2-D Scattering Integral Field Equation Solution Through an IMLS Meshless-Based Approach

In this work, we apply a meshless-based method to a set of integral equations arising in electromagnetic wave propagation and scattering. The objective is not only to solve these equations through a meshless-based method, but also to find a way to build shape functions that could work for any cross-sectional geometry. We have found that the Moving Least Squares (MLS) approximation is not able to provide useful shape functions in every situation. This technique relies on matrix inversions and, according to the geometry, singular matrices can occur. In order to avoid this problem, we have taken the Improved Moving Least Squares (IMLS) approximation, that does not depend upon matrix inversions and then applied it to a number of cross-sectional geometries.