A Reduced Basis Method For Fractional Diffusion Operators I

Tobias Danczul; Joachim Schöberl

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arXiv · 1904.05599

A Reduced Basis Method For Fractional Diffusion Operators I

Tobias Danczul·Joachim Schöberl

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Abstract

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 small dimensional subspace where explicit diagonalization via the eigensystem is feasible. The method relies on several independent evaluations of $(\textrm{I}-t_i^2\Delta)^{-1}f$, which can be computed in parallel. We prove exponential convergence rates for the optimal choice of sampling points $t_i$, provided by the so-called Zolotar\"ev points. Numerical experiments confirm the analysis and demonstrate the efficiency of our algorithm.

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Tobias Danczul, Joachim Schöberl. 2019-04-11. A Reduced Basis Method For Fractional Diffusion Operators I. https://arxiv.org/abs/1904.05599

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