Algorithms for Electromagnetic Scattering Analysis of Electrically Large Structures

Accurate analysis of electrically large antennas is often done using either Physical Optics (PO) or Method of Moments (MoM), where the former typically requires fewer computational resources but has a limited application regime. This study has focused on fast variants of these two methods, with the goal of reducing the computational complexity while maintaining accuracy.

Regarding MoM, the complexity is reduced by applying the Multi-Level Fast Multipole Method (MLFMM) in combination with an iterative solver. Using MLFMM with a MoM implementation based on Higher-Order (HO) basis functions has, by several authors, been dismissed as being too memory intensive. In the present work, we demonstrate for the first time that by including a range of both novel and previously presented modifications to the standard MLFMM implementation, HO MLFMM can achieve both memory reduction and significant speed increase compared to Lower-Order (e.g., RWG) based MLFMM. Further, issues surrounding an iterative solution, such as the iterative solver and preconditioning, are discussed. Numerical results demonstrate the performance and stability of the algorithm for very large problems, including full satellites at Ku band.

Accelerating PO is an entirely different matter. A few authors have discussed applying the Fast-PO technique to far fields, achieving relative errors of 0.1%−1% for moderately sized scatterers. For near-fields, the state-of-the-art implementation of Fast-PO has several difficulties, in particular low accuracy and limited application regime. For the problems considered in this thesis, the error limit for PO is ≈ 0.01%, and the application limitations of the published Fast-PO are too prohibitive for our use. Therefore, results based on an improved Fast-PO implementation for far-fields, as well as a novel algorithm for near-fields, are presented. These results demonstrate that it is possible to achieve very accurate results, with relative errors around 10⁻⁵, at a much reduced time consumption. The method behind this part of the code is deemed confidential by TICRA.