題目一：Direct and inverse problems for Scattering Resonances
内容簡介：Scattering resonances have significant applications across various fields of science and engineering. The associated problem is nonlinear and defined on an unbounded domain. In this talk, we discuss recent advancements in the computation of scattering resonances (poles of the scattering operator) for compact obstacles. We begin by introducing the highly accurate Nyström method for the boundary integral formulation, followed by a finite element method combined with Dirichlet-to-Neumann mapping. The convergence is proved using the abstract approximation theory for eigenvalue problems of holomorphic Fredholm operator functions. The nonlinear matrix eigenvalue problem is solved using a parallel multistep spectral indicator method, with numerical examples serving as benchmarks. The talk concludes with new results on inverse problems related to scattering poles.
報告人：孫繼廣
報告人簡介：1996年獲得清華大學應用數學學士學位，并于2005年獲得美國特拉華大學應用數學博士學位，現為密歇根理工大學Richard and Elizabeth Henes特聘教授。其研究重點包括特征值問題、反問題、偏微分方程的數值方法，以及在地球物理應用中的電磁方法。近年來，針對非線性特征值問題和基于數據驅動技術的稀疏數據反問題求解提出了多種計算方法。目前已發表學術論文超過90篇，并出版專著《特征值問題的有限元方法》（CRC出版社，2016年）。
題目二：A Mixed Finite Element Scheme for Quad-Curl Source and Eigenvalue Problems
内容簡介：The quad-curl problem arises in the resistive magnetohydrodynamics (MHD) and the electromagnetic interior transmission problem. In this paper we study a new mixed finite element scheme using Nedelec’s edge elements to approximate both the solution and its curl for quad-curl problem on Lipschitz polyhedral domains. We impose element-wise stabilization instead of stabilization along mesh interfaces. Thus our scheme can be implemented as easy as standard Nedelec’s methods for Maxwell’s equations. Via a discrete energy norm stability due to element-wise stabilization, we prove optimal convergence under a low regularity condition. We also extend the mixed finite element scheme to the quad-curl eigenvalue problem and provide corresponding convergence analysis based on that of source problem. Numerical examples are provided to show the viability and accuracy of the proposed method for quad-curl source problem.
報告人：王超
報告人簡介：現任職深圳北理莫斯科大學。2019年獲得香港理工大學應用數學系哲學博士學位，本科和碩士畢業于哈爾濱工業大學。2020年至2021年，在南方科技大學數學系從事博士後工作。目前主要從事數學建模和計算數學及相關領域，研究領域涉及到有限元方法、科學計算、反問題理論與計算方法、快速算法等。
時 間：2024年11月4日（周一）上午10：00開始
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