NATAF , Frédéric

In this work we design new interface transmission conditions for a domain decomposition Schwarz algorithm for the Euler equations in 2 dimensions. These new interface conditions are designed to improve the convergence properties of the Schwarz algorithm. These conditions depend on a few parameters and they generalize the classical ones....

In this work we present an overview of some classical and new domain decomposition methods for the resolution of the Euler equations. The classical Schwarz methods are formulated and analyzed in the framework of first order hyperbolic systems and the differences with respect to the scalar problems are presented. This kind of algorithms behave...

In this paper the Smith factorization is used systematically to derive a new domain decomposition method for the Stokes problem. In two dimensions the key idea is the transformation of the Stokes problem into a scalar bi-harmonic problem. We show, how a proposed domain decomposition method for the biharmonic problem leads to a domain...

The purpose of this text is to offer an overview of the most popular domain decomposition methods for partial differential equations (PDE). The presentation is kept as much as possible at an elementary level with a special focus on the definitions of these methods in terms both of PDEs and of the sparse matrices arising from their...

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In this paper the Smith factorization is used systematically to derive a new domain decomposition method for the Stokes problem. In two dimensions the key idea is the transformation of the Stokes problem into a scalar bi-harmonic problem. We show, how a proposed domain decomposition method for the biharmonic problem leads to a domain...

In this paper the Smith factorization is used systematically to derive a new domain decomposition method for the Stokes problem. In two dimensions the key idea is the transformation of the Stokes problem into a scalar bi-harmonic problem. We show, how a proposed domain decomposition method for the bi-harmonic problem leads to a domain...

International audience

Coarse grid correction is a key ingredient in order to have scalable domain decomposition methods. In this work we construct the coarse grid space using the low frequency modes of the subdomain DtN (Dirichlet-Neumann) maps, and apply the obtained two-level preconditioner to the linear system arising from an overlapping domain decomposition. Our...

In this paper we recall a new domain decomposition method for the Stokes problem obtained via the Smith factorization. From the theoretical point of view, this domain decomposition method is optimal in the sense that it converges in two iterations for a decomposition into two equal domains. Previous results illustrated the fast convergence of...

we report on a preliminary convergence analysis of a domain decomposition method for solving the Euler equations for compressible flows. This method was previously described in Dolean and Lanteri. It relies on the formulati- on of an additive Schwarz type algorithm on a non-overlapping decomposition of the computational domain. According to the...

In this paper we develop and analyse domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations. Convergence of domain decomposition methods rely heavily on the efficiency of the coarse space used in the second level. We design adaptive coarse spaces...

Coarse grid correction is a key ingredient in order to have scalable domain decomposition methods. For smooth problems, the theory and practice of such two-level methods is well established, but this is not the case for problems with complicated variation and high contrasts in the coefficients. Stable coarse spaces for high contrast problems...

International audience

International audience

International audience