In this paper, we study some Schwarz methods of Neumann–Neumann type for some vector field problems, discretized with the lowest order Raviart–Thomas and Nédélec finite elements. We consider a hybrid Schwarz preconditioner consisting of a coarse component, which involves the solution of the original problem on a coarse mesh, and local ones, which involve the solution of Neumann problems on the ...

During the last two decades many domain decomposition algorithms have been con8 structed and lot of techniques have been developed to prove the convergence of the 9 algorithms at the continuous level. Among the techniques used to prove the conver10 gence of classical Schwarz algorithms, the first technique is the maximum principle 11 used by Schwarz. Adopting this technique M. Gander and H. Zha...

SUMMARY Solving boundary value problems with optimal eeciency requires adaptivity and multilevel techniques. In 7] an implementation of the AFACx algorithm (cf. 9]) is presented that is based on rectangular cartesian grids. This implementation does not allow for overlap of grids that lie on the same level of reenement. We investigate the case where these grids can overlap. A standard technique ...

Abstract. Optimized Schwarz methods perform better than classical Schwarz methods because 6 they use more e↵ective transmission conditions between subdomains. These transmission conditions 7 are determined by optimizing the convergence factor, which is obtained by Fourier analysis for simple 8 two subdomain model problems. Such optimizations have been performed for many di↵erent types of 9 part...

In this paper we study several overlapping domain decompo sition based iterative algorithms for the numerical solution of some non linear strongly elliptic equations discretized by the nite element methods In particular we consider additive Schwarz algorithms used together with the classical inexact Newton methods We show that the algorithms con verge and the convergence rates are independent o...

In recent years competitive domain decomposed preconditioned iterative tech niques have been developed for nonsymmetric elliptic problems In these tech niques a large problem is divided into many smaller problems whose requirements for coordination can be controlled to allow e ective solution on parallel machines A central question is how to choose these small problems and how to arrange the or...

We propose an integrable bootstrap framework for the computation of correlation functions superstrings in $AdS_3\times S^3\times T^4$ backgrounds supported by arbitrary mixture or Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz fluxes. The extends "hexagon tessellation" approach which was originally proposed $AdS_5\times S^5$ first time it demonstrates its applicability to other (less supersymmet...

Over the last five years, classical and optimized Schwarz methods have been developed for (1) discretized with Discrete Duality Finite Volume (DDFV) schemes. Like for Discontinuous Galerkin methods, it is not a priori clear how to appropriately discretize transmission conditions. Two versions have been proposed for Robin transmission conditions in [? ] and [? ]. Only the second one leads to the...

As many domain decomposition methods the two level Additive Schwarz method may suffer from a lack of robustness with respect to coefficient variation in the underlying set of PDEs. This is the case in particular if the partition into subdomains is not aligned with all jumps in the coefficients. Thanks to the theoretical analysis of two level Schwarz methods (see [11] and references therein) thi...