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Parallel nonlinear preconditioners on multicore architectures

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Abstract

Parallel nonlinear preconditioners, for solving mildly nonlinear systems, are proposed. These algorithms are based on both the Fletcher–Reeves version of the nonlinear conjugate gradient method and a polynomial preconditioner type based on block two-stage methods. The behavior of these algorithms is analyzed when incomplete LU factorizations are used in order to obtain the inner splittings of the block two-stage method. As our illustrative example we have considered a nonlinear elliptic partial differential equation, known as the Bratu problem. The reported experiments show the performance of the algorithms designed in this work on two multicore architectures.

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Authors and Affiliations

  1. Departamento de Física y Arquitectura de Computadores, Universidad Miguel Hernández, 03202, Elche, Alicante, Spain

    Vicente Galiano & Héctor Migallón

  2. Departamento de Ciencia de la Computación e Inteligencia Artificial, Universidad de Alicante, 03071, Alicante, Spain

    Violeta Migallón & José Penadés

Authors
  1. Vicente Galiano
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  2. Héctor Migallón
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  3. Violeta Migallón
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  4. José Penadés
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Corresponding author

Correspondence to Violeta Migallón.

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Galiano, V., Migallón, H., Migallón, V. et al. Parallel nonlinear preconditioners on multicore architectures. J Supercomput 58, 160–167 (2011). https://doi.org/10.1007/s11227-009-0351-0

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  • DOI: https://doi.org/10.1007/s11227-009-0351-0

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