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An iterative substructuring algorithm for equilibrium equations. (English) Zbl 0708.65037

The authors investigate an order reducing, preconditioned conjugate gradient method proposed by J. Barlow, N. Nichols and the second author [SIAM J. Sci. Stat. Comput. 9, 892-906 (1988; Zbl 0659.65040)] for solving the least squares problem with equality constraints formulation and relate the corresponding algorithm to another order reducing scheme known as the nullspace method. Convergence properties and the relation to the p-cyclic SOR theory of R. S. Varga [Pac. J. Math. 9, 617-628 (1959; Zbl 0088.094)] are discussed. The authors suggest a mixed approach for solving equilibrium, consisting of both direct reduction in the substructures and the conjugate gradient iterative algorithm to complete the computations.
Reviewer: K.Najzar

MSC:

65F10 Iterative numerical methods for linear systems
65F20 Numerical solutions to overdetermined systems, pseudoinverses
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
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References:

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