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

Jean-Marc Cadou (1) , Laeticia Duigou (1) , Noureddine Damil (2) , Michel Potier-Ferry (3)

1 LIMATB - Laboratoire d'Ingénierie des Matériaux de Bretagne
2 UH2MC - Université Hassan II [Casablanca]
3 LPMM - Laboratoire de physique et mécanique des matériaux

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 [7] 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 emanating from the thin shell theory, Navier-Stokes equations and vibration of viscoelastic shells, permit to show the advantages and drawbacks of each accelerating technique.

Mots clés: Padé approximants; nonlinear problems; Convergence acceleration; iterative correctors; polynomial extrapolation

Domaines: Mécanique des structures [physics.class-ph]

Jean-Marc Cadou, Laeticia Duigou, Noureddine Damil, Michel Potier-Ferry. Convergence acceleration of iterative algorithms. Applications to thin shell analysis and Navier-Stokes equations. Computational Mechanics, 2009, 43 (2), pp.253-254. ⟨10.1007/s00466-008-0303-1⟩. ⟨hal-00403320⟩