报告题目：Space-Time Spectral Methods and Eigenvalue Analysis of Related Spectral Differentiation Matrices for IVPs

报 告 人：王立联教授（Nanyang Technological University）

报告时间：2022年12月6日  10:00

报告地点：腾讯会议（581961374）

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 discretizations but low-order schemes are used in time discretisations. 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-Gialerkin 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 characterise the eigen-pairs of the spectral discretisation matrices through the generalized IBesel polynomials. Such findings have much implication in, e.g, theoretical foundation of time spectral methods, stability of explicit time discretisations 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 Wang Li-Lian is currently a full Professor of Applied Mathematics in the School of Physical and Mathematical Sciences in Nanyang Technological University (NTU), Singapore. Before joining NTU in 2006, he worked as a Postdoctoral Fellow and Visiting Assistant Professor at Purdue University in USA from 2002 to 2005. He received his PhD from Shanghai University in 2000 and then worked in Shanghai Normal University for two years. His main research interest resides in spectral and high-order methods for PDEs. He has published about 100 papers in top scientific journals including Appl. Comput. Harmon. Anal, SIAm J. Numer. Anal, SIAm J. Appl. Math, Math. Comp, etc.. His Co-authored Springer book on Spectral Methods (2011) has become a standard reference in this subject area.