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

  • Michael KarkulikEmail author
  • Jens Markus Melenk
Article
  • 23 Downloads

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.

Keywords

Hierarchical matrices Fractional Laplacian 

Mathematics Subject Classification (2010)

65N30 65F05 65F30 65F50 

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Notes

Funding information

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidad Técnica Federico Santa MaríaValparaísoChile
  2. 2.Institut für Analysis und Scientific ComputingTechnische Universität WienViennaAustria

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