Nonino, Isacco (2019) A combinatorial approach to PoincarÃ© duality and De Rham isomorphism: an application to electrodynamics. [Laurea triennale]
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Computing eddy currents over conductors (i.e computing line integrals for particular closed 1-forms) is usually a very demanding problem in terms of computational time. During the last years a new computational approach to the solution of Maxwell's equations called the Discrete Geometric Approach (DGA) has been proposed. This particular method relies on the topological nature of Maxwell's equations together with their geometric structure. The aim of this thesis is to introduce the mathematical concepts and tools used by this new computational method. We will analyze the topological foundation of the DGA, describing how the link between a 1-form and the homology of the manifold is created.
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