Grid-robust higher-order vector basis functions for solving integral equations

This paper proposes a set of novel, grid-robust, higher-order vector basis functions for the MoM solution of integral equations for three-dimensional (3D) electromagnetic problems. These basis functions are defined over curvilinear triangular patches and represent the unknown electric current density within each patch using the Lagrange interpolation polynomials. The interpolation points are chosen to be the same as the nodes of the well developed Gaussian quadratures. As a result, the evaluation of the integrals in the MoM is greatly simplified. Additionally, the surface of an object to be analyzed can be easily meshed because the new basis functions do not require the side of a triangular patch to be entirely shared by another triangular patch.