Surface Integral Equation Method for Analyzing Electromagnetic Scattering in Layered Medium

Surface Integral Equation Method for Analyzing Electromagnetic Scattering in Layered Medium
Author: Yongpin Chen
Publisher: Open Dissertation Press
Total Pages:
Release: 2017-01-26
Genre:
ISBN: 9781361289990
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This dissertation, "Surface Integral Equation Method for Analyzing Electromagnetic Scattering in Layered Medium" by Yongpin, Chen, 陈涌频, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Surface integral equation (SIE) method with the kernel of layered medium Green's function (LMGF) is investigated in details from several fundamental aspects. A novel implementation of discrete complex image method (DCIM) is developed to accelerate the evaluation of Sommerfeld integrals and especially improve the far field accuracy of the conventional one. To achieve a broadband simulation of thin layered structure such as microstrip antennas, the mixed-form thin-stratified medium fast-multipole algorithm (MF-TSM-FMA) is developed by applying contour deformation and combining the multipole expansion and plane wave expansion into a single multilevel tree. The low frequency breakdown of the integral operator is further studied and remedied by using the loop-tree decomposition and the augmented electric field integral equation (A-EFIE), both in the context of layered medium integration kernel. All these methods are based on the EFIE for the perfect electric conductor (PEC) and hence can be applied in antenna and circuit applications. To model general dielectric or magnetic objects, the layered medium Green's function based on pilot vector potential approach is generalized for both electric and magnetic current sources. The matrix representation is further derived and the corresponding general SIE is setup. Finally, this SIE is accelerated with the DCIM and applied in quantum optics, such as the calculation of spontaneous emission enhancement of a quantum emitter embedded in a layered structure and in the presence of nano scatterers. DOI: 10.5353/th_b4775283 Subjects: Electromagnetic waves - Scattering - Mathematical models

Analysis and Numerical Solution of an Integral Equation Method for Electromagnetic Scattering from a Cavity in a Ground Plane

Analysis and Numerical Solution of an Integral Equation Method for Electromagnetic Scattering from a Cavity in a Ground Plane
Author: Eric T. Howe
Publisher:
Total Pages: 80
Release: 2001-09-01
Genre: Electromagnetic waves
ISBN: 9781423525530
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In this research the electromagnetic scattering of a plane wave from a two-dimensional cavity embedded in an infinite, perfectly conducting ground plane is investigated. The plane wave is assumed to be under transverse electric (TE) polarization with respect to the x-axis. The cavity may be empty or filled with an arbitrary homogeneous, lossy material. A coupled set of scalar integral equations that govern the electromagnetic scattering is implemented. An approximate solution to the scalar integral equations is found via a Method of Moments (MoM) algorithm. The algorithm is implemented in a computer code, and approximations to the total magnetic field on the cavity surface and aperture as well as the normal derivative of the total magnetic field on the cavity aperture are obtained. These fields are then used to calculate the two-dimensional monostatic RCS signatures of various test cavities. The numerical results from the algorithm are shown to agree well with the RCS signatures calculated by other well-known methods and published results. In addition to being accurate, the algorithm is very computationally efficient. The process results in simply solving a relatively small, well-conditioned matrix system for each incident angle to produce the unknown fields.

Integral Equation Methods for Electromagnetic and Elastic Waves

Integral Equation Methods for Electromagnetic and Elastic Waves
Author: Weng Chew
Publisher: Springer Nature
Total Pages: 241
Release: 2022-05-31
Genre: Technology & Engineering
ISBN: 3031017072
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Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods. Table of Contents: Introduction to Computational Electromagnetics / Linear Vector Space, Reciprocity, and Energy Conservation / Introduction to Integral Equations / Integral Equations for Penetrable Objects / Low-Frequency Problems in Integral Equations / Dyadic Green's Function for Layered Media and Integral Equations / Fast Inhomogeneous Plane Wave Algorithm for Layered Media / Electromagnetic Wave versus Elastic Wave / Glossary of Acronyms

Novel Single Source Integral Equation for Analysis of Electromagnetic Scattering by Penetrable Objects

Novel Single Source Integral Equation for Analysis of Electromagnetic Scattering by Penetrable Objects
Author: Farhad Sheikh Hosseini Lori
Publisher:
Total Pages: 0
Release: 2017
Genre:
ISBN:
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This thesis presents a novel single source surface electric field integral equation (EFIE) for the full-wave scattering problems by homogeneous dielectric objects and magneto-quasi-static characterization of the multiconductor transmission lines (MTLs) to determine inductance and resistance. Both the low and higher order method of moments (MoM) schemes are developed for numerical solution of this novel equation. The required theorems and derivations are given in detail. Numerical validations of this equation are conducted for various formulations such as scalar and vector 2D scattering problems, full-wave 3D scattering problems, and the problems of current flow in the 2D conductors of complex cross-sections. Error controllability of the numerically computed fields confirms that the proposed equation is rigorous in nature and may be an advantageous alternative to the other known single and double source surface integral equations (SIEs). The proposed single source integral equation (SSIE) features only electric type Green's functions, which distinguishes it from the previously know SSIE formulations. As such the new equation can be formulated in the form free of derivatives acting on the kernels. The new SSIE also features only one unknown surface function instead of two unknown functions as featured in the traditional SIEs. Unlike previously known single source surface integral equations derived through restricting of the single source field representation with surface equivalence principle, the new equation is obtained by constraining of the such representation with the volume equivalence principle. As a result, the new equation features integral operators that translate the fields from the surface of the scatterer to its volume and then back to its surface, lending it the name of Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE).

Augmented Surface Integral Equation Method for Low-frequency Electromagnetic Analysis

Augmented Surface Integral Equation Method for Low-frequency Electromagnetic Analysis
Author: Zhiguo Qian
Publisher:
Total Pages: 222
Release: 2009
Genre:
ISBN: 9781109219807
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Several fundamental aspects of the surface integral equation (SIE) method including the low-frequency breakdown, the skin effect, and the substrate effect, have been addressed for full-wave electromagnetic analysis in the low-frequency regime, especially the modeling of electrical interconnects on chip and package levels. The augmentation technique is a simple and efficient remedy for the low-frequency breakdown, which is the bottleneck of the broadband simulation. Based on the augmented formulations, very complicated problems in the real world can be efficiently solved with appropriate preconditioning and fast algorithm acceleration. As required in many applications, a generalized impedance boundary condition (GIBC) formulation is developed to handle the skin effect rigorously and efficiently. It degenerates into traditional methods with two steps of approximations. These new techniques are also combined together into a comprehensive formulation to cover both the skin effect and the substrate effect without any low-frequency instability.

Time Domain Integral Equation-based Methods for Analyzing Electromagnetic Scattering from Objects Residing in Lossy Media

Time Domain Integral Equation-based Methods for Analyzing Electromagnetic Scattering from Objects Residing in Lossy Media
Author: Peilin Jiang
Publisher: ProQuest
Total Pages: 167
Release: 2007
Genre:
ISBN: 9780549365563
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This dissertation is concerned with the development of efficient time domain integral equation (TDIE)-based marching-on-in-time (MOT) schemes pertinent to transient analysis of electromagnetic scattering from objects residing in lossy media. Classical MOT schemes have a computational complexity scaling as O( N2sN2t ) and a memory requirement as O( N2sNt ), respectively. To alleviate the demands of computational resources, two techniques are proposed in this dissertation, viz., the Prony series-based recursive convolution scheme and the multilevel plane wave time domain (PWTD) algorithm. The former reduces the computational cost to O( N2sNt log Nt). The latter is the extension of the PWTD scheme for free space and is able to speed up the evaluation of fields radiated by band-limited and time-limited sources far enough away. When these two techniques are hybridized in the MOT scheme, i.e., the recursive convolution scheme evaluates the near-field interaction, and the multilevel PWTD algorithm evaluates the far-field interactions, the enhanced scheme has a computational complexity of O(NsNt log Ns(log Ns + log 2 Nt)) and a memory requirement of O(NsNt). As applications of the developed solver, the electromagnetic scattering from perfect electric conductors residing in lossy media and the light scattering from homogeneous and inhomogeneous biological cells are analyzed. The corresponding TDIEs are also formulated considering the particularities of application scenarios. Numerous numerical examples are presented to demonstrate the fast solver's efficacy and ability to solve realistic problems.