Displaying similar documents to “On the Schwarz algorithms for the Elliptic Exterior Boundary Value Problems”

On the Schwarz algorithms for the elliptic exterior boundary value problems

Faker Ben Belgacem, Miche Fournié, Nabil Gmati, Faten Jelassi (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Tuning the alternating Schwarz method to the exterior problems is the subject of this paper. We present the original algorithm and we propose a modification of it, so that the solution of the subproblem involving the condition at infinity has an explicit integral representation formulas while the solution of the other subproblem, set in a bounded domain, is approximated by classical variational methods. We investigate many of the advantages of the new Schwarz approach: a geometrical...

A new domain decomposition method for the compressible Euler equations

Victorita Dolean, Frédéric Nataf (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this work we design a new domain decomposition method for the Euler equations in dimensions. The starting point is the equivalence with a third order scalar equation to whom we can apply an algorithm inspired from the Robin-Robin preconditioner for the convection-diffusion equation [Achdou and Nataf, (1997) 1211–1216]. Afterwards we translate it into an algorithm for the initial system and prove that at the continuous level and for a decomposition into sub-domains,...

A brief review of some application driven fast algorithms for elliptic partial differential equations

Prabir Daripa (2012)

Open Mathematics

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Some application driven fast algorithms developed by the author and his collaborators for elliptic partial differential equations are briefly reviewed here. Subsequent use of the ideas behind development of these algorithms for further development of other algorithms some of which are currently in progress is briefly mentioned. Serial and parallel implementation of these algorithms and their applications to some pure and applied problems are also briefly reviewed.

On a 2D vector Poisson problem with apparently mutually exclusive scalar boundary conditions

Jean-Luc Guermond, Luigi Quartapelle, Jiang Zhu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This work is devoted to the study of a two-dimensional vector Poisson equation with the normal component of the unknown and the value of the divergence of the unknown prescribed simultaneously on the entire boundary. These two scalar boundary conditions appear alternative in a standard variational framework. An original variational formulation of this boundary value problem is proposed here. Furthermore, an uncoupled solution algorithm is introduced together with its finite element...

Dirichlet-Neumann alternating algorithm for an exterior anisotropic quasilinear elliptic problem

Baoqing Liu, Qikui Du (2014)

Applications of Mathematics

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In this paper, by the Kirchhoff transformation, a Dirichlet-Neumann (D-N) alternating algorithm which is a non-overlapping domain decomposition method based on natural boundary reduction is discussed for solving exterior anisotropic quasilinear problems with circular artificial boundary. By the principle of the natural boundary reduction, we obtain natural integral equation for the anisotropic quasilinear problems on circular artificial boundaries and construct the algorithm and analyze...