Modeling of dielectric material interfaces for the Radial Point Interpolation Time-Domain method

The Radial Point Interpolation Time-Domain (RPITD) method is a flavor of meshless domain discretization methods applicable to computational electromagnetics. Meshless methods do not require an explicit mesh topology, but rather rely on a representation of a physical model as a node distribution. This is firstly advantageous for modeling of conformal boundaries and multi-scale geometries. But as the most attractive feature, the node arrangements can be adapted on-the-fly. The RPITD method is based on interpolation of the field distribution using radial and monomial basis functions. This paper introduces a technique to model arbitrarily shaped dielectric interfaces in the framework of meshless methods. Using the proposed technique, errors associated to the interpolation of non-smooth fields at material interfaces are reduced, as demonstrated for 2D-TE modes. This allows for accurate modeling of interfaces with dielectric contrast. Unlike previous publications which modify the basis functions at interfaces, a physically motivated correction term is introduced here. Errors in the vicinity of material interfaces decrease significantly and simulation accuracy is generally improved.