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.
Homology in Electromagnetic Boundary Value Problems
Quasistatic Electromagnetic Fields. Duality Theorems for Manifolds With Boundary. A Paradigm Problem.
Manifolds Differential Forms Cohomology. Summary of Notation.
Examples and Tables. Gross , P. From Vector Calculus to Algebraic Topology.
Gross, Paul W.; Kotiuga, P. Robert
Saunders MacLane. Carl de Boor. Bruce Blackadar. Alan H. Emmanuel Breuillard. Calvin C. Yiannis N. Roger C. Robert L. Paul Concus. Greg Friedman.
Electromagnetic Theory and Computation | Marek Lewinson
Silvio Levy. Pavel M. Susan Montgomery. Klaus Kirsten. Richard J. David Dai-Wai Bao.
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Electromagnetic Theory and Computation : A Topological Approach
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.