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Optimization Methods in Electromagnetic Radiation : Springer Monographs in Mathematics - Thomas S. Angell

Optimization Methods in Electromagnetic Radiation

Springer Monographs in Mathematics


Published: 1st January 2004
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This book considers problems of optimization arising in the design of electromagnetic radiators and receivers. The authors develop a systematic general theory that can be applied to a wide class of structures. The theory is illustrated with familiar, simple examples and indications of how the results can be applied to more complicated structures. The final chapter introduces techniques from multicriteria optimization in antenna design. The material is intended for a dual audience of mathematicians and mathematically-sophisticated engineers. References to both the mathematics and engineering literature help guide the reader through the necessary mathematical background.

Prefacep. IX
Arrays of Point and Line Sources, and Optimizationp. 1
The Problem of Antenna Optimizationp. 1
Arrays of Point Sourcesp. 2
The Linear Arrayp. 3
Circular Arraysp. 10
Maximization of Directivity and Super-gainp. 15
Directivity and Other Measures of Performancep. 15
Maximization of Directivityp. 19
Dolph-Tschebysheff Arraysp. 21
Tschebysheff Polynomialsp. 22
The Dolph Problemp. 24
Line Sourcesp. 26
The Linear Line Sourcep. 30
The Circular Line Sourcep. 36
Numerical Quadraturep. 43
Conclusionp. 47
Discussion of Maxwell's Equationsp. 49
Introductionp. 49
Geometry of the Radiating Structurep. 49
Maxwell's Equations in Integral Formp. 50
The Constitutive Relationsp. 51
Maxwell's Equations in Differential Formp. 52
Energy Flow and the Poynting Vectorp. 55
Time Harmonic Fieldsp. 56
Vector Potentialsp. 58
Radiation Condition, Far Field Patternp. 60
Radiating Dipoles and Line Sourcesp. 63
Boundary Conditions on Interfacesp. 68
Hertz Potentials and Classes of Solutionsp. 70
Radiation Problems in Two Dimensionsp. 73
Optimization Theory for Antennasp. 77
Introductory Remarksp. 77
The General Optimization Problemp. 80
Existence and Uniquenessp. 81
The Modeling of Constraintsp. 84
Extreme Points and Optimal Solutionsp. 88
The Lagrange Multiplier Rulep. 93
Methods of Finite Dimensional Approximationp. 96
Far Field Patterns and Far Field Operatorsp. 101
Measures of Antenna Performancep. 103
The Synthesis Problemp. 113
Introductory Remarksp. 113
Remarks on Ill-Posed Problemsp. 115
Regularization by Constraintsp. 121
The Tikhonov Regularizationp. 127
The Synthesis Problem for the Finite Linear Line Sourcep. 133
Basic Equationsp. 134
The Nyström Methodp. 135
Numerical Solution of the Normal Equationsp. 137
Applications of the Regularization Techniquesp. 138
Boundary Value Problems for the Two-Dimensional Helmholtz Equationp. 145
Introduction and Formulation of the Problemsp. 145
Rellich's Lemma and Uniquenessp. 148
Existence by the Boundary Integral Equation Methodp. 151
L2 - Boundary Datap. 157
Numerical Methodsp. 163
Nyström's Method for Periodic Weakly Singular Kernelsp. 164
Complete Families of Solutionsp. 168
Finite Element Methods for Absorbing Boundary Conditionsp. 174
Hybrid Methodsp. 181
Boundary Value Problems for Maxwell's Equationsp. 185
Introduction and Formulation of the Problemp. 185
Uniqueness and Existencep. 188
L2 - Boundary Datap. 193
Some Particular Optimization Problemsp. 195
General Assumptionsp. 195
Maximization of Powerp. 197
Input Power Constraintsp. 198
Pointwise Constraints on Inputsp. 202
Numerical Simulationsp. 204
The Null-Placement Problemp. 211
Maximization of Power with Prescribed Nullsp. 213
A Particular Example - The Line Sourcep. 216
Pointwise Constraintsp. 219
Minimization of Pattern Perturbationp. 221
The Optimization of Signal-to-Noise Ratio and Directivityp. 226
The Existence of Optimal Solutionsp. 227
Necessary Conditionsp. 228
The Finite Dimensional Problemsp. 231
Conflicting Objectives: The Vector Optimization Problemp. 239
Introductionp. 239
General Multi-criteria Optimization Problemsp. 240
Minimal Elements and Pareto Pointsp. 241
The Lagrange Multiplier Rulep. 247
Scalarizationp. 249
The Multi-criteria Dolph Problem for Arraysp. 250
The Weak Dolph Problemp. 251
Two Multi-criteria Versionsp. 253
Null Placement Problems and Super-gainp. 262
Minimal Pattern Deviationp. 264
Power and Super-gainp. 270
The Signal-to-noise Ratio Problemp. 278
Formulation of the Problem and Existence of Pareto Pointsp. 278
The Lagrange Multiplier Rulep. 280
An Examplep. 282
Appendixp. 285
Introductionp. 285
Basic Notions and Examplesp. 286
The Lebesgue Integral and Function Spacesp. 292
The Lebesgue Integralp. 292
Sobolev Spacesp. 295
Orthonormal Systemsp. 298
Linear Bounded and Compact Operatorsp. 300
The Hahn-Banach Theoremp. 307
The Fréchet Derivativep. 310
Weak Convergencep. 312
Partial Orderingsp. 315
Referencesp. 319
Indexp. 327
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387204505
ISBN-10: 0387204504
Series: Springer Monographs in Mathematics
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 331
Published: 1st January 2004
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 0.68