A high-order regularized hybrid BEM–meshless method for electromagnetic scattering: Algorithm, stability analysis, and convergence proofs

This article presents a high-order regularized hybrid boundary element–meshless method for time-harmonic electromagnetic scattering from perfectly conducting obstacles, with particular emphasis on non-smooth geometries where classical high-order BEM may suffer from corner- and edge-induced instabilities. The proposed approach augments a standard single-layer (or CFIE-type) BEM discretization with a localized radial basis function (RBF) smoothing operator acting on the surface current density. This operator serves as an explicit regularization mechanism that suppresses oscillations near geometric singularities and reduces noise amplification in the boundary data. We establish stability and convergence results for the regularized hybrid formulation and show that the resulting operator exhibits favorable spectral properties under suitable parameter scaling. Numerical experiments on five benchmark configurations — including smooth, non-smooth, and multi-body scattering geometries — demonstrate that the proposed method preserves the accuracy of high-order BEM while significantly reducing density roughness and noise amplification. These results confirm the stability and practical effectiveness of the hybrid BEM–meshless regularization framework for challenging electromagnetic scattering problems.