讲座主题：Stabilized Finite Element Methods and Fast Solvers for H(curl) Vector Field Convection-Diffusion Problems

专家姓名：吴朔男

工作单位：北京大学

讲座时间：2024年11月11日14:30-15:30

讲座地点：数学院大会议室341

主办单位：hy590海洋之神平台数学与信息科学学院

内容摘要：

Convection-diffusion equations, as one of the fundamental models for describing the coupling of multiple physical fields, find wide applications across various domains. Traditionally, the unknown functions in convection-diffusion equations are scalar functions. However, in recent years, the importance of convection-diffusion equations in problems involving vector fields such as electromagnetic fields has been increasingly recognized, leading to more complex mathematical formulations and structures of the convection terms. Building upon numerical methods for scalar convection-diffusion problems, this talk discusses two stabilized finite element discretization methods for H(curl) vector field convection-diffusion equations: upwind methods and exponential fitting methods. The former introduces stabilization terms by incorporating convection velocity information into the variational formulation, while the latter utilizes characteristics of boundary layer solutions to incorporate exponential functions into the scheme design. Furthermore, solvers for scalar convection-diffusion problems can be analogously adapted to construct solvers for H(curl) vector problems. We will analyze smoothers and multigrid algorithms from the perspective of Local Fourier Analysis (LFA).

主讲人介绍：

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年加入北京大学数学科学学院信息与计算科学系，现任长聘副教授/研究员。获基金委优秀青年科学基金(2022)、第六届中国工业与应用数学学会应用数学青年科技奖(2022)。主要研究方向为偏微分方程数值解，研究内容包括：磁流体力学中的磁对流的稳定离散、非线性、高阶椭圆型方程的非协调有限元的构造和分析，空间分数阶问题的离散和快速求解器等。研究工作发表在Math. Comp., Numer. Math., SIAM J. Numer. Anal.等核心期刊上。