In a previous paper [Internat. J. Numer. Math. Fluids 37 (2001) 625], we reported on numerical experiments with a non-overlapping domain decomposition method that has been specifically designed for the calculation of ...
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In a previous paper [Internat. J. Numer. Math. Fluids 37 (2001) 625], we reported on numerical experiments with a non-overlapping domain decomposition method that has been specifically designed for the calculation of steady compressible inviscid flows governed by the two-dimensional Euler equations. In the present work, we study this method from the theoretical point of view. The proposed method relies on the formulation of an additive schwarz algorithm which involves interface conditions that are Dirichlet conditions for the characteristic variables corresponding to incoming waves (often referred to as natural or classical interface conditions), thus taking into account the hyperbolic nature of the Euler equations. In the first part of this paper, the convergence of the additive schwarz algorithm is analyzed in the two- and three-dimensional continuous cases by considering the linearized equations and applying a Fourier analysis. We limit ourselves to the cases of two and three-subdomain decompositions with or without overlap and we obtain analytical expressions of the convergence rate of the schwarz algorithm. Besides the fact that the algorithm is always convergent, surprisingly, there exist flow conditions for which the asymptotic convergence rate is equal to zero. Moreover, this behavior is independent of the space dimension. In the second part, we study the discrete counterpart of the non-overlapping additive schwarz algorithm based on the implementation adopted in [Internat. J. Numer. Math. Fluids 37 (2001) 625] but assuming a finite volume formulation on a quadrangular mesh. We find out that the expression of the convergence rate is actually more characteristic of an overlapping additive schwarz algorithm. We conclude by presenting numerical results that confirm qualitatively the convergence behavior found analytically. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.
A finite volume scheme for convection diffusion equations on non-matching grids is presented. Sharp error estimates for H-2 solutions of the continuous problem are obtained. A finite volume version of an adaptation of...
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A finite volume scheme for convection diffusion equations on non-matching grids is presented. Sharp error estimates for H-2 solutions of the continuous problem are obtained. A finite volume version of an adaptation of the schwarz algorithm due to P. L. Lions is then studied. For a fixed mesh, its convergence towards the finite volume scheme on the whole domain is proven. Numerical experiments are performed to illustrate the theoretical rate of convergence of the finite volume sequences of solutions as the mesh is refined, together with the speed of convergence of the schwarz algorithm.
In this paper, we present some iterative algorithms, mainly schwarz algorithms, for an implicit two-sided obstacle problem. The monotonic convergence of the algorithms is proved. (C) 2001 Elsevier Science Ltd. All rig...
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In this paper, we present some iterative algorithms, mainly schwarz algorithms, for an implicit two-sided obstacle problem. The monotonic convergence of the algorithms is proved. (C) 2001 Elsevier Science Ltd. All rights reserved.
Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which...
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Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which can be applied to some nonuniformly elliptic problems.
Focuses on a study which presented monotonic iterative algorithms for solving quasicomplementarity problem (QCP). Details on the sequential complementarity problem (CP) algorithm; Information on the supersolution and ...
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Focuses on a study which presented monotonic iterative algorithms for solving quasicomplementarity problem (QCP). Details on the sequential complementarity problem (CP) algorithm; Information on the supersolution and subsolution of CP to QCP; Equation of schwarz algorithm.
In this paper, a new schwarz algorithm was developed to solve a class of large scale and nonlinear degenerated parabolic systems. The systems discussed in this paper included the nonlinear Schrodinger equations as the...
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In this paper, a new schwarz algorithm was developed to solve a class of large scale and nonlinear degenerated parabolic systems. The systems discussed in this paper included the nonlinear Schrodinger equations as the special case. The detailed computation procedures and the proofs for the discrete solutions converging to the exact solution are also presented in this paper. A numerical example is employed to illustrate the obtained theoretical results.
We discuss implementation of additive schwarz type algorithms on SIMD computers. A recursive, additive algorithm is compared with a two-level scheme. These methods are based on a subdivision of the domain into thousan...
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ISBN:
(纸本)0898712882
We discuss implementation of additive schwarz type algorithms on SIMD computers. A recursive, additive algorithm is compared with a two-level scheme. These methods are based on a subdivision of the domain into thousands of micro-patches that can reflect local properties, coupled with a coarser, global discretization where the `macro' behavior is reflected. The two-level method shows very promising flexibility, convergence and performance properties when implemented on a massively parallel SIMD computer.
In a Hilbert space an iterative process is defined which generalizes the schwarz alternating method for nonlinear monotone problems to more than two subdomains and the convergence of this process is proved. In the cas...
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In a Hilbert space an iterative process is defined which generalizes the schwarz alternating method for nonlinear monotone problems to more than two subdomains and the convergence of this process is proved. In the case of the problems with the solution in a convex of H0(1)(OMEGA), it is proved that the method converges geometrically. Numerical results are given concerning the problem of elastic-plastic torsion of prismatic bars and the problem of seepage of fluids through porous media.
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