Integral equation methods for electromagnetic and elastic waves

Weng Cho Chew, Mei Song Tong, Bin Hu

Research output: Chapter in Book/Report/Conference proceedingChapter

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.

Original languageEnglish (US)
Title of host publicationSynthesis Lectures on Computational Electromagnetics
Pages1-256
Number of pages256
DOIs
StatePublished - Jan 1 2008

Publication series

NameSynthesis Lectures on Computational Electromagnetics
Volume12
ISSN (Print)1932-1252
ISSN (Electronic)1932-1716

Keywords

  • Computational electromagnetics
  • Dyadic green's function
  • Elastic waves
  • Electromagnetic waves
  • Energy conservation theorem
  • Fast inhomogeneous plane wave algorithm
  • Integral equations
  • Linear vector spaces
  • Low-frequency problems

ASJC Scopus subject areas

  • Radiation
  • Modeling and Simulation
  • Computational Mathematics
  • Electrical and Electronic Engineering

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  • Cite this

    Chew, W. C., Tong, M. S., & Hu, B. (2008). Integral equation methods for electromagnetic and elastic waves. In Synthesis Lectures on Computational Electromagnetics (pp. 1-256). (Synthesis Lectures on Computational Electromagnetics; Vol. 12). https://doi.org/10.2200/S00102ED1V01Y200807CEM012