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; (ii) with the substitution, the PAL-equation is free of singular coefficients  and the substituted unknown field   is essentially non-oscillatory in the layer; and (iii) 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. On the other hand, we shall also report some new idea of using 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. This talk is based on joint works with Yang Zhiguo at Shanghai Jiao Tong University.

现为新加坡南洋理工大学数理学院副教授 (Tenured)。并于2003到2005年在美国普渡大学（Purdue University）从事博士后和Visiting Assistant Professor工作。2016年至2019年，受聘为厦门大学闽江讲座教授。长期从事谱和高阶数值方法及其应用研究。他在《SIAM J. Numer. Anal.》、《SIAM J. Sci. Comp.》、《SIAM J. Appl. Math.》、《Math. Comp.》以及《Appl. Comput. Harmonic Anal.》等国际计算应用数学顶级学术期刊上发表学术论文90余篇，并由Springer-Verlag出版社出版学术专著1部《Spectral Methods, 2011》(合著)。目前已主持5项并参加4项新加坡国家自然科学基金和新加坡教育部基金，并在国际重要学术会议作邀请报告60余次，包括2016年, 在第十一届国际谱和高阶方法国际会议（巴西）作一小时特邀报告。目前担任期刊《Communications on Applied Mathematics and Computation》和《Journal of Mathematical Study》编委。