题     目：科学计算中高精度算法谱方法的一些最新进展

报 告 人：Wang Li-Lian(王立联), 新加坡南洋理工大学数理学院

时     间：2024年7月26日（周五）  09:00 – 09:50

地    点：管理科研楼1418

摘    要：

In the past decades, the spectral method has become one of the major tools in scientific computing for solving partial differential equations 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.