Computational Electromagnetism -  Alain Bossavit

Computational Electromagnetism (eBook)

Variational Formulations, Complementarity, Edge Elements
eBook Download: PDF
1998 | 1. Auflage
352 Seiten
Elsevier Science (Verlag)
978-0-08-052966-0 (ISBN)
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96,11 inkl. MwSt
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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.
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.BenefitsTo the EngineerA 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 ModelingThe 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 "e;complementarity."e;To the TeacherAn 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 StudentSolved exercises, with "e;hint"e; and "e;full solution"e; sections, will both test and enhance the understanding of the material. Numerous illustrations will help in grasping difficult mathematical concepts.

Cover 1
Contents 8
Preface 14
Chapter 1. Introduction: Maxwell Equations 22
1.1 Field Equations 22
1.2 Constitutive Laws 27
1.3 Macroscopic Interactions 36
1.4 Derived Models 41
Exercises 45
Solutions 47
References 49
Chapter 2. Magnetostatics: "Scalar Potential" Approach 52
2.1 Introduction: A Model Problem 52
2.2 Honing Our Tools 54
2.3 Weak Formulations 62
2.4 Modelling: The Scalar Potential Formulation 69
Exercises 77
Solutions 78
References 80
Chapter 3. Solving for the Scalar Magnetic Potential 82
3.1 The "Variational" Formulation 82
3.2 Existence of a Solution 86
3.3 Discretization 91
Exercises 105
Solutions 108
References 114
Chapter 4. The Approximate Scalar Potential: Properties and Shortcomings 116
4.1 The "m-weak" Properties 116
4.2 The Maximum Principle 126
4.3 Convergence and Error Analysis 132
Exercises 140
Solutions 141
References 144
Chapter 5. Whitney Elements 146
5.1 A Functional Framework 146
5.2 The Whitney Complex 156
5.3 Trees and Cotrees 170
Exercises 178
Solutions 179
References 182
Chapter 6. The "Curl Side": Complementarity 186
6.1 A Symmetrical Variational Formulation 187
6.2 Solving the Magnetostatics Problem 197
6.3 Why Not Standard Elements? 203
Exercises 210
Solutions 211
References 212
Chapter 7. Infinite Domains 216
7.1 Another Model Problem 216
7.2 Formulation 218
7.3 Discretization 222
7.4 The "Dirichlet-to-Neumann" Map 226
7.5 Back to Magnetostatics 237
Exercises 239
Solutions 240
References 240
Chapter 8. Eddy-Current Problems 242
8.1 The Model in H 243
8.2 Infinite Domains: "Trifou" 248
8.3 Bounded Domains: Trees, H–. 254
8.4 Summing Up 262
Exercises 263
Solutions 266
References 268
Chapter 9. Maxwell's Model in Harmonic Regime 270
9.1 A Concrete Problem: The Microwave Oven 270
9.2 The "Continuous" Problem 273
9.3 The "Discrete" Problem 280
References 285
APPENDIX A. Mathematical Background 286
A.1 Basic Notions 286
A.2 Important Structures 305
A.3 Our Framework for Electromagnetism: E3 317
A.4 Glimpses of Functional Analysis 327
References 340
APPENDIX B. LDL t Factorization and Constrained Linear Systems 342
B.1 Nonnegative Definite Matrices 342
B.2 A Digression about Programming 345
B.3 The LDL t Factorization 347
B.4 Application to Constrained Linear Systems 349
References 351
APPENDIX C. A Cheaper Way to Complementarity 352
C.1 Local Corrections 353
C.2 Solving Problem (14) 356
C.3 Conclusion and Speculations 359
Author Index 362
Subject Index 366

Erscheint lt. Verlag 4.2.1998
Mitarbeit Herausgeber (Serie): Isaak D. Mayergoyz
Sprache englisch
Themenwelt Sachbuch/Ratgeber
Mathematik / Informatik Informatik
Mathematik / Informatik Mathematik
Naturwissenschaften Physik / Astronomie Elektrodynamik
Technik Elektrotechnik / Energietechnik
ISBN-10 0-08-052966-6 / 0080529666
ISBN-13 978-0-08-052966-0 / 9780080529660
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