Application of the Complete Radiation Boundary Condition and the Rational Absorbing Boundary Condition in $\mathbb{R}^2$ and $\mathbb{R}^3$ (Journal of Computational Mathematics, 2025)
In this study, we explore two distinct rational approximations to the radiation conditionfor effectively solving time-harmonic wave propagation problems governed by the Helmholtzequation in $\mathbb{R}^d,$ $d = 2$ or $3.$ First, we focus on the well-known complete radiation boundarycondition (CRBC), which was developed for a transparent boundary condition for two-dimensional problems. The extension of CRBC to three-dimensional problems is a primaryconcern. Applications of CRBC require removing a near-cutoff region for a frequency rangeof a process to minimize reflection errors. To address the limitation faced by the CRBCapplication we introduce another absorbing boundary condition that avoids this demandingtruncation. It is a new rational approximation to the radiation condition, which we calla rational absorbing boundary condition, that is capable of accommodating all types ofpropagating wave modes, including the grazing modes. This paper presents a comparativeperformance assessment of two approaches in two and three-dimensional spaces, providinginsights into their effectiveness for practical application in wave propagation problems.