| Titre : | Finite element methods for maxwell's equations | | Type de document : | texte imprimé | | Auteurs : | Peter Monk, Auteur | | Editeur : | New york : Oxford University Press Inc | | Année de publication : | 2003 | | Collection : | Numerical Mathematics and Scientific Computation | | Importance : | 450 p. | | Présentation : | couv. ill. en coul., ill. | | Format : | 24 cm. | | ISBN/ISSN/EAN : | 978-0-19-850888-5 | | Langues : | Anglais (eng) | | Index. décimale : | 10-06 Electromagnétisme | | Résumé : | Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell's equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism there has also been considerable progress in the mathematical understanding of the properties of Maxwell's equations relevant to numerical analysis. The aim of this book is to provide an up to date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book. The methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book finishes with a short introduction to inverse problems in electromagnetism. | | Note de contenu : | Contents:
1 Mathematical Models of Electromagnetism
2 Functional Analysis and Abstract Error Estimates
3 Sobolev, Spaces, Vector Function Spaces and Regularity
4 Variational Theory for the Cavity Problem
5 Finite Elements on Tetrahedra
6 Finite Elements on Hexahedra
7 Finite Element Methods for the Cavity Problem
8 Topics Concerning Finite Elements
9 Classical Scattering Theory
10 A First Variational Method for the Scattering Problem
11 Scattering by a Bounded Inhomogeneity
12 Scattering by a Buried Object
13 Implementation and Algorithmic Development
14 Inverse Problems
Appendix |
Finite element methods for maxwell's equations [texte imprimé] / Peter Monk, Auteur . - New york : Oxford University Press Inc, 2003 . - 450 p. : couv. ill. en coul., ill. ; 24 cm.. - ( Numerical Mathematics and Scientific Computation) . ISBN : 978-0-19-850888-5 Langues : Anglais ( eng) | Index. décimale : | 10-06 Electromagnétisme | | Résumé : | Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell's equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism there has also been considerable progress in the mathematical understanding of the properties of Maxwell's equations relevant to numerical analysis. The aim of this book is to provide an up to date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book. The methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book finishes with a short introduction to inverse problems in electromagnetism. | | Note de contenu : | Contents:
1 Mathematical Models of Electromagnetism
2 Functional Analysis and Abstract Error Estimates
3 Sobolev, Spaces, Vector Function Spaces and Regularity
4 Variational Theory for the Cavity Problem
5 Finite Elements on Tetrahedra
6 Finite Elements on Hexahedra
7 Finite Element Methods for the Cavity Problem
8 Topics Concerning Finite Elements
9 Classical Scattering Theory
10 A First Variational Method for the Scattering Problem
11 Scattering by a Bounded Inhomogeneity
12 Scattering by a Buried Object
13 Implementation and Algorithmic Development
14 Inverse Problems
Appendix |
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