Introducing a Method-of-Moments Solution for ۲-Dimensional TM Electromagnetic Problems

This paper introduces a new solution for ۲-dimensional (۲D) TM electromagnetic problems by the method of moments (MoM) in polar coordinates. The main idea is to reformulate a ۲D problem according to addition theorem for the zeroth-order Hankel function of the second kind. Recursive formulas in spatial frequency domain are derived and the scattering field is rewritten into inward and outward components. In this way, a ۲D TM problem can be solved using ۱D FFT in the stabilized biconjugate-gradient fast Fourier transform (BCGS-FFT) algorithm. Because the emerging method obtains ۱D FFT over a circle, there is no need to expand an object region by zero padding, whereas it is necessary for the conventional ۲D FFT in cartesian coordinates. Therefore, the polar coordinate approach concludes in less computational burden. Other interesting advantage 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 (MI). The numerical examples for ۲D TM problems demonstrate merits of the proposed technique in terms of the accuracy and computational efficiency.

کلیدواژه ها:

۲-dimensional TM problems ، method of moments (MoM) ، stabilized biconjugate-gradient fast Fourier transform ، Microwave imaging