講座主題：Stabilized Finite Element Methods and Fast Solvers for H(curl) Vector Field Convection-Diffusion Problems
專家姓名：吳朔男
工作單位：北京大學(xué)
講座時(shí)間：2024年11月11日14:30-15:30
講座地點(diǎn)：數(shù)學(xué)院大會(huì)議室341
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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).
主講人介紹：
吳朔男分別于2009年和2014年在北京大學(xué)數(shù)學(xué)科學(xué)學(xué)院獲得學(xué)士和博士學(xué)位，2014年至2018年在美國賓州州立大學(xué)進(jìn)行博士后研究，2018年加入北京大學(xué)數(shù)學(xué)科學(xué)學(xué)院信息與計(jì)算科學(xué)系，現(xiàn)任長聘副教授/研究員。獲基金委優(yōu)秀青年科學(xué)基金(2022)、第六屆中國工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)應(yīng)用數(shù)學(xué)青年科技獎(jiǎng)(2022)。主要研究方向?yàn)槠⒎址匠虜?shù)值解，研究內(nèi)容包括：磁流體力學(xué)中的磁對流的穩(wěn)定離散、非線性、高階橢圓型方程的非協(xié)調(diào)有限元的構(gòu)造和分析，空間分?jǐn)?shù)階問題的離散和快速求解器等。研究工作發(fā)表在Math. Comp., Numer. Math., SIAM J. Numer. Anal.等核心期刊上。
