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  • 1
    Electronic Resource
    Electronic Resource
    Convergence rate estimate for a domain decomposition method (1992)
    Springer
    Numerische Mathematik 61 (1992), S. 153-169 
    Details
    ISSN: 0945-3245
    Keywords: 65N30 ; 65F10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We provide a convergence rate analysis for a variant of the domain decomposition method introduced by Gropp and Keyes for solving the algebraic equations that arise from finite element discretization of nonsymmetric and indefinite elliptic problems with Dirichlet boundary conditions in ℝ2. We show that the convergence rate of the preconditioned GMRES method is nearly optimal in the sense that the rate of convergence depends only logarithmically on the mesh size and the number of substructures, if the global coarse mesh is fine enough.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385503
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  • 2
    Electronic Resource
    Electronic Resource
    Additive Schwarz algorithms for parabolic convection-diffusion equations (1991)
    Springer
    Numerische Mathematik 60 (1991), S. 41-61 
    Details
    ISSN: 0945-3245
    Keywords: 65N30 ; 65F10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper, we consider the solution of linear systems of algebraic equations that arise from parabolic finite element problems. We introduce three additive Schwarz type domain decomposition methods for general, not necessarily selfadjoint, linear, second order, parabolic partial differential equations and also study the convergence rates of these algorithms. The resulting preconditioned linear system of equations is solved by the generalized minimal residual method. Numerical results are also reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385713
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