Analysis of two-level domain decomposition preconditioners based on aggregation

被引:7
作者
Sala, M [1 ]
机构
[1] Ecole Polytech Fed Lausanne, SB, CMCS, CH-1015 Lausanne, Switzerland
来源
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2004年 / 38卷 / 05期
关键词
elliptic equations; domain decomposition; Schwarz methods; aggregation coarse corrections;
D O I
10.1051/m2an:2004038
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:765 / 780
页数:16
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