An Efficient Method for Computing Highly Oscillatory Physical Optics Integral

Abstract

Abstract-In this work, we use the numerical steepest descent path (numerical SDP) method in complex analysis theory to calculate the highly oscillatory physical optics (PO) integral with quadratic phase and amplitude variations on the triangular patch. The Stokes' phenomenon will occur due to various asymptotic behaviors on different domains. The stationary phase point contributions are carefully studied by the numerical SDP method and complex analysis using contour deformation. Its result agrees very well with the leading terms of the traditional asymptotic expansion. Furthermore, the resonance points and vertex points contributions from the PO integral are also extracted. Compared with traditional approximate asymptotic expansion approach, our method has significantly improved the PO integral accuracy by one to two digits (10 −1 to 10 −2 ) for evaluating the PO integral. Moreover, the computation effort for the highly oscillatory integral is frequency independent. Numerical results for PO integral on the triangular patch are given to verify the proposed numerical SDP theory.

THE MODERN HIGH FREQUENCY METHODS FOR SOLVING ELECTROMAGNETIC SCATTERING PROBLEMS (Invited Paper)

“…To remedy the aforementioned limitation from the HFA method, Wu and Chew proposed the numerical steepest descent path (NSDP) method [47,49,50]. On invoking the NSDP method, the PO integrands are transformed to exponentially decay integrands on the complex NSDPs, which could be integrated with workload independent of frequency.…”

“…Compared to the work in [47][48][49][50], in this review paper, we introduced the NSDP solver to calculate the high frequency scattered fields. The NSDP method provides an efficient way to calculate the scattered field from both the PO and the ILDC techniques.…”

“…Based on the aforementioned physical insights, the GTD, PTD, UTD, UAT and ILDC methods were proposed with different asymptotic and mathematical techniques. Recently, there is a progress on the numerical steepest descent path (NSDP) method [44][45][46][47][48][49][50][51][52] to calculate the high frequency scattered fields from the PO and ILDC methods. On invoking the NSDP method, the highly oscillatory wave fields could be transformed to smooth kernels on the complex plane.…”

A Novel Simulation Approach of Aircraft Dynamic RCS

“…Physical Optics (PO) method [7][8][9] with Physical Theory of Diffraction (PTD) revision to edge diffraction is used to evaluate the monostatic RCS of the aircraft for V V polarization. PO is an efficient high frequency method to calculate the scattering of the electrically large target surface.…”

Fringe Waves in an Impedance Half-Plane

“…This concept is valid and accurate for metallic scatterer surfaces and gives exact geometric optics (GO) waves in the high frequencies. There are lots of studies in the literature about the application of the PO method [1][2][3]. The edge diffracted fields which are found from the contribution of the PO surface integral are not correct.…”