Meshless evaluation of domain integrals for solving electromagnetic integral equations

Abstract

Solving electromagnetic (EM) integral equations by numerical methods strongly relies on the domain discretization or the use of meshes. Mesh generation is a tedious task, especially for complex structures with many details, and remeshing could be encountered in many situations. Meshless schemes are very desirable to lower the meshing or remeshing costs and they have been widely studied in mechanical engineering. However, these methods have not received attention in EM community and only very limited publications can be found. In this work, we first apply the traditional meshless methods in mechanical engineering to solve EM surface integral equations (SIEs) based on the moving least square (MLS) approximation for unknown functions and the use of background meshes in domain integrals. Then we develop a novel meshless scheme for evaluating domain integrals, yielding a truly meshless method. The scheme transforms a surface domain integral into a line integral along its boundary by applying the Green's lemma, so one only needs to discretize the boundary with much ease. Numerical examples for EM scattering by flat-surface objects are presented to illustrate the effectiveness of the scheme.