Electromagnetic Theory and Computation: A Topological Approach

by Paul W. Gross , P. Robert Kotiuga

• ISBN13: 9780521175234
• ISBN10: 0521175232
• Edition: Reprint
• Format: Paperback
• Copyright: 2011-04-28
• Publisher: Cambridge University Press

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.

Table of Contents

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

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