汇报标题 (Title)：Spectral Methods: Some Recent Advances and New Perspectives(谱步骤：一些最新进展与新概想)
汇报人 (Speaker)：王立联 教授（南洋理工大学）
汇报功夫 (Time)：2023年11月8日(周三) 10:30
汇报地址 (Place)：腾讯会议(530 994 719)
约请人(Inviter)：李常品、蔡敏
主办部门：理学院数学系
汇报提要：In the past decades, the spectral method has become one of the major tools in scientific computing due to its superior accuracy and efficiency when it is properly designed. In this talk, we shall review the evolution of spectral method and elaborate on some recent advancements from the perspective of (i) Singular, fractional and nonlocal problems; (ii) Complex domains/geometries (e.g., spectral fictitious domain method and spectral methods on pipes, knots etc); and (iii) PDEs with highly oscillatory solutions among others. We shall also outline some new directions that the spectral method can excel itself and unknown areas that the spectral method might be the method of choice.
