Danczul, T., & Schöberl, J. (2022). A reduced basis method for fractional diffusion operators I. Numerische Mathematik, 151(2), 369–404. https://doi.org/10.1007/s00211-022-01287-y
E101-03-1 - Forschungsgruppe Computational Mathematics in Engineering
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Journal:
Numerische Mathematik
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ISSN:
0029-599X
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Date (published):
7-May-2022
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Number of Pages:
36
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Publisher:
SPRINGER HEIDELBERG
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Peer reviewed:
Yes
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Keywords:
Fractional diffusion; Reduced basis method; Hilbert space interpolation
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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 (I-ti2Δ)-1f, which can be computed in parallel. We prove exponential convergence rates for the optimal choice of sampling points ti, provided by the so-called Zolotarëv points. Numerical experiments confirm the analysis and demonstrate the efficiency of our algorithm.
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Project title:
Automatisierte Diskretisierung in der Multiphysik: F 6511-N36 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) Doktoratskolleg "Dissipation and Dispersion in Nonlinear Partial Differential Equations": W1245-N25 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
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Research Areas:
Mathematical and Algorithmic Foundations: 5% Modeling and Simulation: 95%
