Based on the perfectly matched layer (PML) technique, this paper develops a highly accurate boundary integral equation (BIE) solver for acoustic scattering problems in locally defected layered media in both two and three dimensions. The original scattering problem is truncated onto a bounded domain by the PML. Assuming the vanishing of the scattered field on the PML boundary, we derive BIEs on local defects only in terms of using PML-transformed free-space Green’s function, and the four standard integral operators: single-layer, double-layer, transpose of double-layer, and hyper-singular boundary integral operators. The hyper-singular integral operator is transformed into a combination of weakly-singular integral operators and tangential derivatives. We develop a high-order Chebyshev-based rectangular-polar singular-integration solver to discretize all weakly singular integrals. Numerical experiments for both two- and three-dimensional problems are carried out to demonstrate the accuracy and efficiency of the proposed solver.  

　　Publication:  

　　SIAM Journal on Scientific Computing, Volume 45, Issue 4 (2023)  

　　http://dx.doi.org/10.1137/22M1532457  

　　Author:  

　　Wangtao Lu  

　　School of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, China.  

　　Liwei Xu  

　　School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China.  

　　Tao Yin  

　　LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.  

　　Email: yintao@lsec.cc.ac.cn  

　　Lu Zhang  

　　School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China.