A Chebyshev-based rectangular-polar integral solver for scattering by geometries described by non-overlapping patches
A Chebyshev-based rectangular-polar integral solver for scattering by geometries described by non-overlapping patches
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DOI：
10.1016/j.jcp.2020.109740
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
O. Bruno;Emmanuel Garza
中科院分区：
文献类型：
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作者：
O. Bruno;Emmanuel Garza
本文介绍了在声散射问题的边界积分方程中出现的奇异核和边缘奇异积分密度的高阶精确积分策略。特别地，所提出的方法被设计用于与一组任意非重叠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计算机辅助设计（CAD）几何。算法中引入了fej<s:1>第一积分规则，提供了一种光谱精度的方法来评估远积分区域的贡献，同时利用二维切比雪夫变换和适当的曲面变化变量的“矩形极坐标”变化，对某些“表面斑块”上的奇异和近奇异积分进行高精度的预计算，以获得奇异和近奇异相互作用的贡献。然后将整体集成方法与线性代数解算器GMRES结合使用，以生成声软开放和封闭表面散射障碍物的解，包括通过CAD表示方式描述的飞机应用。该方法具有鲁棒性、快速性和高度准确性：每个波长使用几个点足以使算法产生远场精度达到百分之一的几分之一，并且离散密度的轻微增加可以显著提高精度。
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.