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Integral Equation Methods for Electromagnetic and Elastic Waves

Synthesis Lectures on Computational Electromagnetics

Weng Cho Chew​‌
University of Hong Kong and University of Illinois at Urbana-Champaign
Mei Song Tong​‌
University of Illinois at Urbana-Champaign
Bin Hu​‌
Intel Research

Abstract

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

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M. Saillard, G. Soriano​‌. (2011) Rough surface scattering at low-grazing incidence: A dedicated model. Radio Science 46:5, n/a-n/a.
Online publication date: 19-Oct-2011.
Crossref
Mei Song Tong​‌. (2011) Efficient electromagnetic analysis for curved open thin-wire structures using intervallic wavelets in the method of moments. Waves in Random and Complex Media 21:2, 231-247.
Online publication date: 10-Mar-2011.
Crossref
Valdelírio da Silva e Silva, Cícero Régis, Allen Q. Howard​‌. (2011) Numerical integration in the calculation of the 2.5‐D response of a very large loop. SEG Technical Program Expanded Abstracts 2011, 756-760.
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Authors:
Weng Cho Chew
Mei Song Tong
Bin Hu
Keywords:
integral equations
computational electromagnetics
electromagnetic waves
linear vector spaces
energy conservation theorem
low-frequency problems
dyadic green's function
fast inhomogeneous plane wave algorithm
elastic waves
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