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Integral Equation Methods for Electromagnetics : Microwave Library - N. Morita

Integral Equation Methods for Electromagnetics

Microwave Library

By: N. Morita, Nobuaki Kumagai, J. Mautz (Translator)


Published: 19th October 1991
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Details the methods for solving electromagnetic wave problems using the integral equation formula. This text limits the use of mathematics to the level of standard undergraduate students and explains all the derivations and transformations of equations in detail.

Prefacep. ix
Fundamentals of Electromagnetic Field Analysisp. 1
Basic Equations for Electromagnetic Fieldsp. 1
The Vector Potential, the Scalar Potential, and the Hertz Vectorsp. 5
Electromagnetic Fields in Regions That Are Uniform in One Directionp. 9
Boundary Conditions and the Radiation Conditionp. 11
Green's Functions and the Dirac Delta Functionp. 14
Free-space Green's Functionsp. 16
Green's Function for the Three-Dimensional Scalar Helmholtz Equationp. 16
Green's Function for the Two-Dimensional Scalar Helmholtz Equationp. 17
Green's Function for Laplace's Equationp. 18
Solutions of the Scalar Helmholtz Equationp. 19
Expressions in Cartesian Coordinatesp. 19
Expressions in Cylindrical Coordinatesp. 20
Expressions in Spherical Coordinatesp. 22
Plane Wavesp. 25
Expressions in Cylindrical Coordinatesp. 26
Expression in Spherical Coordinatesp. 28
Scattering by Simply Shaped Objectsp. 31
The Dielectric Circular Cylinderp. 31
The Perfectly Conducting Circular Cylinderp. 37
The Dielectric Spherep. 38
The Perfectly Conducting Spherep. 41
Reflection and Refraction at a Plane Surfacep. 41
TM Wave Incidencep. 42
TE Wave Incidencep. 43
Electromagnetic Fields in the Vicinity of a Wedgep. 44
The Dielectric Wedgep. 44
The Perfectly Conducting Wedgep. 50
Referencesp. 52
Integral Representationsp. 55
Scalar Field Problemsp. 56
The Derivationp. 56
Two-Dimensional Scattering Problemsp. 58
Electrostatic Field Problemsp. 63
Vector Field Problemsp. 65
Transformation of Three-Dimensional Expressions into Two-Dimensional Expressionsp. 74
Vectorial Integral Representations in the Cross-sectional Planep. 74
Integral Representations for the Axial Field Componentsp. 78
Dielectric Waveguide Mode Fieldsp. 82
Fields in Terms of the Source Distributionsp. 90
Derivation Based on the Reciprocity Theoremp. 92
Far Fields and Scattering Cross Sectionsp. 94
Three-Dimensional Problemsp. 94
Two-Dimensional Problemsp. 99
Reciprocity Between Incident and Scattered Wavesp. 102
Integral Representations Applied to the Problem of Reflection and Refraction at a Plane Interfacep. 104
Local Rectangular Coordinatesp. 108
Derivatives of the Unit Vectors of a Curvilinear Coordinate Systemp. 120
Referencesp. 124
Integral Equationsp. 127
Integral Representations with the Observation Point on the Boundaryp. 128
A Limiting Procedure for Three-Dimensional Scalar Field Problemsp. 128
A Limiting Procedure for Two-Dimensional Scalar Field Problemsp. 131
Integral Representations with the Observation Point on the Boundary for Scalar Field Problemsp. 134
Treatment of the Second Partial Derivative of the Green's Functionp. 136
Integral Representations with the Observation Point on the Boundary for Vector Field Problemsp. 138
Fundamental Integral Equationsp. 140
General Formulationp. 140
Scattering by a Perfectly Conducting Cylinder: TM Wave Incidencep. 149
Scattering by a Perfectly Conducting Cylinder: TE Wave Incidencep. 151
Scattering by a Dielectric Cylinder: TM Wave Incidencep. 156
Scattering by a Dielectric Cylinder: TE Wave Incidencep. 160
A Perfectly Conducting Body in an Electrostatic Fieldp. 163
A Dielectric Body in an Electrostatic Fieldp. 167
Guided Modes of a Dielectric Waveguidep. 167
Modes of a Closed Waveguidep. 174
Integral Equations When There are Conditions on Other Boundariesp. 177
Involvement of Resonant Solutionsp. 180
General Theoryp. 180
The Perfectly Conducting Cylinderp. 182
The Dielectric Cylinderp. 187
A Summary on Resonant Solutionsp. 193
Methods of Eliminating Resonant Solutionsp. 196
Utilization of the Extended Boundary Conditionp. 196
A Method for Combining Interior and Exterior Field Expressionsp. 207
A Combined-Field Solutionp. 215
A Combined-Source Solutionp. 218
Integration over the Infinitesimal Area Around an Apexp. 222
Referencesp. 228
The Numerical Solution of Integral Equationsp. 233
The Discretization of Integral Equations and the Boundary Element Methodp. 234
The Method of Momentsp. 236
General Conceptsp. 236
The Expansion Functionsp. 238
The Weighting Functionsp. 247
Ways to Obtain a Matrix Equation from Fundamental Integral Equationsp. 251
The Pulse Function Expansion: A Constant Element Approximationp. 255
The Triangle Function Expansion: A Linear Element Approximationp. 275
The Numerical Solution of the Matrix Equationp. 288
The Method of the Generalized Inverse of Matricesp. 290
The Conjugate Gradient Methodp. 291
The Direct Iterative Methodp. 299
Notes on the Calculation of Physical Quantities and Computer Programmingp. 301
Integration Over the Arc-Shaped Boundary Element Containing the Observation Pointp. 309
The Conjugate Gradient Method for Solving a Matrix Equation When the Elements of the Matrix Are Complex Numbersp. 315
Referencesp. 320
Some Useful Formulasp. 329
Indexp. 339
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780890064825
ISBN-10: 0890064822
Series: Microwave Library
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 356
Published: 19th October 1991
Publisher: Artech House Publishers
Country of Publication: US
Dimensions (cm): 22.9 x 15.2  x 2.3
Weight (kg): 0.69