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Integral equation methods for electromagnetic and elastic waves

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....

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Bibliographic Details
Main Author: Chew, Weng Cho.
Other Authors: Hu, Bin, 1972-, Tong, Mei Song.
Format: Electronic
Language:English
Published: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2009.
Edition:1st ed.
Series:Synthesis lectures on computational electromagnetics (Online), #12.
Subjects:
Elastic waves > Mathematics.
Electromagnetic waves > Mathematics.
Integral equations > Numerical solutions.
Online Access:Abstract with links to full text
Table of Contents:
  • Preface
  • Acknowledgements
  • 1. Introduction to computational electromagnetics
  • 1.1. Mathematical modeling
  • a historical perspective
  • 1.2. Some things do not happen in CEM frequently
  • nonlinearity
  • 1.3. The morphing of electromagnetic physics
  • 1.4. Matched asymptotics
  • 1.5. Why CEM?
  • 1.6. Time domain versus frequency domain
  • 1.7. Differential equation versus integral equation
  • 1.8. Nondissipative nature of electromagnetic field
  • 1.9. Conclusions
  • 2. Linear vector space, reciprocity, and energy conservation
  • 2.1. Introduction
  • 2.2. Linear vector spaces
  • 2.3. Inner products for electromagnetics
  • 2.4. Transpose and adjoint of an operator
  • 2.5. Matrix representation
  • 2.6. Compact versus noncompact operators
  • 2.7. Extension of Bra and Ket notations
  • 2.8. Orthogonal basis versus nonorthogonal basis
  • 2.9. Integration by parts
  • 2.10. Reciprocity theorem
  • a new look
  • 2.11. Energy conservation theorem
  • a new look
  • 2.12. Conclusions
  • 3. Introduction to integral equations
  • 3.1. Introduction
  • 3.2. The dyadic Green's function
  • 3.3. Equivalence principle and extinction theorem
  • 3.4. Electric field integral equation
  • a simple physical description
  • 3.5. Understanding the method of moments
  • a simple example
  • 3.6. Choice of expansion function
  • 3.7. Closed surface versus open surface
  • 3.8. Internal resonance and combined field integral equation
  • 3.9. Other boundary conditions
  • impedance boundary condition, thin dielectric sheet, and r-card
  • 3.10. Matrix solvers
  • a pedestrian introduction
  • 3.11. Conclusions
  • 4. Integral equations for penetrable objects
  • 4.1. Introduction
  • 4.2. Scattering by a penetrable object using SIE
  • 4.3. Gedanken experiments for internal resonance problems
  • 4.4. Volume integral equations
  • 4.5. Curl conforming versus divergence conforming expansion functions
  • 4.6. Thin dielectric sheet
  • 4.7. Impedance boundary condition
  • 4.8. Conclusions
  • 5. Low-frequency problems in integral equations
  • 5.1. Introduction
  • 5.2. Low-frequency breakdown of electric field integral equation
  • 5.3. Remedy
  • loop-tree decomposition and frequency normalization
  • 5.4. Testing of the incident field with the loop function
  • 5.5. The multi-dielectric-region problem
  • 5.6. Multiscale problems in electromagnetics
  • 5.7. Conclusions
  • 6. Dyadic Green's function for layered media and integral equations
  • 6.1. Introduction
  • 6.2. Dyadic Green's function for layered media
  • 6.3. Matrix representation
  • 6.4. The [delta]Ge operator
  • 6.5. The [lambda] and [kappa] operators
  • 6.6. The Ez-Hz formulation
  • 6.7. Validation and result
  • 6.8. Conclusions
  • 7. Fast inhomogeneous plane wave algorithm for layered media
  • 7.1. Introduction
  • 7.2. Integral equations for layered medium
  • 7.3. FIPWA for free space
  • 7.4. FIPWA for layered medium
  • 7.5. Numerical results
  • 7.6. Conclusions
  • 8. Electromagnetic wave versus elastic wave
  • 8.1. Introduction
  • 8.2. Derivation of the elastic wave equation
  • 8.3. Solution of the elastic wave equation
  • a succinct derivation
  • 8.4. Alternative solution of the elastic wave equation via Fourier-Laplace transform
  • 8.5. Boundary conditions for elastic wave equation
  • 8.6. Decomposition of elastic wave into SH, SV and P waves for layered media
  • 8.7. Elastic wave equation for planar layered media
  • 8.8. Finite difference scheme for the elastic wave equation
  • 8.9. Integral equation for elastic wave scattering
  • 8.10. Conclusions
  • Glossary of acronyms
  • About the authors.

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