The Efficient Method for Calculating the Physical Optics Scattered Fields from the Concave Surfaces

Yu Mao Wu,Ya-Qiu Jin,Hanzhang Zhou,Haijing Zhou,Jun Hu,Weijie Wang

doi:10.1155/2020/5296754

Abstract

In this work, the numerical steepest descent path (NSDP) method is proposed to compute the highly oscillatory physical optics (PO) scattered fields from the concave surfaces, including both the monostatic and the bistatic cases. Quadratic variations are adopted to approximate the integrands of the PO type integral into the canonical form. Then, on involving the NSDP method, we deform the integration paths of the integrals into several NSDPs on the complex plain, through which the highly oscillatory integrands are converted to exponentially decay integrands. The RCS results of the PO scattered field are calculated and are compared with the high frequency asymptotic (HFA) method and the brute force (BF) method. The results demonstrate that the proposed NSDP method for calculating PO scattered fields from concave surfaces is frequency-independent and error-controllable. Numerical examples are provided to verify the efficiencies of the NSDP method.

Highlights

In electromagnetics (EM) community, as the product of the wavenumber k and the electrical size of the considered object d are large enough, the calculation of the scattered EM field belongs to high frequency scattering problems
The physical optics (PO) integral under the PO approximation is derived, and the considered concave surface is discretized into several triangular patches. e Lagrange interpolation polynomial approximation and the affine transformation are used to approximate the amplitude function and phase function of the PO type integral
Method introduced above. e computational results and the corresponding consumed CPU time with increasing wavenumber k are calculated by the high frequency asymptotic (HFA) method and the brute force (BF)

Summary

Introduction

In electromagnetics (EM) community, as the product of the wavenumber k and the electrical size of the considered object d are large enough, the calculation of the scattered EM field belongs to high frequency scattering problems. The exponential of the phase function term is highly oscillatory as the frequency k increases In this sense, the computational effort of a direct numerical method [2, 11] for calculating the PO type integral is extremely high. Erefore, the traditional high frequency asymptotic (HFA) method [6, 18,19,20,21] was proposed, approximating the phase terms of the integral into quadratic forms. E contributions of this work are that, first, physical optics scattered fields from concave surfaces are considered. In this case, the phase function term of the PO integrand takes the quadratic concave behavior, which differs from works in [26, 27]. Numerical examples of calculating PO scattered fields from concave surfaces are provided, and comparisons with the brute force method and HFA method are given

PO Surface Integral

Calculating the PO Scattered Fields With the Concave Phase Function Term

An Example of Calculating PO Surface Integral by Adopting the NSDP Method

Numerical Results

Conclusion