| Electromagnetic Theory and Computation: A Topological Approach Contributor(s): Gross, Paul W. (Author), Kotiuga, P. Robert (Author) |
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ISBN: 051175633X ISBN-13: 9780511756337 Publisher: Cambridge University Press OUR PRICE: $140.25 Product Type: Open Ebook - Other Formats Published: July 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Topology - General |
| Dewey: 514 |
| Series: Mathematical Sciences Research Institute Publications |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 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. |