Absorbing boundary condition for scalar-wave propagation problems in infinite media based on a root-finding algorithm

In this study, we propose a new approach for development of absorbing boundary conditions for scalar-wave propagation problems in infinite media based on a root-finding algorithm for the solution of the exact wave dispersion relation. We select the Newton-Raphson method as the root-finding algorithm in the present study and assess the accuracy of the newly developed boundary condition by estimating its reflection coefficient. Furthermore, we evaluate and verify the stability of the boundary condition. We apply our development to various scalar-wave propagation problems and demonstrate that the proposed approach leads to accurate and stable computations.