H-matrix approximability of inverses of discretizations of the fractional Laplacian

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...

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Bibliographic Details
Published inAdvances in computational mathematics Vol. 45; no. 5-6; pp. 2893 - 2919
Main Authors Karkulik, Michael, Melenk, Jens Markus
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2019
Springer Nature B.V
Subjects
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Discretization
Galerkin method
Linear functions
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Stiffness matrix
Visualization
65F50
Hierarchical matrices
Fractional Laplacian
65F30
65N30
65F05
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Summary: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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ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-019-09718-5