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Title
A reduced basis method for fractional diffusion operators / Tobias Danczul
AuthorDanczul, Tobias
CensorSchöberl, Joachim
PublishedWien, 2018
DescriptionV, 57 Seiten : Illustrationen, Diagramme
Institutional NoteTechnische Universität Wien, Diplomarbeit, 2018
LanguageEnglish
Document typeThesis (Diplom)
Keywords (EN)Fractional Diffusion / Reduced Basis Method
URNurn:nbn:at:at-ubtuw:1-112880 Persistent Identifier (URN)
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 The work is publicly available
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A reduced basis method for fractional diffusion operators [2.12 mb]
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Abstract (German)

in Englisch

Abstract (English)

Several authors have proposed and analyzed numerical methods for fractional differential oper- ators, in particular Fourier Galerkin schemes and Caffarelli-Silvestre extensions. In this thesis we consider a different approach. By means of a reduced basis method, the desired operator is projected to a low dimensional space V r , where the fractional power can be directly evaluated via the eigen-system. The optimal choice of V r is provided by the so called Zolotarëv points, en- suring exponential convergence. Numerical experiments evaluating the operator and the inverse operator confirm the analysis. The time-dependent Fractional Cahn-Hilliard Equation (FCHE) is examined for further tests. By a splitting method, the non-linear operator is decoupled from the regular Laplacian, such that the linear parabolic equation is solved exactly on the low dimensional reduced space. Different choices of the fractional power s are discussed and tested.

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