MLPG-MOM HYBRID MESHLESS METHOD APPLIED TO 2D UNBOUNDED SCATTERING PROBLEMS USING RPIM SHAPE FUNCTIONS

Resumo

Meshless methods have increasingly gained attention in recent years. Nonetheless, similar
to the Finite Element Method (FEM), they cannot properly handle unbounded domains. For scattering

problems, however, the Method of Moments (MoM) is fairly well consolidated, efficient, and easily ap-
plied to unbounded homogeneous mediums. This work couples the MoM used to model the unbounded

free space, with the traditional Meshless Local Petrov-Galerkin modeling of a dielectric bounded object.
In the inner region, the meshless method uses shape functions generated by radial point interpolation
with polynomial reproduction, whereas in the outer region, the MoM uses triangular shape functions to
describe the surface currents. As both shape functions possess the delta Kronecker property, the coupling

is straightforwardly imposed by forcing the continuity of the tangential components of the electromag-
netic field. In order to evaluate the convergence of the method, the TEz and TMz plane wave scattering

from a homogeneous dielectric circular cylinder was analyzed since it has a modal analytical solution,

providing means to study the precision of the numerical results. Nevertheless, the formulation is appli-
cable to any arbitrary cylindrical contour shape. Also knowing that meshless methods are quite flexible

to handle material inhomogeneity, a 2-dimensional Luneburg lens, which has a continuous permittivity ̈

profile, was analyzed, and its results were compared to FEM solutions. For both TMz and TEz polar-
izations, it was observed that the convergence rate remains nearly the same for the electromagnetic field

and equivalent current densities. This technique also provided a good agreement for the near and far
electromagnetic field calculation.