Comparison of the Grote-Keller and unsplit PML absorbing boundary conditions for Maxwell's equations in spherical coordinates

The exact absorbing boundary condition for Maxwell's equations in spherical coordinates, first derived and demonstrated by Grote and Keller, is evaluated against the unsplit perfectly matched layer. The latter approach is a recent generalization of the unsplit PML technique to the cylindrical and spherical coordinate systems. With numerical simulations we compare the convergence properties of both approaches, the evolution of various norms of the error they produce, and their behavior as a function of distance from the scatterer to the computational domain boundary where they are imposed. These results demonstrate that both conditions are remarkably robust, and highly accurate.