新加坡南洋理工大学Wang Li-Lian教授将于近日来访我校并做系列报告，欢迎感兴趣的师生参加。

报告信息如下：

报告1 题目：Spectral methods: Past, Recent Advances and New Perspectives --- Part I

摘要：In the past decades, the spectral method has become one of the major tools in scientific computing due to its superior accuracy and efficiency when it is properly designed. In this talk, we shall review the evolution of spectral methods and elaborate on some recent advancements from the perspective of (i) Singular, fractional and nonlocal problems; (ii) Complex domains and geometries (e.g., spectral fictitious domain method and spectral methods on pipes, knots etc); and (iii) PDEs with highly oscillatory solutions among others. We shall also outline some new directions that the spectral method can excel itself and unknown areas that the spectral method might be the method of choice.

时间：2023-12-26 08:30-10:00

地点：理学楼609

报告2 题目：How do researchers choose a topic for scientific research?

时间：2023-12-26 11:00-12:30

地点：理学楼609

报告3 题目：Spectral methods: Past, Recent Advances and New Perspectives --- Part II

摘要：同报告1

时间：2023-12-26 13:30-15:00

地点：理学楼609

报告4 题目：How to write research papers？

时间：2023-12-26 08:30-10:00

地点：理学楼609

报告5 题目：Numerical Study of Nonlinear Schrodinger’s Equations with Singular Nonlinearities

摘要：In this talk, we present new tools for the analysis of the semi-implicit and time-splitting schemes for the Schrodinger’s equations with singular nonlinear terms such as logarithmic nonlinearity f(u)=u log |u| and f(u)=u |u|^alpha for |alpha|<1.

时间：2023-12-27 08:30-10:00

地点：理学楼609

报告6 题目：Time-space Spectral Methods and Eigenvalue Analysis of related Differentiation Matrices for IVPs

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.

时间：2023-12-27 10:00-11:30

地点：理学楼609

报告人简介：Wang Li-Lian，新加坡南洋理工大学教授，长期从事谱和高阶数值方法及其应用研究。他在《SIAM Journal on Numerical Analysis》、《SIAM Journal on Scientific Computing》、《SIAM Journal on Applied Mathematics》、《Mathematics of Computation》以及《Applied and Computational Harmonic Analysis》等国际计算应用数学顶级学术期刊上发表学术论文100余篇，并由Springer-Verlag出版社出版学术专著1部《Spectral Methods, 2011》(合著)，该专著当前被引用2000多次。在国际重要学术会议作邀请报告60余次，包括2016年, 在第十一届国际谱和高阶方法国际会议（巴西）作一小时特邀报告，2019年在中国举办的第12届中国计算数学年会上做大会报告。