This study builds on a recent paper by Lai et al [Appl. Comput. Harmon. Anal., 2018] in which a novel boundary integral formulation is presented for scalar wave scattering analysis in two-dimensional layered and half-spaces. The seminal paper proposes a hybrid integral representation that combines the Sommerfeld integral and layer potential to efficiently deal with the boundaries of infinite length. In this work, we modify the integral formulation to eliminate the fictitious eigenvalues by employing Burton-Miller's approach. We also discuss reasonable parameter settings for the hybrid integral equation to ensure efficient and accurate numerical solutions. Furthermore, we extend the modified formulation for the scattering from a cavity in a half-space whose boundary is locally perturbed. To address the cavity scattering, we introduce a virtual boundary enclosing the cavity and couple the integral equation on it with the hybrid equation. The effectiveness of the proposed method is demonstrated through numerical examples.

翻译：本研究基于Lai等人近期发表的一篇论文[Appl. Comput. Harmon. Anal., 2018]，该文针对二维分层及半空间中的标量波散射分析提出了一种新型边界积分公式。该奠基性论文提出了一种混合积分表示方法，将Sommerfeld积分与层势相结合，以有效处理无限长边界。本文中，我们通过采用Burton-Miller方法对积分公式进行修正，以消除伪特征值。同时，我们讨论了混合积分方程中合理的参数设置，以确保数值解的准确性与高效性。此外，我们将修正后的公式扩展应用于边界局部扰动的半空间空腔散射问题。为处理空腔散射，我们在空腔外部引入虚拟边界，将虚拟边界上的积分方程与混合方程耦合。通过数值算例验证了所提方法的有效性。