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).

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

An Integral Equation Method for Electromagnetic Scattering Problems
An Integral Equation Method for Electromagnetic Scattering Problems

Author: Arthur K. Jordan

Publisher:

Published: 1975

Total Pages: 55

ISBN-13:

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The purpose of this memorandum report is to document the analysis which was performed to obtain the matrix equation which represents the electromagnetic fields scattered from axially symmetric targets. Although these results are not new, the analysis is presented in a concise, logical manner which is suitable for computer programming and which provides the foundation for the solution of diverse transient electromagnetic scattering problems by the newer methods of natural mode representations and singularity expansion techniques. The motivation for this study was to formulate in an understandable manner the necessarily complicated and tedious electromagnetic scattering calculations. Even relatively simple targets, e.g., missiles and torpedoes, require lengthy calculations. The integral equation for electromagnetic scattering from axially symmetric targets is derived. The boundary conditions for the case of metallic (perfectly conducting) and for the case of lossy dielectric targets are applied. The integral equation is reduced to matrix form by application of the method of moments. The scattering cross section is derived. A typical target geometry (sphere-cone-sphere) is used as an example. The detailed calculations are documented for reference with future computer calculations.

Iterative Methods for Calculating Static Fields and Wave Scattering by Small Bodies
Iterative Methods for Calculating Static Fields and Wave Scattering by Small Bodies

Author: Alexander G. Ramm

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 131

ISBN-13: 1461257158

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Iterative methods for calculating static fields are presented in this book. Static field boundary value problems are reduced to the boundary integral equations and these equations are solved by means of iterative processes. This is done for interior and exterior problems and for var ious boundary conditions. Most problems treated are three-dimensional, because for two-dimensional problems the specific and often powerful tool of conformal mapping is available. The iterative methods have some ad vantages over grid methods and, to a certain extent, variational methods: (1) they give analytic approximate formulas for the field and for some functionals of the field of practical importance (such as capacitance and polarizability tensor), (2) the formulas for the functionals can be used in a computer program for calculating these functionals for bodies of arbitrary shape, (3) iterative methods are convenient for computers. From a practical point of view the above methods reduce to the cal culation of multiple integrals. Of special interest is the case of inte grands with weak singularities. Some of the central results of the book are some analytic approximate formulas for scattering matrices for small bodies of arbitrary shape. These formulas answer many practical questions such as how does the scattering depend on the shape of the body or on the boundary conditions, how does one calculate the effective field in a medium consisting of many small particles, and many other questions.

Time Domain Boundary Integral Equations Analysis
Time Domain Boundary Integral Equations Analysis

Author: Amir Geranmayeh

Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG

Published: 2011-01

Total Pages: 208

ISBN-13: 9783838123936

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The present research study mainly involves a survey of diverse time-domain boundary element methods that can be used to numerically solve the retarded potential integral equations. The aim is to address the late-time stability, accuracy, and computational complexity concerns in time-domain surface integral equation approaches. The study generally targets the transient electromagnetic scattering of three- dimensional perfectly conducting bodies. Efficient algorithms are developed to numerically solve the electric, magnetic, and combined field integral equations for the unknown induced surface current. The algorithms are mainly categorized into three major discretization schemes, namely the marching-on- in-time, the marching-on-in-order, and the convolution quadrature methods or finite difference delay modeling. Possible choices of space-time integration are examined and the results are compared with the finite integration technique's solution. The outcome is applied to the non- dispersive modeling of the field propagation in particle accelerator structures, when travelling bunches of charged particles passes through the beam line elements.