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Electromagnetic Theory and Computation: A Topological Approach. Mathematical Sciences Research Institute Publications 48.

Author: Gross, Paul W.; P Robert Kotiuga
Publisher: Cambridge University Press 2004.
Edition/Format:   eBook : Document : English
Database:WorldCat
Summary:
Although topology was recognized by Gauss and Maxwell to play apivotal 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  Read more...
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Details

Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Gross, Paul W.; P Robert Kotiuga
ISBN: 128054127X 9781280541278
OCLC Number: 819634886
Description: 1 online resource (288 p.)

Abstract:

Although topology was recognized by Gauss and Maxwell to play apivotal 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 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. Appendices bridge the gap between the material presented and standard expositions of differential forms, Hodge decompositions, and tools for realizing representatives of homology classes as embedded manifolds.

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