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T. Danczul:
"Model Order Reduction for Fractional Diffusion Problems";
Supervisor, Reviewer: J. Schöberl, A. Bonito, G. Rozza; Institut für Analysis und Scientific Computing, 2021; oral examination: 2021-12-01.

Abstract
In this thesis we present a unified framework to efficiently approximate solutions to fractional diffusion problems of elliptic and parabolic type. After finite element discretization, we take the point of view that the solution is obtained by a matrix-vector product of the form fτ(L)b, where L is the discretization matrix of the spatial operator, b a prescribed vector,and fτa parametric function, such as a fractional power or the Mittag-Leffler function.
To alleviate the computational expenses, a model order reduction strategy in the form of a rational Krylov method is applied which projects the matrix to a low-dimensional space where a direct evaluation of the eigensystem is feasible.