A Hybrid Approach for Fast Computation of Multiple Incident Angles Electromagnetic Scattering Problems with Compressive Sensing and Adaptive Cross Approximation

Yu-Fa Sun,Guo-Hua Wang

doi:10.1155/2016/1416094

Abstract

A hybrid compressive approach for fast computation of the electromagnetic scattering problems with multiple incident angles is proposed. The compressive sensing (CS) technique is firstly introduced to the method of moment (MoM) to reduce the number of the right-hand sides (RHS), but since the resulting excitation matrix contains linear dependency and has low-rank characteristics, the adaptive cross approximation (ACA) algorithm is used to recompress such excitation matrix, keeping only the necessary physical information. The hybrid compressive approach can reduce the number of the RHS to lower level. In fact, the ratio of the number of the RHS between the compressed excitation matrix and the original excitation matrix in the conventional MoM is close to one to fifteen. Numerical results are presented to validate the efficiency and accuracy of this method, which turns out to be highly efficient and accurate for the solution to multiple incident angles electromagnetic scattering problems.

Highlights

Accurate and efficient analysis of the electromagnetic scattering with multiple incident angles has attracted increasing attention from academia and industry
The method of moment (MoM) [1, 2] together with iterative methods is often used for the accurate analysis of electromagnetic scattering problems, and some fast algorithms like the multilevel fast multipole algorithm (MLFMA) [3], the adaptive integral method (AIM) [4], and the adaptive cross approximation (ACA) [5, 6] are generally applied to reduce both the computation time and the memory requirements for electrically large radiation and scattering problems
A new excitation matrix is firstly constructed with smaller right-hand side (RHS) number than traditional MoM, and the measurement values of the induced current coefficients can be calculated by direct method or iterative method

Summary

Introduction

Accurate and efficient analysis of the electromagnetic scattering with multiple incident angles has attracted increasing attention from academia and industry. A new excitation matrix is firstly constructed with smaller RHS number than traditional MoM, and the measurement values of the induced current coefficients can be calculated by direct method or iterative method. To reduce the number of measurements to a lower level than the CS technique, a hybrid compressive method named CS-ACA is advised. Such method utilizes the low-rank characteristics of the new excitation matrix generated by the CS. The CS technique is firstly used with a reduced number of RHS; the ACA algorithm is introduced into CS to recompress the new excitation matrix so as to reduce the number of RHS further, so as to realize the efficient calculation of the multiple excitation 3D electromagnetic problems

A Hybrid Compressive Technique of the Excitation Matrix

Numerical Results

Method