Explicit time-stepping scheme for radial perfectly matched layers in staggered meshless methods

Meshless methods have attracted attention recently as versatile algorithms in computational electromagnetics. The Radial Point Interpolation Method (RPIM) is one particular type of meshless method based on radial basis functions implemented in a collocation time-domain framework. The possibility of free node placement allows conformal modeling of complex geometries with potentially significantly lower memory consumption and higher accuracy than the finite-difference time-domain (FDTD) method. Open boundaries have been implemented in the form of uniaxial perfectly matched layers (PMLs). A natural next step for this method is the implementation of locally conformal PMLs. A special case of conformal PMLs are the radial PMLs, which are characterized by an anisotropy in radial direction. In this paper, a methodology to obtain explicit update equations for the electric and magnetic field components from an originally implicit dependence of the magnetic field is presented.