Localized Iterative Generalized Multipole Technique for Large Two-Dimensional Scattering Problems

In this work, we propose a novel and efficient solution for the generalized multipole technique (GMT): the localized iterative generalized multipole technique (LIGMT). In LIGMT, an analytic constraint is imposed on the power radiated by the set of multipole sources sharing the same origin, rendering it minimum over a given angular sector. In this way, the power radiated by each set of multipoles is confined to a different section of the scatterer surface. It follows that each set of multipole coefficients can be solved step by step via an iterative process, which circumvents the need to solve the large and full matrix equation. This implies a significant reduction of the computational and storage cost, enhancing the scope of application of the GMT method to larger problems.