Electromagnetic Theory and Computation: A Topological Approach: 48 - Rilegato

Gross, Paul W.; Kotiuga, P. Robert

Rilegato

ISBN 10: 0521801605 ISBN 13: 9780521801607

Casa editrice: Cambridge University Press, 2004

Riassunto

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.

Su questo libro

Descrizione del libro:

This book explores the connection between algebraic structures in topology and computational methods for 3-dimensional electric and magnetic field computation. Although a connection between topology and electromagnetism has been known since the 1800s, there has been very little exposition of it. This book takes steps to close that gap.

Contenuti:

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.

Su questa edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 2004
• ISBN 10: 0521801605
• ISBN 13: 9780521801607
• Rilegatura: Copertina rigida
• Numero di pagine: 284