Eddy Current Approximation of Maxwell Equations Theory, algorithms a
This book deals with the mathematical analysis and the numerical approximation of time-harmonic eddy current problems. It is self-contained and suitable for mathematicians and engineers working in the field, and also accessible for beginners. Depending on
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MS&A Series Editors: Alfio Quarteroni (Editor-in-Chief ) • Tom Hou • Claude Le Bris • Anthony T. Patera • Enrique Zuazua
Ana Alonso Rodríguez and Alberto Valli
Eddy Current Approximation of Maxwell Equations Theory, algorithms and applications
Ana Alonso Rodríguez
Alberto Valli
Department of Mathematics University of Trento Trento, Italy
Department of Mathematics University of Trento Trento, Italy
ISBN 978-88-470-1505-0
e-ISBN 978-88-470-1506-7
DOI 10.1007/978-88-470-1506-7
Library of Congress Control Number: 2010929481
Springer Milan Dordrecht Heidelberg London New York © Springer-Verlag Italia 2010
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the Italian Copyright Law in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the Italian Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. 9 8 7 6 5 4 3 2 1 The image on the cover shows the eddy current in a trefoil knot (real and imaginary part) Cover-Design: Beatrice B , Milano Typesetting with LATEX: PTP-Berlin, Protago TEX-Production GmbH, Germany (www.ptp-berlin.eu) Printing and Binding: Grafiche Porpora, Segrate (Mi) Printed in Italy Springer-Verlag Italia srl – Via Decembrio 28 – 20137 Milano Springer is a part of Springer Science+Business Media (www.springer.com)
Preface
Continuamente nascono i fatti a confusione delle teorie 1 Carlo Dossi 2 Electromagnetism is without any doubt a fascinating area of physics, engineering and mathematics. Since the early pioneering works of Ampère, Faraday, and Maxwell, the scientific literature on this subject has become immense, and books devoted to almost all of its aspects have been published in the meantime. However, we believe that there is still some place for new books dealing with electromagnetism, particularly if they are focused on more specific models, or try to mix different levels of analysis: rigorous mathematical results, sound numerical approximation schemes, real-life examples from physics and engineering. The complete mathematical description of electromagnetic problems is provided by the celebrated Maxwell equations, a system of partial differential equations expressed in terms of physical quantities like the electric field, the magnetic field and the current density. Maxwell’s contribution to the formulation of these equations is related to the introduction of a specific term, called displacement current, that he proposed to add to the set of equations generally assumed t
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