论文标题
窗户的绿色功能方法通过2D障碍的周期性阵列进行波浪散射
Windowed Green function method for wave scattering by periodic arrays of 2D obstacles
论文作者
论文摘要
本文介绍了一种新颖的边界积分方程（BIE）方法，用于通过二维渗透障碍的周期性线阵列的PlaneWave散射问题的数值解决方案。我们的方法建立在直接的BIE公式之上，该公式利用了自由空间绿色功能的简单性，但反过来又需要评估单位细胞边界的积分。此类积分在这里通过窗口绿色函数方法处理。窗口近似以及有限级操作员校正（用于正确施加瑞利辐射条件）产生了可靠的第二种bie，可在整个频谱中产生超代数收敛的溶液，包括在挑战性的雷利河谷异常情况下。校正后的BIE可以通过现成的NyStröm和边界元素方法离散化，并且会导致适合迭代线性algebra求解器以及标准快速矩阵矢量乘积算法的线性系统。各种数值示例证明了所提出方法的准确性和鲁棒性
This paper introduces a novel boundary integral equation (BIE) method for the numerical solution of problems of planewave scattering by periodic line arrays of two-dimensional penetrable obstacles. Our approach is built upon a direct BIE formulation that leverages the simplicity of the free-space Green function but in turn entails evaluation of integrals over the unit-cell boundaries. Such integrals are here treated via the window Green function method. The windowing approximation together with a finite-rank operator correction -- used to properly impose the Rayleigh radiation condition -- yield a robust second-kind BIE that produces super-algebraically convergent solutions throughout the spectrum, including at the challenging Rayleigh-Wood anomalies. The corrected windowed BIE can be discretized by means of off-the-shelf Nyström and boundary element methods, and it leads to linear systems suitable for iterative linear-algebra solvers as well as standard fast matrix-vector product algorithms. A variety of numerical examples demonstrate the accuracy and robustness of the proposed methodology
