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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Electromagnetic Theory and Computation: A Topological Approach

Electromagnetic Theory and Computation: A Topological Approach

Gross, Paul W.
Kotiuga, P. Robert
Gross

Paperback

Series: Mathematical Sciences Research Institute Publications, Book 48

General MathematicsGeometryPhysics

ISBN10: 0521175232
ISBN13: 9780521175234
Publisher: Cambridge University Press
Published: Apr 28 2011
Pages: 290
Weight: 0.90
Height: 0.61 Width: 6.14 Depth: 9.21
Language: English
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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