论文标题
一个高度准确的完全匹配的层边界积分方程求解器，用于声学分层问题
A highly accurate perfectly-matched-layer boundary integral equation solver for acoustic layered-medium problems
论文作者
论文摘要
基于完美匹配的层（PML）技术，本文在两个和三个维度的本地缺陷的分层介质中开发了一个高准确的边界积分方程（BIE）求解器，用于声音散射问题。原始的散射问题被PML截断到有限的域上。假设PML边界上散射场的消失，我们仅在使用PML转换的自由空间Green的功能和四个标准积分运算符方面才能在局部缺陷上得出BIES：单层，双层，双层双层透过双层，双层型和超细胞边界积分器。超细积分运算符转化为弱小的积分算子和切向衍生物的组合。我们开发了一个高阶Chebyshev的矩形矩形奇异整合求解器，以离散所有弱呈弱的积分。进行了二维问题和三维问题的数值实验，以证明所提出的求解器的准确性和效率。
Based on the perfectly matched layer (PML) technique, this paper develops a high-accuracy 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.
