報告題目：Exponentially fitting schemes for general convection-dominated PDEs and applications
報 告 人：吳朔男 助理教授 北京大學數學科學學院
報告時間：2020年7月29日10:00
報告地點：騰訊會議 ID：125 424 154
會議鍊接：https://meeting.tencent.com/s/PFOoJGUPECca
校内聯系人：王翔 wxjldx@jlu.edu.cn
報告摘要：
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.
報告人簡介：
吳朔男分别于2009年和2014年在北京大學數學科學學院獲得學士和博士學位，2014年至2018年在美國賓州州立大學進行博士後研究，2018年秋季加入北京大學數學科學學院信息與計算科學系任助理教授。主要研究方向為偏微分方程數值解，研究内容包括：線彈性問題的非協調混合元的構造和分析、線彈性問題的雜交化方法 和多重網格求解器、多相場的建模和計算、高階橢圓型方程的非協調有限元的構造和分析、和磁流體力學中的磁對流的穩定離散等。研究工作發表在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。
