MULTIPLICATIVE SCHWARZ ALGORITHMS FOR SOME NONSYMMETRIC AND INDEFINITE PROBLEMS

Authors
Citation
Xc. Cai et Ob. Widlund, MULTIPLICATIVE SCHWARZ ALGORITHMS FOR SOME NONSYMMETRIC AND INDEFINITE PROBLEMS, SIAM journal on numerical analysis, 30(4), 1993, pp. 936-952
Citations number
40
Categorie Soggetti
Mathematics,Mathematics
ISSN journal
00361429
Volume
30
Issue
4
Year of publication
1993
Pages
936 - 952
Database
ISI
SICI code
0036-1429(1993)30:4<936:MSAFSN>2.0.ZU;2-E
Abstract
The classical Schwarz alternating method has recently been generalized in several directions. This effort has resulted in a number of new po werful domain decomposition methods for elliptic problems, in new insi ght into multigrid methods, and in the development of a very useful fr amework for the analysis of a variety of iterative methods. Most of th is work has focused on positive definite, symmetric problems. In this paper, a general framework is developed for multiplicative Schwarz alg orithms for nonsymmetric and indefinite problems. Several applications are then discussed including two- and multilevel Schwarz methods and iterative substructuring algorithms. Some new results on additive Schw arz methods are also presented.