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  • Constructing least-squares multivariate polynomial approximation

    发布者:文明办发布时间:2019-11-18浏览次数:51


    主讲人:王立联 新加坡南洋理工大学教授


    时间:2019年11月22日10:15


    地点:3号楼322报告厅


    举办单位:数理学院


    主讲人介绍: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》.


    内容介绍:In recent years, spectral methods have become one of the major tools for  computational scientists and engineers due to their superior accuracy and  efficiency when they are properly designed and implemented. In this lecture, we  shall elaborate on the evolution of spectral algorithms, analysis and  applications from the traditional Legendre/Chebyshev methods to Jacobi  polynomials, generalised Jacobi polynomials (GJPs), and generalised Jacobi  functions (GJFs). We shall present essential ingredients for fast spectral  methods and new frameworks of spectral approximation theory and error analysis.  We shall also present, as examples of applications, efficient spectral methods for  acoustic/electromagnetic scattering, singular/unbounded domains, and  high-dimensional problems. In particular, we shall introduce a novel perfect  absorbing layer (PAL) technique constructed from transformation optics pertinent  to inside-out invisibility cloak, which leads to exact truncation of the  time-harmonic wave scattering problems in unbounded domains.