报告人：王立联（南洋理工大学）

报告题目：A new framework for singularity analysis  and efficient spectral methods for PDEs with fractional/nonlocal Laplacian operators

报告摘要：This talk consists of two parts. In the first part, we discuss optimal spectral approximation of singular functions in fractional Sobolev-type spaces, and demonstrate that how fractional calculus can radically impact the polynomial approximation theory. In the second part, we introduce an efficient spectral method using Hermite functions for PDEs with nonlocal Laplacian operators in unbounded domains, and show that such a basis enjoys the de-convolution property and ease of removal of kernel singularities.  We also discuss spectral algorithms using finite Fourier transforms for such problems in finite domains. This talk is based on joint works with Wenjie Liu (Harbin Institute of Technology) and/or Huiyuan Li (CAS).

报告人简介：王立联，新加坡南洋理工大学副教授，博士生导师。主要研究领域为谱方法求解偏微分方程，电磁学中的高性能计算方法等。在SIAM J. Numer. Anal., SIAM J. Appl. Math., SIAM J. Sci. Comput., Math. Comp.等国际知名计算数学期刊上发表论文七十余篇，并且由Springer出版合著《SPECTRAL METHODS: Algorithms, Analysis and Applications》.

报告时间：2018年6月2日（星期六）上午9:30-10:20

报告地点：科技楼南702