Electromagnetic theory and computation : a topological approach

Bibliographic Information

Electromagnetic theory and computation : a topological approach

Paul W. Gross, P. Robert Kotiuga

(Mathematical Sciences Research Institute publications, 48)

Cambridge University Press, 2011, c2004

  • : pbk

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Note

Includes bibliographical references (p. 261-266) and index

Description and Table of Contents

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.

Table of Contents

  • 1. From vector calculus to algebraic topology
  • 2. Quasistatic electromagnetic fields
  • 3. Duality theorems for manifolds with boundary
  • 4. The finite element method and data structures
  • 5. Computing eddy currents on thin conductors with scalar potentials
  • 6. An algorithm to make cuts for magnetic scalar potentials
  • 7. A paradigm problem.

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Details
  • NCID
    BB08337439
  • ISBN
    • 9780521175234
  • Country Code
    uk
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cambridge
  • Pages/Volumes
    ix, 278 p.
  • Size
    24 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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