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.

翻译：本文以极地协调的瞬时法为两维 TM 电磁集成方程式提供了一个新的配方,并由此为两维 TM 电磁集成方程式提供了一个新的解决方案。 主要的想法是重新定义二维问题,在2D同质介质的绿色功能中出现汉克尔函数的附加理论。 在这方面,空间频域的循环公式是导出,散射场被改写成内向和外向组件,然后,主要二维问题可以使用稳定的双向梯度快速FFFFFFFFFF来解决。由于正在形成的方法在圆上获得 1D FFFFT,因此没有必要以零划线扩展一个对象区域,而常规 2D FFT 方法则需要这样做。因此,这种方法在常规2D FFFT 法方法中节省了大量的记忆和时间。 拟议方法的另一个有意思的方面是,使用分析公式来计算一个圆外圆的圆形区域。这在电磁反散射问题和微波成像中尤其具有吸引力。 2D 的数值分析方法的精确性和精确性。