Multi-resolution approach to three-dimensional method-of-moments problems

Abstract

Objectives, expectations and difficulties associated to the use of multi-resolution (MR) constructs in integral equation, method of moments (MoM) are reviewed and put in a contemporary perspective. A MR approach is presented that can be applied to any mesh without any constrain on the structure topology. The so-obtained MR basis positively affects the spectrum of the MoM matrix, affording an efficient (multiplicative) preconditioner. The reasons of this are explained in terms of the dual spatial-spectral resolution of the MR basis.

A review on the design and optimization of antennas using machine learning algorithms and techniques

“…In addition, MoM is not efficient to inhomogeneous and composite structures 47 . Although some solutions are found for several drawbacks of MoM, such as the use of pre‐conditioners to solve the low‐frequency breakdown, 47 recovery to solve the charge cancelation problem, 48 and the multi‐resolution approach to improve the spectrum of MoM, 49 the computational cost, CPU memory and timing required can be further enhanced. MoM is also considered as computationally expensive since it requires dense systems of equations to solve the integral equations.…”

Review on Computational Electromagnetics

“…Th is enhancement is achieved by using regularizing diagonal basis functions obtained by using near field part of MOM in standard basis functions that has low computational cost and memory occupation [37]. Electrically large structures like Vivaldi array [4, 8 element array] are analy zed and numerical results shows that MLFMA, accelerat ion of MOM is better than other methods (FDTD, FEM, conventional MOM) when electrical size of structure increases [38].…”