报告人：王立联（南洋理工大学）

报告时间：2026年7月17日（星期五）15:30-17:30

报告地点：科技楼南楼706会议室

报告摘要：The spectral collocation method is easy to implement--one simply replaces derivatives by spectral differentiation matrices at Gaussian-type collocation points. This plug-and-play nature makes it well suited for variable-coefficient and nonlinear problems. However, the collocation method is often severely ill-conditioned, which limits its application, particularly in multiple dimensions for solutions that require high resolutions. In this talk, we introduce optimal preconditioners for multi-dimensional collocation methods by using the notion of preconditioning differentiation by integration via Birkhoff interpolation and stable matrix diagonalization techniques. With this at our disposal, we discuss the preconditioning of the Hierarchical Poincare–Steklov (HPS) spectral-element method, which is a fast and accurate direct spectral solver using the collocation methods as local solvers.

报告人简介：王立联，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,在SIAM J. Numer. Anal.、SIAM J. Sci. Comput.、SIAM J. Appl. Math.、Math. Comp.、Appl. Comput. Harm. Anal.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《Spectral Methods: Algorithms, Analysis and Applications》(合著)，该专著当前被引用3000多次。王立联教授在国际重要学术会议作邀请报告70余次。

邀请人：王海永