Comparison of high-order absorbing boundary conditions and perfectly matched layers in the frequency domain

The need for numerical schemes for wave problems in large and unbounded domains appears in various applications, including modeling of pressure waves in arteries and other problems in biomedical engineering. Two powerful methods to handle such problems via domain truncation are the use of high-order absorbing boundary conditions (ABCs) and perfectly matched layers (PMLs). A numerical study is presented to compare the performance of these two types of methods, for two-dimensional problems governed by the Helmholtz equation. The high-order ABCs employed here are of the Hagstrom-Warburton type; they are adapted and applied to the frequency domain for the first time. Four PMLs are examined, with linear, quadratic, constant and unbounded decay functions. Two planar configurations are considered: a waveguide and a quarter plane. In the latter case, special corner conditions are developed and used in conjunction with the ABC. One of the main conclusions from the ABC-PML comparison is that in the high-accuracy regime, the ABC scheme and the unbounded PML are equally effective.