Differential Geometry in Computational Electromagnetics
Forgy, Eric Alan
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https://hdl.handle.net/2142/80788
Description
Title
Differential Geometry in Computational Electromagnetics
Author(s)
Forgy, Eric Alan
Issue Date
2002
Doctoral Committee Chair(s)
Chew, Weng Cho
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
The algebraic model of Part II represents a somewhat radical approach to computation. In this approach, rather than take the classical theory based on the continuum as a given and constructing approximate numerical techniques from there, work is done toward constructing an alternative to the continuum theory that is built up from scratch in a discrete setting. The goal is to take each mathematical objects that is necessary in order to write down the classical electromagnetic theory and develop a corresponding discrete analog. The theory builds upon standard concepts in algebraic topology and is motivated by recent progress in noncommutative differential geometry.
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