学术报告通知

报告题目：A FD/FE method for Anisotropic Elliptic Interface Problems

报告人：李治林教授 （北卡罗莱纳州立大学）

报告时间：2019年12月28日下午3:00-4:00

报告地点：数统院307 教室

报告摘要：Anisotropic elliptic interface problems are important but hard to solve. There is limited literature on numerical methods based on structured meshes. Finite element methods are often preferred but the average error estimates cannot guarantee accuracy of the solution near or at the interface. Using a finite difference discretization, the coefficient matrix of the resulting linear system of equations is neither an SPD nor an M-matrix. In this work, we combine a finite element discretization at regular grid points whose coefficient part matrix is an SPD, while at irregular grid points, a finite difference discretization based on the maximum principle preserving method whose coefficient part matrix is an M-matrix. A multigrid method based a nine-point stencil is employed to solve the linear system of equations. A scaling strategy along the interface is proposed along with the discretization. Error analysis show that the global error is nearly second order accurate in the L-infinity norm except a fact of |log h|. Numerical examples including an application of flow past anisotropic materials will be presented.

报告人简介：李治林，教授，美国北卡罗莱纳州立大学数学系终身教授，是国际上著名的计算数学专家，1988年硕士毕业于南京师范大学，1989年赴美在华盛顿大学留学，师从LeVeque教授，1994年获博士学位后在UCLA从事博士后研究工作，1996年在密西西比州立大学工作，1997年开始在北卡罗莱纳州立大学数学系工作至今，是江苏省首批特聘教授。他在SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, Journal of Computational Physics, Numerische Mathematik等计算数学顶级杂志发表论文100多篇。担任Nmerical Mathematics: Theory, Methods and Applications等多个杂志的编委。主要研究领域为：计算数学，浸入界面法（IIM）、浸入有限元法（IFEM）以及快速浸入界面法（AIIM）等求解含有奇异源项、不连续物理参数及不规则区域上的偏微分方程的数值方法。