Title: Jacobi Spectral Methods: Recent Advances and New Perspectives
Speaker: Prof. Li-Lian Wang (Nanyang Technological University)
Time: 2019-11-22 (Friday) 15:30
Inviter: Heping Ma
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, generalized Jacobi polynomials (GJPs), and generalized 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.