4 papers
A Unified Rational Krylov Method for Elliptic and Parabolic Fractional Diffusion Problems
Tobias Danczul, Clemens Hofreither, Joachim Schöberl
We present a unified framework to efficiently approximate solutions to fractional diffusion problems of stationary and parabolic type. After discretization, we can take the point o…
On Rational Krylov and Reduced Basis Methods for Fractional Diffusion
Tobias Danczul, Clemens Hofreither
We establish an equivalence between two classes of methods for solving fractional diffusion problems, namely, Reduced Basis Methods (RBM) and Rational Krylov Methods (RKM). In part…
A Reduced Basis Method For Fractional Diffusion Operators II
Tobias Danczul, Joachim Schöberl
We present a novel numerical scheme to approximate the solution map to partial differential equations involving fractional elliptic operators.…
A Reduced Basis Method For Fractional Diffusion Operators I
Tobias Danczul, Joachim Schöberl
We propose and analyze new numerical methods to evaluate fractional norms and apply fractional powers of elliptic operators. By means of a reduced basis method, we project to a sma…