A surface dipole-based framework for fast and efficient solution of electromagnetic scattering problems

Abstract

This thesis introduces a surface-based fast method for solving large-scale electromagnetic scattering problems within the Method of Moments (MoM) framework. Addressing the parallelization and low-frequency challenges of the Multilevel Fast Multipole Algorithm, the proposed approach represents conventional Rao-Wilton-Glisson (RWG) basis functions with uniformly distributed Hertzian dipoles placed on subdomain surfaces. This structural simplification facilitates translation operations, improves implementation efficiency, and supports parallel computing. The method comprises three stages: mapping the original current that is modeled with RWG basis functions to dipoles, translating fields via Green's function, and reconstructing local fields through inverse mapping. Numerical results are provided at both subdomain and full problem levels. Accuracy is first tested on isolated box interactions and then validated in a complete scattering problem involving a perfectly conducting sphere across different frequencies. The proposed method is benchmarked against MoM, a volumetric dipole-based approach, and the analytical Mie series solution, showing excellent agreement in all cases. Aimed to implement the method in Python with just-in-time (JIT) parallelization via Numba, the method is expected to demonstrate practical efficiency. Future work may explore symmetry-based translation reuse, machine learning for operator modeling, and GPU acceleration, making the method a promising candidate for hardware-friendly electromagnetic simulations that is strongly scalable for parallelization.