报告题目：A Truly Exact Perfect Absorbing Layer for Time-Harmonic Wave Scattering Problems

报 告 人：王立联教授（新加坡南洋理工大学）

报告时间：2021年3月10日  10:00-11:00

报告地点：数统院5楼数学研究中心多功能研讨室（线上报告）

报告摘要：

In this talk, we shall present a truly exact and optimal perfect absorbing layer (PAL) for domain truncation of the Helmholtz equation in an unbounded domain with a bounded scatterer. This technique is based on a complex compression coordinate transformation in polar coordinates, and a suitable substitution of the unknown field in the artificial layer. Compared with the widely-used perfectly matched layer (PML) methods, the distinctive features of PAL lie in that(i) it is truly exact in the sense that the PAL-solution is identical to the original solution in the bounded domain reduced by the truncation layer; (i) with the substitution, the PAL -equation is free of singular coefficients and the substituted unknown field is essentially non-oscillatory in the layer; and (ii) the construction is valid for general star-shaped domain truncation. By formulating the variational formulation in Cartesian coordinates, the implementation of this technique using standard spectral-element or finite- element methods can be made easy as a usual coding practice. We provide ample numerical examples to demonstrate that this method is highly accurate and robust for very high wave-number and thin layer. Moreover, we shall report our very recent attempt to a real coordinate transformation to construct a layer that can act as a PML and also produce an accurate approximation of far- field scattering waves like infinite finite elements.

报告人简介：

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70余篇，并且由Springer出版合著《SPECTRAL METHODS: Algorithms, Analysis and Applications》。