A scattered field formulation of the time-domain Radial Point Interpolation Method using radial perfectly matched layers

Meshless methods are a new type of numerical schemes in computational electromagnetics, combining the advantages of conformal unstructured modeling with the flexibility of a node distribution without an explicit mesh topology. A scattered field formulation of the meshless Radial Point Interpolation Method (RPIM) is introduced for efficient simulation of metallic structures. Scattering problems generally result in spherically radiated wavefronts, hence truncating the computational domain with locally radial perfectly matched layers (PML) appears more effective than with classical uniaxial PML. Therefore, such problems can be modelled using less memory and shorter computation times with spherical or cylindrical PML. The scattered field RPIM formulation with radial PML is verified in a classical scattering problem from a perfectly conducting cylinder. A comparison with the analytical Mie solution shows fast convergence rates which are indicative of low reflections from the PML boundary. A convergence analysis and a study on the PML thickness demonstrates how to extend the limits of the PML formulation.