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Author Gross, Paul W. (Paul Wolfgang), 1967-

Title Electromagnetic theory and computation : a topological approach / Paul W. Gross, P. Robert Kotiuga.

Imprint Cambridge, UK ; New York : Cambridge University Press, ©2004.

Item Status

Description 1 online resource (ix, 278 pages) : illustrations.
Series Mathematical Sciences Research Institute publications ; 48
Mathematical Sciences Research Institute publications ; 48.
Bibliography Includes bibliographical references (pages 261-266) and index.
Contents 1. From vector calculus to algebraic topology -- 2. Quasistatic electromagnetic fields -- 3. Duality theorems for manifolds with boundary -- 4. The finite element method and data structures -- 5. Computing eddy currents on thin conductors with scalar potentials -- 6. An algorithm to make cuts for magnetic scalar potentials -- 7. A paradigm problem -- Mathematical appendix: Manifolds, differential forms, cohomology, Riemannian structures.
Summary Although topology was recognized by Gauss and Maxwell to play a pivotal role in the formulation of electromagnetic boundary value problems, it is a largely unexploited tool for field computation. The development of algebraic topology since Maxwell provides a framework for linking data structures, algorithms, and computation to topological aspects of three-dimensional electromagnetic boundary value problems. This book, first published in 2004, attempts to expose the link between Maxwell and a modern approach to algorithms. The first chapters lay out the relevant facts about homology and cohomology, stressing their interpretations in electromagnetism. These topological structures are subsequently tied to variational formulations in electromagnetics, the finite element method, algorithms, and certain aspects of numerical linear algebra. A recurring theme is the formulation of and algorithms for the problem of making branch cuts for computing magnetic scalar potentials and eddy currents.
Local Note eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America
Subject Electromagnetic theory.
Genre/Form Electronic books.
Electronic books.
Added Author Kotiuga, P. Robert (Peter Robert), 1958-
Other Form: Print version: Gross, Paul W. (Paul Wolfgang), 1967- Electromagnetic theory and computation. Cambridge, UK ; New York : Cambridge University Press, ©2004 0521801605 (DLC) 2004052644 (OCoLC)55588045
ISBN 9781601197405 (electronic bk.)
1601197403 (electronic bk.)
0511216890 (electronic bk.)
9780511216893 (electronic bk.)
0511207948 (electronic bk. ; Adobe Reader)
9780511207945 (electronic bk. ; Adobe Reader)
051121510X (electronic bk.)
9780511215100 (electronic bk.)
9780511756337 (ebook)
051175633X (ebook)
9780511211522 (e-book)
051121152X (e-book)