一、题目
Jacobi Spectral Methods for Singular Problems: Theory, Algorithms and Applications
二、主讲人
王立联
三、摘要
It is known that the accuracy and performance of a usual spectral method might be deleteriously degraded when the solution exhibits local singular behaviors with very limited regularity. In practice, the singularity may occur in many problems under various scenarios such as PDEs in nonsmooth computational domains with sharp corners or with degenerate or discontinuous coefficients, non-matching boundary conditions, singular kernels or potentials, and non-differentiable nonlinear terms among others. In this talk, we shall elaborate on the evolution of spectral methods from the traditional Legendre/Chebyshev methods to Jacobi polynomials, generalised Jacobi polynomials (GJPs), and generalised Jacobi functions (GJFs), and present fundamental spectral approximation theory of Jacobi approximation to typical singular solutions under fractional Sobolev framework. We then develop fast and accurate spectral algorithms for various singular and nonlocal problems and problems with highly oscillatory solutions.
四、主讲人简介
王立联,现为新加坡南洋理工大学教授。2000年在上海大学获计算数学博士学位。2002至2005年,在美国普渡大学(Purdue University)从事博士后研究工作并担任访问助理教授,并于2005年底加入新加坡南洋理工大学。在2016年至2019年,受聘为厦门大学闽江讲座教授。王立联教授长期从事高精度数值方法及其应用研究,是该方向的国际知名专家。他在Appl. Comp. Harmo. Anal.、SIAM J. Numer. Anal.、SIAM J. Sci. Comp.、SIAM J. Appl. Math.、Math. Comp.和IEEE Transactions on Image Processing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, 2011》(合著)1部。目前已主持多项新加坡国家自然科学基金和新加坡教育部基金,并在国际重要学术会议作邀请报告70余次。
五、邀请人
蒋晓芸,数学学院教授
六、时间
11月22日(周二)10:00
七、地点
腾讯会议
八、联系人
王淑鹏,联系方式:17853727213
九、主办
山东大学数学学院