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Konečné prvky v elektromagnetismu kompatibilní s De Rhamovým diagramem / Konečné prvky v elektromagnetismu kompatibilní s De Rhamovým diagramem

Title: Finite elements for electromagnetics compatible with de Rham di- agram Author: Vojtěch Rybář Department: Department of Numerical Mathematics Supervisor: prof. Ing. Ivo Doležel, CSc. Abstract: The present work is devoted to the lowest-order finite elements for solving time-harmonic Maxwell's equations in two dimensions. Suc- cessful approximation of these equations requires the finite element spaces to be compatible with the de Rham diagram. However, the most often used basis functions (the Whitney functions) do not comply with this diagram. Therefore, we construct compatible bases and study their prop- erties. Since the construction is not unique, we investigate the influence of the particular choice on the conditioning of the corresponding finite element matrices. Finally, we utilize the special structure of the stiffness matrices, propose a few iterative schemes, and compare their convergence. Keywords: Maxwell's equations, edge finite element, de Rham diagram, finite element basis 1

Identiferoai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:296438
Date January 2011
CreatorsRybář, Vojtěch
ContributorsDoležel, Ivo, Vejchodský, Tomáš
Source SetsCzech ETDs
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/masterThesis
Rightsinfo:eu-repo/semantics/restrictedAccess

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