Acceleration of the non-symmetrized two-level iteration Original Research Article

In this paper we discuss two-level multiplicative Schwarz methods, which result in unsymmetric systems in their solution spaces. We introduce a new algorithm to accelerate this iteration by applying the conjugate gradient (CG) scheme to a subspace. It will be shown that this algorithm possesses a CG-type convergence rate. Our algorithm has obvious advantages over the existing Schwarz-CG algorithms. Its application to two-level grid methods will be also considered.