Finite Element Methods for Maxwells Equations

Hardcover | August 26, 2003

byPeter Monk

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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 computationalelectromagnetism 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 computationalelectromagnetism. 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 areparticularly 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.

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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 computationalelectromagnetism there has also been considerable progress ...

Prof. P. Monk Department of Mathematical Sciences University of Delaware Newark DE 19716 USA Tel +1-302-831-1873 Fax +1-302-831-4511 monk@udel.edu UNIDEL Professor of Mathematical Sciences, University of Delaware, USA British, Shrewsbury UK, 18th December 1956

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Format:HardcoverDimensions:464 pages, 9.21 × 6.14 × 1.19 inPublished:August 26, 2003Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198508883

ISBN - 13:9780198508885

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Table of Contents

1. Mathematical Models of Electromagnetism2. Functional Analysis and Abstract Error Estimates3. Sobolev, Spaces, Vector Function Spaces and Regularity4. Variational Theory for the Cavity Problem5. Finite Elements on Tetrahedra6. Finite Elements on Hexahedra7. Finite Element Methods for the Cavity Problem8. Topics Concerning Finite Elements9. Classical Scattering Theory10. A First Variational Method for the Scattering Problem11. Scattering by a Bounded Inhomogeneity12. Scattering by a Buried Object13. Implementation and Algorithmic Development14. Inverse ProblemsAppendix