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Robust BPX Preconditioner for Fractional Laplacians on Bounded Lipschitz Domains

Numerical Analysis 2021-06-04 v2 Numerical Analysis

Abstract

We propose and analyze a robust BPX preconditioner for the integral fractional Laplacian on bounded Lipschitz domains. 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. The results apply also to the spectral and censored fractional Laplacians.

Keywords

Cite

@article{arxiv.2103.12891,
  title  = {Robust BPX Preconditioner for Fractional Laplacians on Bounded Lipschitz Domains},
  author = {Juan Pablo Borthagaray and Ricardo H. Nochetto and Shuonan Wu and Jinchao Xu},
  journal= {arXiv preprint arXiv:2103.12891},
  year   = {2021}
}