Numerical solution of EFIE using MLPG methods

Meshless local Petrov-Galerkin (MLPG) methods are applied to the electric-field integral equation (EFIE), including seven previously reported schemes and two new suggested. The required dyadic weightings are provided. Especially, the dyadic Green's function for the differential part of the equation is derived for the first time. Guidelines are suggested for both meshless discretization and efficient implementation. It is shown that by proper selection of the MLPG scheme and its parameters, the stiffness matrix corresponding to the problem can be computed using closed-form expressions, without the need to perform numerical integration. It is shown that using weightings other than the Dirac delta can significantly improve the convergence trend of the meshless solution and increase the accuracy up to two orders of magnitude. It is, also, demonstrated that a meshfree IE solver can more accurately track singularities of the surface current density at conductive edges compared to the method of moments (MoM). In addition, it is shown that such solvers can potentially supersede high-order (HO) MoM as their mesh-based counterpart.