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
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.