This paper introduces a high-order-accurate strategy for integration of singular kernels and edge-singular integral densities that appear in the context of boundary integral equation formulations for the problem of acoustic scattering. In particular, the proposed method is designed for use in conjunction with geometry descriptions given by a set of arbitrary non-overlapping logically-quadrilateral patches—which makes the algorithm particularly well suited for computer-aided design (CAD) geometries. Fejér's first quadrature rule is incorporated in the algorithm, to provide a spectrally accurate method for evaluation of contributions from far integration regions, while highly-accurate precomputations of singular and near-singular integrals over certain “surface patches” together with two-dimensional Chebyshev transforms and suitable surface-varying “rectangular-polar” changes of variables, are used to obtain the contributions for singular and near-singular interactions. The overall integration method is then used in conjunction with the linear-algebra solver GMRES to produce solutions for sound-soft open- and closed-surface scattering obstacles, including an application to an aircraft described by means of a CAD representation. The approach is robust, fast, and highly accurate: use of a few points per wavelength suffices for the algorithm to produce far-field accuracies of a fraction of a percent, and slight increases in the discretization densities give rise to significant accuracy improvements.

本文介绍了一种高精确度的积分策略，用于积分在边界积分方程公式化的背景下出现的，针对声学散射问题的奇异核和边奇异积分密度的积分。尤其是，所提出的方法被设计为与由一组任意不重叠的逻辑四边形补丁给出的几何描述结合使用，这使得该算法特别适合于计算机辅助设计（CAD）几何。Fejér的第一个正交规则已纳入算法，以提供一种光谱精确的方法来评估远积分区域的贡献，同时使用某些“表面补丁”上的奇异积分和近奇积分的高精度预计算以及二维Chebyshev变换和变量的适当的表面变化“矩形-极”变化，来获得对奇异和近奇的贡献。奇异的相互作用。然后，将整体积分方法与线性代数求解器GMRES结合使用，以产生声软的开放和闭合表面散射障碍的解决方案，包括通过CAD表示描述的飞机应用。该方法是鲁棒，快速且高度准确的：每个波长使用几个点就足以使算法产生百分之一的远场精度，而离散密度的略微增加会带来显着的精度提高。