Extension of the PML absorbing boundary condition to 3D spherical coordinates: scalar case

The perfectly matched layer (PML) absorbing boundary condition has been shown to be an extremely efficient way to truncate the computational domain in finite-difference time-domain (FDTD) simulation of scattering and radiation problems in open regions. In this work we extend the PML concept to spherical coordinates by using an analytic continuation of the Helmholtz equation to complex coordinates (complex coordinate stretching). A 3D PML-FDTD code is written on a spherical grid to validate the formulation against results from pseudo-analytical solutions in free-space.