MULTIPLICATIVE SCHWARZ ALGORITHMS FOR SOME NONSYMMETRIC AND INDEFINITE PROBLEMS

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.