The problem of constructing a conformal mapping from the upper half-plane to circular polygon is considered. preimages vertices and accessory parameters are determined by generalized method P. Kufarev for determining in Christoffel–Schwarz integral. based on Loewner equation with boundary normalization. onto exterior consisting straight-line segments solved separately. Examples mappings whose f...

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...

We consider a multigrid method for solving the discretized optimality system of a PDE-constrained optimization problem. In particular, we discuss the construction of an additive Schwarz-type smoother for a class of elliptic optimal control problems. A rigorous multigrid convergence analysis yields level-independent convergence rates. Numerical experiments indicate that the convergence rates are...

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...

We consider a scalar wave propagation in harmonic regime modelled by Helmholtz equation with heterogeneous coefficients. Using the Multi-Trace Formalism (MTF), we propose new variant of Optimized Schwarz Method (OSM) that remains valid presence cross-points subdomain partition. This leads to derivation strongly coercive formulation our problem posed on union all interfaces. The corresponding op...

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...