Well Conditioned Formulations for Open Surface Scattering
Well Conditioned Formulations for Open Surface Scattering

Author:

Publisher:

Published: 2008

Total Pages: 59

ISBN-13:

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The electric field integral equation (EFIE) is a first-kind integral equation formulation that is used to solve a wide variety of electromagnetic scattering problems in the frequency domain. It is the only integral equation that can be applied to both open and closed targets. It is also a poorly conditioned integral equation, which means that solving it using iterative solution methods is generally impractical because the iteration count is uncontrollable and can be very large. This reduces the effectiveness of fast iterative solver methods for solving open surface problems. This report describes an analytical preconditioner method for the EFIE on open surface PEC targets that converts the EFIE to a well conditioned, second-kind integral equation. We present theory and the results from a numerical implementation. We also discuss a 2d extension of the Poincare-Bertrand identity could be used to develop an explicitly second-kind integral equation for open surface scattering problems.

The Nystrom Method in Electromagnetics
The Nystrom Method in Electromagnetics

Author: Mei Song Tong

Publisher: John Wiley & Sons

Published: 2020-06-29

Total Pages: 528

ISBN-13: 1119284880

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A comprehensive, step-by-step reference to the Nyström Method for solving Electromagnetic problems using integral equations Computational electromagnetics studies the numerical methods or techniques that solve electromagnetic problems by computer programming. Currently, there are mainly three numerical methods for electromagnetic problems: the finite-difference time-domain (FDTD), finite element method (FEM), and integral equation methods (IEMs). In the IEMs, the method of moments (MoM) is the most widely used method, but much attention is being paid to the Nyström method as another IEM, because it possesses some unique merits which the MoM lacks. This book focuses on that method—providing information on everything that students and professionals working in the field need to know. Written by the top researchers in electromagnetics, this complete reference book is a consolidation of advances made in the use of the Nyström method for solving electromagnetic integral equations. It begins by introducing the fundamentals of the electromagnetic theory and computational electromagnetics, before proceeding to illustrate the advantages unique to the Nyström method through rigorous worked out examples and equations. Key topics include quadrature rules, singularity treatment techniques, applications to conducting and penetrable media, multiphysics electromagnetic problems, time-domain integral equations, inverse scattering problems and incorporation with multilevel fast multiple algorithm. Systematically introduces the fundamental principles, equations, and advantages of the Nyström method for solving electromagnetic problems Features the unique benefits of using the Nyström method through numerical comparisons with other numerical and analytical methods Covers a broad range of application examples that will point the way for future research The Nystrom Method in Electromagnetics is ideal for graduate students, senior undergraduates, and researchers studying engineering electromagnetics, computational methods, and applied mathematics. Practicing engineers and other industry professionals working in engineering electromagnetics and engineering mathematics will also find it to be incredibly helpful.

Integral Equation Methods for Electromagnetic and Elastic Waves
Integral Equation Methods for Electromagnetic and Elastic Waves

Author: Weng Cho Chew

Publisher: Morgan & Claypool Publishers

Published: 2009

Total Pages: 259

ISBN-13: 1598291483

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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:

Published: 2017

Total Pages: 0

ISBN-13:

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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).

K-Space Formulation of the Electromagnetic Scattering Problem
K-Space Formulation of the Electromagnetic Scattering Problem

Author: Norbert N. Bojarski

Publisher:

Published: 1971

Total Pages: 216

ISBN-13:

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The Electromagnetic Scattering problem is solved by means of a k-space formulation of the Electromagnetic Field equations, thereby replacing the conventional integral equation formulation of the scattering problem by a set of two algebraic equations in two unknowns in two spaces (the constitutive equation being an algebraic equation in x-space). These equations are solved by an iterative method executed with the aid of Fast Fourier Transform (FFT) algorithm connecting the two spaces, requiring very simple zero order initial approximations. Since algebraic and FFT equations are used, the number of arithmetic multiply-add operations and storage allocations required for a numerical solution is reduced from the order of N squared (for solving the matrix equations resulting from the conventional integral equations) to the order of N log(sub 2)N (where N is the number of data points required for the specification of the scatterer). The advantage gained in speed and storage is thus of the order of N/log(sub 2)N and N respectively. This method is thus considerably more efficient, and permits exact numerical solutions for much larger scatterers, than possible with the conventional matrix method. (Author).

Electromagnetic Scattering using the Iterative Multi-Region Technique
Electromagnetic Scattering using the Iterative Multi-Region Technique

Author: Mohamed H. Al Sharkawy

Publisher: Springer Nature

Published: 2022-06-01

Total Pages: 99

ISBN-13: 3031017021

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In this work, an iterative approach using the finite difference frequency domain method is presented to solve the problem of scattering from large-scale electromagnetic structures. The idea of the proposed iterative approach is to divide one computational domain into smaller subregions and solve each subregion separately. Then the subregion solutions are combined iteratively to obtain a solution for the complete domain. As a result, a considerable reduction in the computation time and memory is achieved. This procedure is referred to as the iterative multiregion (IMR) technique. Different enhancement procedures are investigated and introduced toward the construction of this technique. These procedures are the following: 1) a hybrid technique combining the IMR technique and a method of moment technique is found to be efficient in producing accurate results with a remarkable computer memory saving; 2) the IMR technique is implemented on a parallel platform that led to a tremendous computational time saving; 3) together, the multigrid technique and the incomplete lower and upper preconditioner are used with the IMR technique to speed up the convergence rate of the final solution, which reduces the total computational time. Thus, the proposed iterative technique, in conjunction with the enhancement procedures, introduces a novel approach to solving large open-boundary electromagnetic problems including unconnected objects in an efficient and robust way. Contents: Basics of the FDFD Method / IMR Technique for Large-Scale Electromagnetic Scattering Problems: 3D Case / IMR Technique for Large-Scale Electromagnetic Scattering Problems: 2D Case / The IMR Algorithm Using a Hybrid FDFD and Method of Moments Technique / Parallelization of the Iterative Multiregion Technique / Combined Multigrid Technique and IMR Algorithm / Concluding Remarks / Appendices

Low Frequency Iterative Solution of Integral Equations in Electromagnetic Scattering Theory
Low Frequency Iterative Solution of Integral Equations in Electromagnetic Scattering Theory

Author: George A. Gray

Publisher:

Published: 1978

Total Pages: 197

ISBN-13:

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This report investigates the scattering of electromagnetic waves by a perfectly conducting object. The incident field is assumed to be time harmonic and the scatterer a closed bounded Lyapunov surface with no holes. A boundary integral equation for the total field (incident plus scattered) is derived using an integral representation of the total field analogous to Green's formula. The proof that this boundary integral equation can be solved by iteration rests on showing that the spectral radius of the resulting integral operator is less than one for small perturbations of the corresponding potential operator. (Author).