报告题目：Eigenvalue Analysis of Spectral Discretisation for IVPs and Space-Time Spectral Methods
报告人：王立联 教授（新加坡南洋理工大学）
报告时间：2023年6月21日（周三）下午:4:30-5:30
报告地点：数学院425
邀请人：雷渊
报告摘要： Spectral methods typically use global orthogonal polynomials/functions as basis functions which enjoy high-order accuracy and gain increasingly popularity in scientific and engineering computations. In most applications, spectral methods are employed in spatial discretization, but low-order schemes are used in time discretization. This may create a mismatch of accuracy in particular for problems with evolving dynamics that require high-resolution in both space and time, e.g., oscillatory wave propagations. In this talk, we conduct eigenvalue analysis for the spectral discretization matrices for initial value problems based on the Legendre dual-Petrov-Galerkin spectral method (LDPG). While the spectrum of second-order derivative operators for boundary value problems are well understood, the spectrum of spectral approximations of initial value problems are far under explored. Here, we precisely characterize the eigen-pairs of the spectral discretisation matrices through the generalized Bessel polynomials. Such findings have much implication in, e.g., theoretical foundation of time spectral methods, stability of explicit time discretization of spectral methods for hyperbolic problems and parallel-in-time algorithms among others. We also introduce effective matrix decomposition algorithms to alleviate the burden of the extra works for spectral methods in time. This talk is based on joint works with Desong Kong (Central South China University), Jie Shen (Purdue University) and Shuhuang Xiang (CSU).
报告人简介：Professor Li-Lian Wang is currently a full Professor of Nanyang Technological University (NTU) in Singapore. He received his PhD from Shanghai University in 2000. Before he joined NTU as an Assistant Professor in 2006, he worked as a Visiting Assistant Professor and Postdoctoral Fellow in Purdue University since 2002. He was the Min Jiang Chair
