Diploma and Master Theses (authored and supervised):
"A Reduced Basis Method For Fractional Diffusion Operators";
Supervisor: J. Schöberl, M. Blümlinger;
Institut für Analysis und Scientific Computing,
final examination: 2018-06-14.
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.
Created from the Publication Database of the Vienna University of Technology.