Performance evaluation and absorption enhancement of the Grote-Keller and unsplit PML boundary conditions for the 3-D FDTD method in spherical coordinates

A new absorption performance evaluation of the exact Grote and Keller boundary conditions versus a generalization of the unsplit PML for the FDTD method in spherical coordinates, is thoroughly conducted in this paper. The attenuation capabilities of the latter absorber are further enhanced via novel approaches concerning its termination by the Bayliss-Turkei ABCs, in conjunction with higher-order finite difference schemes in the layer. Moreover, an expanded curvilinear mesh algorithm for the interior of the PML is introduced in order to achieve the required reflection with a reduced number of cells. Numerical vector spherical-wave simulations investigate the convergence properties in respect to grid resolution of both ABCs, the evolution of various error norms, and their behavior as a function of distance from the scatterer, with the 3-D curvilinear FDTD method. Numerical results demonstrate that both conditions are remarkably robust and highly accurate, while the proposed developments provide significant savings in the computational cost.