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Convergence acceleration of iterative algorithms. Applications to thin shell analysis and Navier–Stokes equations

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Abstract

This work deals with the convergence acceleration of iterative nonlinear methods. Two convergence accelerating techniques are evaluated: the Modified Mininal Polynomial Extrapolation Method (MMPE) and the Padé approximants. The algorithms studied in this work are iterative correctors: Newton’s modified method, a high-order iterative corrector presented in Damil et al. (Commun Numer Methods Eng 15:701–708, 1999) and an original algorithm for vibration of viscoelastic structures. We first describe the iterative algorithms for the considered nonlinear problems. Secondly, the two accelerating techniques are presented. Finally, through several numerical tests from the thin shell theory, Navier–Stokes equations and vibration of viscoelastic shells, the advantages and drawbacks of each accelerating technique is discussed.

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Authors and Affiliations

  1. Laboratoire d’Ingénierie des Matériaux de Bretagne, Université Européenne de Bretagne, Université de Bretagne Sud, Rue de Saint Maudé, B.P. 92116, 56321, Lorient Cedex, France

    J. M. Cadou & L. Duigou

  2. Laboratoire de Calcul Scientifique en Mécanique, Faculté des Sciences Ben M’Sik, Université Hassan II—Mohammedia Sidi Othman, Casablanca, Morocco

    N. Damil

  3. Laboratoire de Physique et Mécanique des Matériaux, Université Paul Verlaine, Ile du Saulcy, 57045, Metz, France

    M. Potier-Ferry

Authors
  1. J. M. Cadou
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  2. L. Duigou
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  3. N. Damil
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  4. M. Potier-Ferry
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Correspondence to J. M. Cadou.

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Cadou, J.M., Duigou, L., Damil, N. et al. Convergence acceleration of iterative algorithms. Applications to thin shell analysis and Navier–Stokes equations. Comput Mech 43, 253–264 (2009). https://doi.org/10.1007/s00466-008-0303-1

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  • DOI: https://doi.org/10.1007/s00466-008-0303-1

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