Rodriguez A.A., Valli A. Eddy Current Approximation of Maxwell Equations: Theory, Algorithms and Applications

Springer, 2010. — 355 p. — (MS&A Volume 04). — ISBN: 978-88-470-1505-0.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.
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.Setting the problem
A mathematical justification of the eddy current model
Existence and uniqueness of the solution
Hybrid formulations for the electric and magnetic fields
Formulations via scalar potentials
Formulations via vector potentials
Coupled FEM–BEM approaches
Voltage and current intensity excitation
Selected applications
Appendix