Multilevel additive schwarz methods for nonsymmetric and indefinite elliptic problems

Abstract

Multilevel additive Schwarz methods are domain decomposition techniques. These methods are parallel algorithms and hence can be powerful in parallel computers. We apply it for the nonsymmetric and indefinite elliptic problems. The iterative scheme is the GMRES method. We prove that the number of iterations is independent of the mesh sizes and the number of levels. We give some numerical experiments for our theory.