The paper is devoted to the numerical solution of both elliptic and parabolic problems by overlapping Schwarz methods. It demonstrates that while the two-level Schwarz method is necessary for the efficient solution of discrete elliptic problems, the one-level Schwarz method can be sufficiently...

This paper addresses the use of space decomposition preconditioners for the numerical solution of boundary value problems. As special cases, it deals with the displacement decomposition (DiD) and overlapping domain decomposition (DD) preconditioners. A special attention is also devoted to...