TY - JOUR
T1 - Application of the Complete Radiation Boundary Condition and the Rational Absorbing Boundary Condition in $\mathbb{R}^2$ and $\mathbb{R}^3$
AU - Lee , Jungwon
AU - Kim , Seungil
JO - Journal of Computational Mathematics
VL - 5
SP - 1318
EP - 1348
PY - 2025
DA - 2025/09
SN - 43
DO - http://doi.org/10.4208/jcm.2509-m2024-0238
UR - https://global-sci.org/intro/article_detail/jcm/24483.html
KW - Absorbing boundary condition, Complete radiation condition, Rational absorbing boundary condition, Helmholtz equation.
AB - <p style="text-align: justify;">In this study, we explore two distinct rational approximations to the radiation condition
for effectively solving time-harmonic wave propagation problems governed by the Helmholtz
equation in $\mathbb{R}^d,$ $d = 2$ or $3.$ First, we focus on the well-known complete radiation boundary
condition (CRBC), which was developed for a transparent boundary condition for two-dimensional problems. The extension of CRBC to three-dimensional problems is a primary
concern. Applications of CRBC require removing a near-cutoff region for a frequency range
of a process to minimize reflection errors. To address the limitation faced by the CRBC
application we introduce another absorbing boundary condition that avoids this demanding
truncation. It is a new rational approximation to the radiation condition, which we call
a rational absorbing boundary condition, that is capable of accommodating all types of
propagating wave modes, including the grazing modes. This paper presents a comparative
performance assessment of two approaches in two and three-dimensional spaces, providing
insights into their effectiveness for practical application in wave propagation problems.</p>