报告题目：Towards effective spectral and $hp$ methods for PDEs with integral  fractional Laplacian

报 告 人：王立联教授（新加坡南洋理工大学）

报告时间：2019年6月11日 10:00-11:00

报告地点：数统院307学术报告厅

报告摘要：

The anomalous diffusion governed by PDEs involving fractional Laplacian in multi-dimensional bounded domains poses significant challenges in numerical solutions. In particular, the integral fractional Laplacian presents even more notorious numerical difficulties among several different definitions of fractional Laplacian. The numerics actually lags behind the PDE theory and even the numerical analysis (of FEM). In this talk, we report our recent attempts and results (some of them are preliminary) on spectral and $hp$ methods on rectangular domains. The key is to compute the stiffness matrix is in the Fourier domains, where the explicit form of the Fourier transforms of spectral and FEM basis can be derived explicitly. This allows for easy imposition of  continuity across elements. We shall also present fast algorithm for FPDEs in multidimensional unbounded domains.

报告人简介：

王立联，新加坡南洋理工大学教授，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》.