Finite Element Methods for Maxwell's Equations

Erscheinungsjahr 2003
ISBN: 978-0-19-850888-5
Verlag: OUP Oxford

Buch, Englisch, 468 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 863 g

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.

Autoren/Hrsg.

Monk, P.

Monk, Peter

Fachgebiete

• Naturwissenschaften Physik Elektromagnetismus Magnetismus
• Naturwissenschaften Physik Elektromagnetismus Elektrizität, Elektrodynamik
• Naturwissenschaften Chemie Chemie Allgemein Chemometrik, Chemoinformatik
• Mathematik | Informatik Mathematik Geometrie
• Naturwissenschaften Physik Elektromagnetismus Halbleiter- und Supraleiterphysik
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis

Inhaltsverzeichnis

- 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

Über Autor(innen)

Prof. P. Monk
Department of Mathematical Sciences
University of Delaware
Newark DE 19716
USA
Tel [phone]
Fax [phone]
[e-mail]

UNIDEL Professor of Mathematical Sciences, University of Delaware, USA

British, Shrewsbury UK, 18th December 1956