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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 the choice of the physical unknowns, these problems are formulated in different variational ways, with specific attention to the topology of the computational domain. Finite elements of nodal or edge type are used for numerical approximation, and a complete analysis of convergence is performed. A specific feature of the book is the emphasis given to saddle-point formulations in terms of the magnetic and electric fields. New results for voltage or current intensity excitation problems are also presented.
List of contents
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.
About the author
Since more than ten years the authors have performed researches in the field of numerical approximation of partial differential equations, especially the finite element approximation of problems in electromagnetics. They have published many papers on numerical approximation of partial differential equations on some of the most important journal devoted to this topic. The second author has written two other books on the subject: A. Quarteroni and A. Valli, Numerical Approximation of Partial Differential Equations, Springer, 1997 (second edition); A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations, Oxford University Press, 1999
Report
From the reviews:
"A comprehensive survey of the magneto-quasistatic reduction of Maxwell's equations-usually called the eddy current approximation. ... There is a comprehensive bibliography of almost 250 items that provides an excellent coverage of the current literature. ... It provides a unique description of some important problems that the authors have studied in recent years and will, I am sure, stimulate a lot more research on related phenomena. The authors are to be commended for their broad perspective and their innovative coverage of these topics." (Giles Auchmuty, SIAM Review, Vol. 53 (4), 2011)
