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\({\mathscr{H}}\)-matrix approximability of inverses of discretizations of the fractional Laplacian

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Abstract

The integral version of the fractional Laplacian on a bounded domain is discretized by a Galerkin approximation based on piecewise linear functions on a quasiuniform mesh. We show that the inverse of the associated stiffness matrix can be approximated by blockwise low-rank matrices at an exponential rate in the block rank.

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Funding

MK was supported by Conicyt Chile through project FONDECYT 1170672. JMM was supported by the Austrian Science Fund (FWF) project F 65.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile

    Michael Karkulik

  2. Institut für Analysis und Scientific Computing, Technische Universität Wien, Wiedner Hauptstrasse 8-10, Vienna, Austria

    Jens Markus Melenk

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  1. Michael Karkulik
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  2. Jens Markus Melenk
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Correspondence to Michael Karkulik.

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Communicated by: Ivan Oseledets

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Karkulik, M., Melenk, J.M. \({\mathscr{H}}\)-matrix approximability of inverses of discretizations of the fractional Laplacian. Adv Comput Math 45, 2893–2919 (2019). https://doi.org/10.1007/s10444-019-09718-5

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