Electromagnetic Theory and Computation: A Topological Approach (Mathematical Sciences Research Institute Publications) [Hardcover]

Paul W. Gross (Author), P. Robert Kotiuga (Author)

Book Description

Publication Date: June 14, 2004 | ISBN-10: 0521801605 | ISBN-13: 978-0521801607

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.

Editorial Reviews

Book Description

This book explores the connection between algebraic structures in topology and computational methods for 3-dimensional electric and magnetic field computation. The connection between topology and electromagnetism has been known since the 19th century, but there has been little exposition of its relevance to computational methods in modern topological language. This book is an effort to close that gap. It will be of interest to people working in finite element methods for electromagnetic computation and those who have an interest in numerical and industrial applications of algebraic topology.

Product Details

• Hardcover: 288 pages
• Publisher: Cambridge University Press (June 14, 2004)
• Language: English
• ISBN-10: 0521801605
• ISBN-13: 978-0521801607
• Product Dimensions: 9.5 x 6.4 x 0.8 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #3,184,561 in Books (See Top 100 in Books)

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