Get access

Bifurcation indicator based on meshless and asymptotic numerical methods for nonlinear poisson problems

Authors

  • Abdeljalil Tri,

    1. Laboratoire de Mécanique, Faculté des Sciences Ain Chok Université Hassan II, Casablanca, Morocco
    Search for more papers by this author
  • Hamid Zahrouni,

    Corresponding author
    1. Université de Lorraine, Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (LEM3)UMR CNRS 7239, Ile du Saulcy, Metz, France
    • Correspondence to:Université de Lorraine, Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (LEM3), UMR CNRS 7239, Ile du Saulcy, 57045 Metz, France (e-mail: hamid.zahrouni@univ-lorraine.fr)

    Search for more papers by this author
  • Michel Potier-Ferry

    1. Université de Lorraine, Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (LEM3)UMR CNRS 7239, Ile du Saulcy, Metz, France
    Search for more papers by this author

Abstract

We propose in this work new algorithms associating asymptotic numerical method and meshless discretization (MFS-MPS: Method of fundamental solutions-Method of particular solutions) to compute branch solutions of nonlinear Poisson problems. To detect singular points on these branches, geometrical indicator, Padé approximants, and analytical bifurcation indicator are proposed. Numerical applications show the robustness and the effectiveness of the proposed algorithms. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 978–993, 2014

Get access to the full text of this article

Ancillary