In this paper we present two-level overlapping domain decomposition preconditioners for the finite-element discretisation of elliptic problems in two and three dimensions. The computational domain is partitioned into overlapping subdomains, and a coarse space correction is added. We present an algebraic way to define the coarse space, based on the concept of aggregation. This employs a (smoothed) aggregation technique and does not require the introduction of a coarse grid. We consider a set of assumptions on the coarse basis functions, to ensure bound for the resulting preconditioned system. These assumptions only involve geometrical quantities associated to the aggregates, namely their diameter and the overlap. A condition number which depends on the product of the relative overlap among the subdomains and the relative overlap among the aggregates is proved. Numerical experiments on a model problem are reported to illustrate the performance of the proposed preconditioners.
Mots-clés : elliptic equations, domain decomposition, Schwarz methods, aggregation coarse corrections
@article{M2AN_2004__38_5_765_0,
author = {Sala, Marzio},
title = {Analysis of two-level domain decomposition preconditioners based on aggregation},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {765--780},
publisher = {EDP-Sciences},
volume = {38},
number = {5},
year = {2004},
doi = {10.1051/m2an:2004038},
mrnumber = {2104428},
zbl = {1078.65120},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2004038/}
}
TY - JOUR AU - Sala, Marzio TI - Analysis of two-level domain decomposition preconditioners based on aggregation JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 765 EP - 780 VL - 38 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2004038/ DO - 10.1051/m2an:2004038 LA - en ID - M2AN_2004__38_5_765_0 ER -
%0 Journal Article %A Sala, Marzio %T Analysis of two-level domain decomposition preconditioners based on aggregation %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 765-780 %V 38 %N 5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2004038/ %R 10.1051/m2an:2004038 %G en %F M2AN_2004__38_5_765_0
Sala, Marzio. Analysis of two-level domain decomposition preconditioners based on aggregation. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 5, pp. 765-780. doi : 10.1051/m2an:2004038. http://archive.numdam.org/articles/10.1051/m2an:2004038/
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