TY - JOUR
T1 - Adaptive aggregation on graphs
AU - Xu, Wenfang
AU - Zikatanov, Ludmil T.
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - We generalize some of the functional (hypercircle) a posteriori estimates from finite element settings to general graphs or Hilbert space settings. Several theoretical results in regard to the generalized a posteriori error estimators are provided. We use these estimates to construct aggregation based coarse spaces for graph Laplacians. The estimator is used to assess the quality of an aggregation adaptively. Furthermore, a reshaping based algorithm is tested on several numerical examples.
AB - We generalize some of the functional (hypercircle) a posteriori estimates from finite element settings to general graphs or Hilbert space settings. Several theoretical results in regard to the generalized a posteriori error estimators are provided. We use these estimates to construct aggregation based coarse spaces for graph Laplacians. The estimator is used to assess the quality of an aggregation adaptively. Furthermore, a reshaping based algorithm is tested on several numerical examples.
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U2 - 10.1016/j.cam.2017.10.032
DO - 10.1016/j.cam.2017.10.032
M3 - Article
AN - SCOPUS:85034655541
VL - 340
SP - 718
EP - 730
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
ER -