J. Lottes and P. Fischer in [J. Sci. Comput., 24:45–78, 2005] studied many smoothers or preconditioners for hybrid Multigrid-Schwarz algorithms for the spectral element method. The behavior of several of these smoothers or preconditioners are analyzed in the present paper. Here it is shown that the Schwarz smoother that best performs in the above reference, is equivalent to a special case of th...

Convergence properties are presented for Newton additive and multiplicative Schwarz iterative methods for the solution of nonlinear systems in several variables. These methods consist of approximate solutions of the linear Newton step using either additive or multiplicative Schwarz iterations, where overlap between subdomains can be used. Restricted versions of these methods are also considered...

The convergence of additive and multiplicative Schwarz methods for computing certain characteristics of Markov chains such as stationary probability vectors and mean first passage matrices is studied. Our main result is a convergence theorem for multiplicative Schwarz iterations when applied to singular systems. As a by-product we also obtain a convergence result for alternating iterations. It ...

The Schwarz alternating method can be used to solve linear elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an innnite sequence of functions which result from solving a sequence of elliptic boundary value problems in each of the subdomains. This paper considers four Schwarz alternating methods for the N-dimensional,...

We write down one-to-one mappings between the singular vectors of the Neveu-Schwarz N=2 superconformal algebra and 16 + 16 types of singular vectors of the Topological and of the Ramond N=2 superconformal algebras. As a result one obtains construction formulae for the latter using the construction formulae for the Neveu-Schwarz singular vectors due to Dörrzapf. The indecomposable singular vecto...

We propose a non-overlapping Schwarz algorithm for solving “Discrete Duality Finite Volume” schemes (DDFV for short) on general meshes. In order to handle this problem, the first step is to propose and study a convenient DDFV scheme for anisotropic elliptic problems with mixed Dirichlet/Fourier boundary conditions. Then, we are able to build the corresponding Schwarz algorithm and to prove its ...

The Schwarz map of the hypergeometric differential equation is studied since the beginning of the last century. Its target is the complex projective line, the 2-sphere. This paper introduces the hyperbolic Schwarz map, whose target is the hyperbolic 3-space. This map can be considered to be a lifting to the 3-space of the Schwarz map. This paper studies the singularities of this map, and visual...

This paper derives a linear convergence for the Schwarz overlapping domain decomposition method when applied to constrained minimization problems. The convergence analysis is based on a minimization approach to the corresponding functional over a convex set. A general framework of convergence is established for some multiplicative Schwarz algorithm. The abstract theory is particularly applied t...

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