Computational Electromagnetism : Variational Formulations, Complementarity, Edge Elements

Content: Foreword , Page v Preface , Pages xiii-xviii Chapter 1 - Introduction: Maxwell Equations , Pages 1-30 Chapter 2 - Magnetostatics: “Scalar Potential” Approach , Pages 31-60 Chapter 3 - Solving for the Scalar Magnetic Potential , Pages 61-94 Chapter 4 - The Approximate Scalar Potential: Properties and Shortcomings , Pages 95-124 Chapter 5 - Whitney Elements , Pages 125-162 Chapter 6 - The “Curl Side”: Complementarity , Pages 163-192 Chapter 7 - Infinite Domains , Pages 193-218 Chapter 8 - Eddy-current Problems , Pages 219-246 Chapter 9 - Maxwell's Model in Harmonic Regime , Pages 247-262 Appendix A - Mathematical Background , Pages 263-318 Appendix B - LDL t Factorization and Constrained Linear Systems , Pages 319-328 Appendix C - A Cheaper Way to Complementarity , Pages 329-338 Author Index , Pages 339-342 Subject Index , Pages 343-352 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. 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 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 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. Content: Foreword, __Page v__Preface, __Pages xiii-xviii__Chapter 1 - Introduction: Maxwell Equations, __Pages 1-30__Chapter 2 - Magnetostatics: “Scalar Potential” Approach, __Pages 31-60__Chapter 3 - Solving for the Scalar Magnetic Potential, __Pages 61-94__Chapter 4 - The Approximate Scalar Potential: Properties and Shortcomings, __Pages 95-124__Chapter 5 - Whitney Elements, __Pages 125-162__Chapter 6 - The “Curl Side”: Complementarity, __Pages 163-192__Chapter 7 - Infinite Domains, __Pages 193-218__Chapter 8 - Eddy-current Problems, __Pages 219-246__Chapter 9 - Maxwell's Model in Harmonic Regime, __Pages 247-262__Appendix A - Mathematical Background, __Pages 263-318__Appendix B - LDLt Factorization and Constrained Linear Systems, __Pages 319-328__Appendix C - A Cheaper Way to Complementarity, __Pages 329-338__Author Index, __Pages 339-342__Subject Index, __Pages 343-352__ Theoretical in nature, this book addresses main computational techniques, especially finite elements as applied to electromagnetic calculations. The book is aimed at graduate students and researchers involved in computer simulation of electromagnetic phenomena, and originates from courses the author taught on the subject on numerical analysis of electromagnetism. Computational Electromagnetism should also be useful to practitioners in the industry working on numerical computations of electromagnetic fields and design of electromagnetic devices, in addition to applied mathematicians interested in applied PDE's and the finite element community.