Continued fraction absorbing boundary conditions for convex polygonal domains

Continued fraction absorbing boundary conditions (CFABCs) are highly effective boundary conditions for modelling wave absorption into unbounded domains. They are based on rational approximation of the exact dispersion relationship and were originally developed for straight computational boundaries. In this paper, CFABCs are extended to the more general case of polygonal computational domains. The key to the current development is the surprising link found between the CFABCs and the complex co-ordinate stretching of perfectly matched layers (PMLs). This link facilitates the extension of CFABCs to oblique corners and, thus, to polygonal domains. It is shown that the proposed CFABCs are easy to implement, expected to perform better than PMLs, and are effective for general polygonal computational domains. In addition to the derivation of CFABCs, a novel explicit time-stepping scheme is developed for efficient numerical implementation. Numerical examples presented in the paper illustrate that effective absorption is attained with a negligible increase in the computational cost for the interior domain. Although this paper focuses on wave propagation, its theoretical development can be easily extended to the more general class of problems where the governing differential equation is second order in space with constant coefficients.