Optimization Methods in Electromagnetic Radiation

1. Front Matter

   Pages I-XIII

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2. Arrays of Point and Line Sources, and Optimization

   • Thomas S. Angell, Andreas Kirsch

   Pages 1-48

3. Discussion of Maxwell’s Equations

   • Thomas S. Angell, Andreas Kirsch

   Pages 49-75

4. Optimization Theory for Antennas

   • Thomas S. Angell, Andreas Kirsch

   Pages 77-111

5. The Synthesis Problem

   • Thomas S. Angell, Andreas Kirsch

   Pages 113-143

6. Boundary Value Problems for the Two-Dimensional Helmholtz Equation

   • Thomas S. Angell, Andreas Kirsch

   Pages 145-184

7. Boundary Value Problems for Maxwell’s Equations

   • Thomas S. Angell, Andreas Kirsch

   Pages 185-194

8. Some Particular Optimization Problems

   • Thomas S. Angell, Andreas Kirsch

   Pages 195-238

9. Conflicting Objectives: The Vector Optimization Problem

   • Thomas S. Angell, Andreas Kirsch

   Pages 239-284

10. Back Matter

    Pages 285-331

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The subject of antenna design, primarily a discipline within electrical en- neering, is devoted to the manipulation of structural elements of and/or the electrical currents present on a physical object capable of supporting such a current. Almost as soon as one begins to look at the subject, it becomes clear that there are interesting mathematical problems which need to be addressed, in the ?rst instance, simply for the accurate modelling of the electromagnetic ?elds produced by an antenna. The description of the electromagnetic ?elds depends on the physical structure and the background environment in which thedeviceistooperate. It is the coincidence of a class of practical engineering applications and theapplicationofsomeinterestingmathematicaloptimizationtechniquesthat is the motivation for the present book. For this reason, we have thought it worthwhile to collect some of the problems that have inspired our research in appliedmathematics,andtopresenttheminsuchawaythattheymayappeal to two di?erent audiences: mathematicians who are experts in the theory of mathematical optimization and who are interested in a less familiar and importantareaofapplication,andengineerswho,confrontedwithproblemsof increasing sophistication, are interested in seeing a systematic mathematical approach to problems of interest to them. We hope that we have found the right balance to be of interest to both audiences. It is a di?cult task. Our ability to produce these devices at all, most designed for a part- ular purpose, leads quite soon to a desire to optimize the design in various ways. The mathematical problems associated with attempts to optimize p- formance can become quite sophisticated even for simple physical structures.

• Helmholtz equation
• Maxwell
• Maxwell's equations
• Potential
• Signal
• antenna
• finite element method
• linear optimization
• modeling
• multi-objective optimization
• numerical methods
• numerical quadrature
• operator
• optimization
• simulation

• Department of Mathematical Sciences, University of Delaware, Newark, USA

  Thomas S. Angell

• Mathematics Institute II, University of Karlsruhe, Karlsruhe, Germany

  Andreas Kirsch

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