学术报告

报告题目：Towardseffective 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日上午10:00-11:00  

报告地点：数统院307

                                                红世一足666814 

                                                           2019.6.10 

报告简介：Theanomalous diffusion governed by PDEs involving fractional Laplacian inmulti-dimensional bounded domains poses significant challenges in numericalsolutions. In particular, the integral fractional Laplacian presents even morenotorious numerical difficulties among several different definitions offractional Laplacian. The numerics actually lags behind the PDE theory and eventhe numerical analysis (of FEM). In this talk, we report our recent attemptsand results (some of them are preliminary) on spectral and $hp$ methods onrectangular domains. The key is to compute the stiffness matrix is in theFourier domains, where the explicit form of the Fourier transforms of spectraland FEM basis can be derived explicitly. This allows for easy impositionof  continuity across elements. We shallalso 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》.