Electromagnetic Theory and Computation : A Topological Approach

A Topological Approach

By: Paul W. Gross, P. Robert Kotiuga, Gross

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Paperback | 1 September 2010

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290 Pages

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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.

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From vector calculus to algebraic topology
Quasistatic electromagnetic fields
Duality theorems for manifolds with boundary
The finite element method and data structures
Computing eddy currents on thin conductors with scalar potentials
An algorithm to make cuts for magnetic scalar potentials
A paradigm problem
Table of Contents provided by Publisher. All Rights Reserved.

Electromagnetic Theory and Computation : A Topological Approach

A Topological Approach

At a Glance

Paperback

Shipping

How to return your order

Defective items

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