Application of Two-Dimensional Compressive Sensing to Wavelet Method of Moments for Fast Analysis of Wide-Angle Electromagnetic Scattering Problems

Qi Qi,Zhixiang Huang,Mingsheng Chen,Yi Liu,Xianliang Wu,Guoqing Deng,Paolo Baccarelli,Xinyuan Cao

doi:10.1155/2021/9912502

Abstract

To efficiently solve the electromagnetic scattering problems over a wide incident angle, a novel scheme by introducing the two-dimensional compressive sensing theory into the wavelet method of moments is proposed. In this scheme, a linear system of equations with multiple right-hand sides in wavelet domain is formed firstly, and one side of the bilateral sparse transform to the induced current matrix is simultaneously accomplished and then the bilateral measurement of the induced current matrix is operated by the linear superposition of the right-hand side vectors a few times and the extraction of rows from the impedance matrix. Finally, after completing the other side of the bilateral sparse transform, the wide-angle problems can be solved rapidly by two times of recovery algorithm with prior knowledge. The basic principle is elaborated in detail, and the effectiveness is demonstrated by numerical experiments.

Highlights

Method of moments (MoM) [1] is an accurate and efficient method for solving electromagnetic scattering problems
A new source including much information from different incident angles is constructed, and the measurement of induced currents is obtained by multiple calculations of the traditional MoM under the new source, and the original induced currents over the wide angle can be approximated by means of the sparse transform and recovery algorithm
The two-dimensional (2-D) compressive sensing (CS) theory [13] is employed in the wavelet MoM to build a more efficient scheme for wide-angle problems, in which the bilateral measurement and the bilateral sparse transform are used to the induced currents and the reconstruction of induced currents is operated by the twice recovery algorithm. e specific formulas are deduced in detail, and numerical examples of differently shaped objects are presented

Summary

Introduction

Method of moments (MoM) [1] is an accurate and efficient method for solving electromagnetic scattering problems. Unless the approximated technique (e.g., asymptotic waveform evaluation [6]) is applied, the traditional MoM needs to be implemented repeatedly at every incident angle increment for solving the wide-angle electromagnetic scattering problems, which leads to a huge computing amount. By combining the CS theory and the traditional MoM, a scheme for the rapid analysis of wideangle problems has been formed [12] In this scheme, a new source including much information from different incident angles is constructed, and the measurement of induced currents is obtained by multiple calculations of the traditional MoM under the new source, and the original induced currents over the wide angle can be approximated by means of the sparse transform and recovery algorithm. The two-dimensional (2-D) CS theory [13] is employed in the wavelet MoM to build a more efficient scheme for wide-angle problems, in which the bilateral measurement and the bilateral sparse transform are used to the induced currents and the reconstruction of induced currents is operated by the twice recovery algorithm. e specific formulas are deduced in detail, and numerical examples of differently shaped objects are presented

Formulations

Numerical Results

Conclusions