We describe and compare some recent domain decomposition algorithms of Schwarz type with respect to parallel performance. A new, robust domain decomposition algorithm { Additive Average Schwarz is compared with a classical overlapping Schwarz code. Complexity estimates are given in both two and three dimensions and actual implementations are compared on a Paragon machine as well as on a cluster...

This paper focuses on the acceleration of Schwarz method by Aitken’s convergence technique considering special structure Schwarz’s error operator between two consecutive iterates domain decomposition’s interfaces. The new proposed method, called Sparse Aitken-Schwarz builds a low-rank space for each subdomain to approximate true solution its interfaces instead building associated gathered subdo...

We focus on high order edge element approximations of waveguide problems. For the associated linear systems, we analyze the impact of two Schwarz preconditioners, the Optimized Additive Schwarz (OAS) and the Optimized Restricted Additive Schwarz (ORAS), on the convergence of the iterative solver.

The type specimens of Elateridae described by Otto Schwarz from Mesoamerica are redescribed, reassessed and lectotypes designated. Acanthathous championi (Schwarz), Smiliceroides quadrilineatus Anoplischiopsis divisus Schwarz, Anoplischius dorsalis Atractosomus nigerrimus Anchastomorphus minutus retained in their current status. Monocrepidius restinctus is reduced to synonymy under rugicollis C...

In the paper [7] we defined a map, called the hyperbolic Schwarz map, from the one-dimensional projective space to the three-dimensional hyperbolic space by use of solutions of the hypergeometric differential equation, and thus obtained closed flat surfaces belonging to the class of flat fronts. We continue the study of such flat fronts in this paper. First, we introduce the notion of derived S...

Abstract The classical Schwarz alternating method has recently been generalized in several directions This e ort has resulted in a number of new powerful domain decomposition methods for elliptic problems in new insight into multigrid methods and in the development of a very useful framework for the analysis of a variety of iterative methods Most of this work has focused on positive de nite sym...

In this paper, we partially answer open questions about the convergence of overlapping Schwarz methods. We prove that overlapping Schwarz methods with Dirichlet transmission conditions for semilinear elliptic and parabolic equations always converge, while overlapping Schwarz methods with Robin transmission conditions only converge for semilinear parabolic equations, but the convergence is not g...