An Efficient Method for Computing Highly Oscillatory Physical Optics Integral
TL;DR: In this article, the authors used the numerical steepest descent path (numerical SDP) method in complex analysis theory to calculate the highly oscillatory physical optics integral with quadratic phase and amplitude variations on the triangular patch.
read more
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 difierent 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 signiflcantly improved the PO integral accuracy by one to two digits (10 i1 to 10 i2 ) for evaluating the PO integral. Moreover, the computation efiort 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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
The Numerical Steepest Descent Path Method for Calculating Physical Optics Integrals on Smooth Conducting Quadratic Surfaces
TL;DR: In this paper, the numerical steepest descent path (NSDP) method was used to analyze the highly oscillatory physical optics (PO) integral on smooth conducting parabolic surfaces, including both monostatic and bistatic cases.
69
Efficient Algorithm for the Evaluation of the Physical Optics Scattering by NURBS Surfaces With Relatively General Boundary Condition
Cristian Della Giovampaola,Giorgio Carluccio,Federico Puggelli,Alberto Toccafondi,Matteo Albani +4 more
TL;DR: An adaptive integration algorithm is presented for the computation of the Physical Optics (PO) electric and magnetic field scattered by electrically large objects modeled by Non-Uniform Rational B-Splines (NURBS).
35
Computing highly oscillatory physical optics integral on the polygonal domain by an efficient numerical steepest descent path method
TL;DR: Compared to the traditional high frequency asymptotic (HFA) method, when the wave frequency is not very high but in the high frequency regime, the NSDP method has improved the PO integral accuracy by one to two digits.
28
References
•Book
Field computation by moment methods
Roger F. Harrington
- 01 Jan 1968
TL;DR: This first book to explore the computation of electromagnetic fields by the most popular method for the numerical solution to electromagnetic field problems presents a unified approach to moment methods by employing the concepts of linear spaces and functional analysis.
7.6K
•Book
Introduction to Numerical Analysis
Josef Stoer,Roland Bulirsch +1 more
- 16 Feb 2013
TL;DR: This well written book is enlarged by the following topics: B-splines and their computation, elimination methods for large sparse systems of linear equations, Lanczos algorithm for eigenvalue problems, implicit shift techniques for theLR and QR algorithm, implicit differential equations, differential algebraic systems, new methods for stiff differential equations and preconditioning techniques.
6.4K
Introduction to Numerical Analysis
Arnold Neumaier
- 26 Sep 2001
TL;DR: 1. The numerical evaluation of expressions 2. Linear systems of equations 3. Interpolation and numerical differentiation 4. Numerical integration 5. Univariate non linear equations 6. Systems of nonlinear equations.
4.8K
•Book
Waves and Fields in Inhomogeneous Media
Weng Cho Chew
- 28 Jun 1990
TL;DR: Inverse scattering problems in planar and spherically layered media have been studied in this article, where Dyadic Green's functions have been applied to the mode matching method to solve the problem.
4.8K