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Computational Electromagnetism

Author Alain Bossavit , Isaak D. Mayergoyz
Release Date: 1997/12/01
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Book Description

Computational Electromagnetism refers to the modern concept of computer-aided analysis, and design, of virtually all electric devices such as motors, machines, transformers, etc., as well as of the equipment inthe currently booming field of telecommunications, such as antennas, radars, etc.

The present book is uniquely written to enable the reader-- be it a student, a scientist, or a practitioner-- to successfully perform important simulation techniques and to design efficient computer software for electromagnetic device analysis. Numerous illustrations, solved exercises, original ideas, and an extensive and up-to-date bibliography make it a valuable reference for both experts and beginners in the field. A researcher and practitioner will find in it information rarely available in other sources, such as on symmetry, bilateral error bounds by complimentarity, edge and face elements, treatment of infinite domains, etc.

At the same time, the book is a useful teaching tool for courses in computational techniques in certain fields of physics and electrical engineering. As a self-contained text, it presents an extensive coverage of the most important concepts from Maxwells equations to computer-solvable algebraic systems-- for both static, quasi-static, and harmonic high-frequency problems.

Benefits
To the Engineer
A sound background necessary not only to understand the principles behind variational methods and finite elements, but also to design pertinent and well-structured software.

To the Specialist in Numerical Modeling
The book offers new perspectives of practical importance on classical issues: the underlying symmetry of Maxwell equations, their interaction with other fields of physics in real-life modeling, the benefits of edge and face elements, approaches to error analysis, and "complementarity."

To the Teacher
An expository strategy that will allow you to guide the student along a safe and easy route through otherwise difficult concepts: weak formulations and their relation to fundamental conservation principles of physics, functional spaces, Hilbert spaces, approximation principles, finite elements, and algorithms for solving linear systems. At a higher level, the book provides a concise and self-contained introduction to edge elements and their application to mathematical modeling of the basic electromagnetic phenomena, and static problems, such as eddy-current problems and microwaves in cavities.

To the Student
Solved exercises, with "hint" and "full solution" sections, will both test and enhance the understanding of the material. Numerous illustrations will help in grasping difficult mathematical concepts.

Table of Contents

  1. Front Cover
  2. Computational Electromagnetism: Variational Formulations, Complementarity, Edge Elements
  3. Copyright Page
  4. Contents (1/2)
  5. Contents (2/2)
  6. Preface (1/2)
  7. Preface (2/2)
  8. Chapter 1. Introduction: Maxwell Equations
    1. 1.1 Field Equations
    2. 1.2 Constitutive Laws (1/2)
    3. 1.2 Constitutive Laws (2/2)
    4. 1.3 Macroscopic Interactions
    5. 1.4 Derived Models
    6. Exercises
    7. Solutions
    8. References
  9. Chapter 2. Magnetostatics: "Scalar Potential" Approach
    1. 2.1 Introduction: A Model Problem
    2. 2.2 Honing Our Tools (1/2)
    3. 2.2 Honing Our Tools (2/2)
    4. 2.3 Weak Formulations (1/2)
    5. 2.3 Weak Formulations (2/2)
    6. 2.4 Modelling: The Scalar Potential Formulation (1/2)
    7. 2.4 Modelling: The Scalar Potential Formulation (2/2)
    8. Exercises
    9. Solutions
    10. References
  10. Chapter 3. Solving for the Scalar Magnetic Potential
    1. 3.1 The "Variational" Formulation
    2. 3.2 Existence of a Solution
    3. 3.3 Discretization (1/3)
    4. 3.3 Discretization (2/3)
    5. 3.3 Discretization (3/3)
    6. Exercises
    7. Solutions (1/2)
    8. Solutions (2/2)
    9. References
  11. Chapter 4. The Approximate Scalar Potential: Properties and Shortcomings
    1. 4.1 The "m-weak" Properties
    2. 4.2 The Maximum Principle (1/2)
    3. 4.2 The Maximum Principle (2/2)
    4. 4.3 Convergence and Error Analysis (1/2)
    5. 4.3 Convergence and Error Analysis (2/2)
    6. Exercises
    7. Solutions
    8. References
  12. Chapter 5. Whitney Elements
    1. 5.1 A Functional Framework
    2. 5.2 The Whitney Complex (1/3)
    3. 5.2 The Whitney Complex (2/3)
    4. 5.2 The Whitney Complex (3/3)
    5. 5.3 Trees and Cotrees (1/2)
    6. 5.3 Trees and Cotrees (2/2)
    7. Exercises
    8. Solutions
    9. References
  13. Chapter 6. The "Curl Side": Complementarity
    1. 6.1 A Symmetrical Variational Formulation (1/2)
    2. 6.1 A Symmetrical Variational Formulation (2/2)
    3. 6.2 Solving the Magnetostatics Problem (1/2)
    4. 6.2 Solving the Magnetostatics Problem (2/2)
    5. 6.3 Why Not Standard Elements? (1/2)
    6. 6.3 Why Not Standard Elements? (2/2)
    7. Exercises
    8. Solutions
    9. References
  14. Chapter 7. Infinite Domains
    1. 7.1 Another Model Problem
    2. 7.2 Formulation
    3. 7.3 Discretization
    4. 7.4 The "Dirichlet-to-Neumann" Map (1/3)
    5. 7.4 The "Dirichlet-to-Neumann" Map (2/3)
    6. 7.4 The "Dirichlet-to-Neumann" Map (3/3)
    7. 7.5 Back to Magnetostatics
    8. Exercises
    9. Solutions
    10. References
  15. Chapter 8. Eddy-Current Problems
    1. 8.1 The Model in H
    2. 8.2 Infinite Domains: "Trifou" (1/2)
    3. 8.2 Infinite Domains: "Trifou" (2/2)
    4. 8.3 Bounded Domains: Trees, H–Ф (1/2)
    5. 8.3 Bounded Domains: Trees, H–Ф (2/2)
    6. 8.4 Summing Up
    7. Exercises
    8. Solutions
    9. References
  16. Chapter 9. Maxwell's Model in Harmonic Regime
    1. 9.1 A Concrete Problem: The Microwave Oven
    2. 9.2 The "Continuous" Problem (1/2)
    3. 9.2 The "Continuous" Problem (2/2)
    4. 9.3 The "Discrete" Problem
    5. References
  17. APPENDIX A. Mathematical Background
    1. A.1 Basic Notions
    2. A.2 Important Structures (1/3)
    3. A.2 Important Structures (2/3)
    4. A.2 Important Structures (3/3)
    5. A.3 Our Framework for Electromagnetism: E3 (1/2)
    6. A.3 Our Framework for Electromagnetism: E3 (2/2)
    7. A.4 Glimpses of Functional Analysis (1/3)
    8. A.4 Glimpses of Functional Analysis (2/3)
    9. A.4 Glimpses of Functional Analysis (3/3)
    10. References
  18. APPENDIX B. LDL t Factorization and Constrained Linear Systems
    1. B.1 Nonnegative Definite Matrices
    2. B.2 A Digression about Programming
    3. B.3 The LDL t Factorization
    4. B.4 Application to Constrained Linear Systems
    5. References
  19. APPENDIX C. A Cheaper Way to Complementarity
    1. C.1 Local Corrections
    2. C.2 Solving Problem (14)
    3. C.3 Conclusion and Speculations
  20. Author Index
  21. Subject Index (1/2)
  22. Subject Index (2/2)
3.142.195.24