Introduction of a Novel MoM Solution for 2-D Source-type EFIE in MI Problems

TL;DR

This paper introduces a new method for solving 2-D TM electromagnetic integral equations using a novel MoM formulation with FFT, reducing memory and computation time while maintaining accuracy, especially useful in inverse scattering and imaging.

Contribution

The paper proposes a novel MoM solution for 2-D TM EFIE using Hankel function addition theorem and 1D FFT, eliminating zero padding and improving efficiency.

Findings

Method reduces memory usage and computation time.

Achieves high accuracy in numerical examples.

Efficient calculation of fields outside scattering objects.

Abstract

This paper presents a novel formulation and consequently a new solution for two dimensional TM electromagnetic integral equations by the method of moments in polar coordination. The main idea is the reformulation of the 2-D problem according to addition theorem for Hankel functions that appear in Green function of 2-D homogeneous media. In this regard, recursive formulas in spatial frequency domain are derived and the scattering field is rewritten into inward and outward components and, then, the primary 2-D problem can be solved using 1D FFT in the stabilized biconjugate-gradient fast Fourier transform BCGS-FFT algorithm. Because the emerging method obtains 1D FFT over a circle, there is no need to expand an object region by zero padding, whereas it is necessary for conventional 2D FFT approach. Therefore, the method saves lots of memory and time over the conventional approach. other interesting aspect of the proposed method is that the field on a circle outside a scattering object, can be calculated efficiently using an analytical formula. This is, particularly, attractive in electromagnetic inverse scattering problems and microwave imaging. The numerical examples for 2-D TM problems demonstrate merits of proposed technique in terms of the accuracy and computational efficiency.