ROBUST BPX PRECONDITIONER FOR FRACTIONAL LAPLACIANS ON BOUNDED LIPSCHITZ DOMAINS

Juan Pablo Borthagaray; Ricardo H. Nochetto; Shuonan Wu; Jinchao Xu

doi:10.1090/mcom/3857

ROBUST BPX PRECONDITIONER FOR FRACTIONAL LAPLACIANS ON BOUNDED LIPSCHITZ DOMAINS

Juan Pablo Borthagaray, Ricardo H. Nochetto, Shuonan Wu, Jinchao Xu

Applied Mathematics and Computational Science

Research output: Contribution to journal › Article › peer-review

Abstract

We propose and analyze a robust Bramble-Pasciak-Xu (BPX) preconditioner for the integral fractional Laplacian of order s ∈ (0, 1) on bounded Lipschitz domains. Compared with the standard BPX preconditioner, an additional scaling factor 1 − ˜γ^s, for some fixed ˜γ ∈ (0, 1), is incorporated to the coarse levels. For either quasi-uniform grids or graded bisection grids, we show that the condition numbers of the resulting systems remain uniformly bounded with respect to both the number of levels and the fractional power.

Original language	English (US)
Pages (from-to)	2439-2473
Number of pages	35
Journal	MATHEMATICS OF COMPUTATION
Volume	92
Issue number	344
DOIs	https://doi.org/10.1090/mcom/3857
State	Published - 2023

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© 2023 American Mathematical Society

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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abstract = "We propose and analyze a robust Bramble-Pasciak-Xu (BPX) preconditioner for the integral fractional Laplacian of order s ∈ (0, 1) on bounded Lipschitz domains. Compared with the standard BPX preconditioner, an additional scaling factor 1 − ˜γs, for some fixed ˜γ ∈ (0, 1), is incorporated to the coarse levels. For either quasi-uniform grids or graded bisection grids, we show that the condition numbers of the resulting systems remain uniformly bounded with respect to both the number of levels and the fractional power.",

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AU - Wu, Shuonan

AU - Xu, Jinchao

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AB - We propose and analyze a robust Bramble-Pasciak-Xu (BPX) preconditioner for the integral fractional Laplacian of order s ∈ (0, 1) on bounded Lipschitz domains. Compared with the standard BPX preconditioner, an additional scaling factor 1 − ˜γs, for some fixed ˜γ ∈ (0, 1), is incorporated to the coarse levels. For either quasi-uniform grids or graded bisection grids, we show that the condition numbers of the resulting systems remain uniformly bounded with respect to both the number of levels and the fractional power.

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JF - MATHEMATICS OF COMPUTATION

IS - 344

ER -

ROBUST BPX PRECONDITIONER FOR FRACTIONAL LAPLACIANS ON BOUNDED LIPSCHITZ DOMAINS

Abstract

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