报告题目：Exponentially fitting schemes for general convection-dominated PDEs and applications

报 告 人：吴朔男 助理教授 北京大学数学科学学院

报告时间：2020年7月29日10:00

报告地点：腾讯会议 ID：125 424 154

会议链接：https://meeting.tencent.com/s/PFOoJGUPECca

校内联系人：王翔 wxjldx@jlu.edu.cn

报告摘要：

Convection-diffusion problems, especially the convection dominated ones, are known to have many important applications and numerical challenges. In this talk, we present a robust discretization and solver developed for convection-dominated PDEs discretized on unstructured simplicial grids. The proposed methods can be applied to any one of the following operators: gradient, curl, and divergence. The derivation of the lowest order scheme makes use of some intrinsic properties of differential forms and in particular some crucial identities from differential geometry. We further give a systematic way for deriving high order schemes, by considering the properties of quasi-polynomial spaces defined as (exponentially) weighted spaces with polynomial coefficients. The analysis can be generalized to discrete differential forms of arbitrary order in any spatial dimension and any quasi-polynomial Hilbert complex of the first kind (Nédélec–Raviart–Thomas) or second kind (Nédélec–Brezzi–Douglas–Marini). Both theoretical analysis and numerical experiments show that the new upwinding finite element schemes provide an accurate and robust discretization and a fast solver in many applications and in particular for simulation of magnetohydrodynamics systems when the magnetic Reynolds number Rm is large.

报告人简介：

吴朔男分别于2009年和2014年在北京大学数学科学学院获得学士和博士学位，2014年至2018年在美国宾州州立大学进行博士后研究，2018年秋季加入北京大学数学科学学院信息与计算科学系任助理教授。主要研究方向为偏微分方程数值解，研究内容包括：线弹性问题的非协调混合元的构造和分析、线弹性问题的杂交化方法 和多重网格求解器、多相场的建模和计算、高阶椭圆型方程的非协调有限元的构造和分析、和磁流体力学中的磁对流的稳定离散等。研究工作发表在Math. Comp., Numer. Math., SIAM J. Numer. Anal., J. Comput. Phys., Comput. Methods Appl. Mech. Engrg.,Math. Models Methods Appl. Sci.等核心期刊上。