TY - JOUR
T1 - ROBUST BPX PRECONDITIONER FOR FRACTIONAL LAPLACIANS ON BOUNDED LIPSCHITZ DOMAINS
AU - Borthagaray, Juan Pablo
AU - Nochetto, Ricardo H.
AU - Wu, Shuonan
AU - Xu, Jinchao
N1 - Publisher Copyright:
© 2023 American Mathematical Society
PY - 2023
Y1 - 2023
N2 - 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.
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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U2 - 10.1090/mcom/3857
DO - 10.1090/mcom/3857
M3 - Article
AN - SCOPUS:85170714785
SN - 0025-5718
VL - 92
SP - 2439
EP - 2473
JO - Mathematics of Computation
JF - Mathematics of Computation
IS - 344
ER -