simulations over domains consisting of multiple materials leading to discontinuous coefficients in the involved partial differential equations whose solutions are inevitably less smooth around the material interfaces. Traditional finite element (FE) methods handle challenges from this deficiency of global regularity by using body-fitting meshes in which each element essentially contains one of the materials; otherwise, their convergence cannot be guaranteed. This presentation will start from a few examples to show that unstructured body-fitting meshes can hinder efficient applications of FE methods in some applications, and this motivates the need for developing FE methods based on structured or Cartesian meshes for interface problems. After surveying related FE methods, the presentation will focus on the recently developed immersed finite element (IFE) methods that can utilize interface-independent, such as structured or Cartesian, meshes even for interfaces with non-trivial geometries. Fundamental mathematical properties of IFE methods and some essential differences between FE and IFE methods will be highlighted. A few application examples will be presented to illustrate features of IFE methods. The presentation will conclude with a few research topics in IFE methods.

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