题目一：Direct and inverse problems for Scattering Resonances
内容简介：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.
报告人：孙继广
报告人简介：1996年获得清华大学应用数学学士学位，并于2005年获得美国特拉华大学应用数学博士学位，现为密歇根理工大学Richard and Elizabeth Henes特聘教授。其研究重点包括特征值问题、反问题、偏微分方程的数值方法，以及在地球物理应用中的电磁方法。近年来，针对非线性特征值问题和基于数据驱动技术的稀疏数据反问题求解提出了多种计算方法。目前已发表学术论文超过90篇，并出版专著《特征值问题的有限元方法》（CRC出版社，2016年）。
题目二：A Mixed Finite Element Scheme for Quad-Curl Source and Eigenvalue Problems
内容简介：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.
报告人：王超
报告人简介：现任职深圳北理莫斯科大学。2019年获得香港理工大学应用数学系哲学博士学位，本科和硕士毕业于哈尔滨工业大学。2020年至2021年，在南方科技大学数学系从事博士后工作。目前主要从事数学建模和计算数学及相关领域，研究领域涉及到有限元方法、科学计算、反问题理论与计算方法、快速算法等。
时 间：2024年11月4日（周一）上午10：00开始
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信息科学技术学院
2024年10月28日