Electromagnetism, in view of modeling
type: Item
instance of: scholarly article
title: Electromagnetism, in view of modeling
zbMATH Open document ID: 0787.65090
author: Alain Bossavit
published in: Mathématiques \& Applications (Berlin)
publication date: 1994-02-20T00:00:00Z
review text: 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).
reviewed by: Laura Iulia Aniţa
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65-01
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 78A05
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 78-01
Mathematics Subject Classification ID: 78M10
zbMATH DE Number: 515686
zbMATH Keywords: finite element method
zbMATH Keywords: textbook
zbMATH Keywords: electrical motors
zbMATH Keywords: micro-wave ovens
zbMATH Keywords: resonant cavities
zbMATH Keywords: Maxwell's equations
zbMATH Keywords: Ohm's law
zbMATH Keywords: Whitney's elements
zbMATH Keywords: Foucault's currents
zbMATH Keywords: conduction
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 515686