Electromagnetism, in view of modeling.
(Électromagnétisme, en vue de la modélisation.)

*(French)*Zbl 0787.65090
Mathématiques & Applications (Berlin). 14. Paris: Springer-Verlag,. xiii, 174 p. (1993).

The aim of this book is to present some tools of modeling the physical situations where the electromagnetic phenomena are important: electrical motors, micro-wave ovens, resonant cavities. The book is based on the author’s notes for a 6 months course at the University Orsay (Paris 11) for students of the third cycle. There are 9 chapters and 9 appendices.

Chapter 1 is concerned with Maxwell’s equations and Ohm’s law. Some elements of potential theory are recalled. Chapter 2 covers the material of Maxwell’s equations in bounded domains, with the boundary condition \(n\times e=0\). The main applications are the micro-waves ovens and the resonant cavities, which are presented in detail. Chapter 3 is dedicated to the properties of the complex formed by Whitney’s elements.

Chapters 4-6 are devoted to the study of Foucault’s currents. Chapter 7 concerns the problem of conduction, when all the fields are supposed stationary. Chapters 8-9 are concerned with the surface effects and the geometry of Maxwell’s equations. The appendices contain some technical proofs and theoretical results concerning potentials, functional spaces and Laplace and Fourier transformations.

For every mathematical model studied in this book the author gives an appropriate weak formulation and a “discrete” version (which can be used for computer implementation).

Chapter 1 is concerned with Maxwell’s equations and Ohm’s law. Some elements of potential theory are recalled. Chapter 2 covers the material of Maxwell’s equations in bounded domains, with the boundary condition \(n\times e=0\). The main applications are the micro-waves ovens and the resonant cavities, which are presented in detail. Chapter 3 is dedicated to the properties of the complex formed by Whitney’s elements.

Chapters 4-6 are devoted to the study of Foucault’s currents. Chapter 7 concerns the problem of conduction, when all the fields are supposed stationary. Chapters 8-9 are concerned with the surface effects and the geometry of Maxwell’s equations. The appendices contain some technical proofs and theoretical results concerning potentials, functional spaces and Laplace and Fourier transformations.

For every mathematical model studied in this book the author gives an appropriate weak formulation and a “discrete” version (which can be used for computer implementation).

Reviewer: L.-I.Anita (Iaşi)

##### MSC:

65Z05 | Applications to the sciences |

65-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

78A25 | Electromagnetic theory, general |

78A05 | Geometric optics |

35Q60 | PDEs in connection with optics and electromagnetic theory |

78-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to optics and electromagnetic theory |

78M10 | Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory |