Diploma and Master Theses (authored and supervised):

T. Danczul:
"A Reduced Basis Method For Fractional Diffusion Operators";
Supervisor: J. Schöberl, M. Blümlinger; Institut für Analysis und Scientific Computing, 2018; final examination: 2018-06-14.

English abstract:
Several authors have proposed and analyzed numerical methods for fractional differential operators, in particular Fourier Galerkin schemes and Gaffarelli-Silvestre extensions. In this thesis we consider a different approach. By means of a reduced basis method, the desired opeator is projected to a low dimensional space Vr, where the fractional power can be directly evaluated via the eigen-system. The optimal choice of Vr is provided by the so called Zolotarev points, ensuring exponential convergence. Numerical experiments evaluating the operator and the inverse operator confirm the analysis.

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