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Electromagnetic Theory and Computation - A Topological Approach (Paperback)
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Electromagnetic Theory and Computation - A Topological Approach (Paperback)
Series: Mathematical Sciences Research Institute Publications
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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.
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