This paper continues Part I (Hagstrom and Kim in Numer Math 141(4):917–966, 2019) of the investigation on the complete radiation boundary condition (CRBC) in waveguides. In this paper, we propose corner compatibility conditions for CRBC applied to the Helmholtz equation posed in \(\mathbb {R}^2\). Since CRBC is developed as a high-order absorbing boundary condition approximating the radiation condition by using rational functions via the cross-sectional Fourier analysis, it is well-studied and its accurate performance is validated on a straight/planar fictitious boundary in waveguides. However in the presence of corners on artificial absorbing boundaries such as boundaries of rectangular domains, a special treatment for corner conditions is required. We design and validate the accurate CRBC with the corner compatibility conditions on rectangular domains. We also analyze the existence and uniqueness of solutions to the Helmholtz equation coupled with CRBC with the corner compatibility conditions. Finally, numerical experiments illustrating the accuracy of CRBC will be presented.

本文继续第一部分（Hagstrom 和 Kim in Numer Math 141(4):917–966, 2019）对波导中完全辐射边界条件 (CRBC) 的研究。在本文中，我们提出了适用于\(\mathbb {R}^2\)中亥姆霍兹方程的 CRBC 的角兼容条件. 由于 CRBC 是通过横截面傅里叶分析使用有理函数开发为近似辐射条件的高阶吸收边界条件，因此对其进行了充分研究，并在波导中的直/平面虚拟边界上验证了其准确性能。然而，在矩形域边界等人工吸收边界上存在角点的情况下，需要对角点条件进行特殊处理。我们在矩形域上设计并验证了具有角兼容条件的准确 CRBC。我们还分析了 Helmholtz 方程与 CRBC 耦合的角兼容条件解的存在性和唯一性。最后，将展示说明 CRBC 准确性的数值实验。