Bifurcation indicator based on meshless and asymptotic numerical methods for nonlinear poisson problems |
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| Authors: | Abdeljalil Tri Hamid Zahrouni Michel Potier‐Ferry |
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| Institution: | 1. Laboratoire de Mécanique, Faculté des Sciences Ain Chok Université Hassan II, , Casablanca, Morocco;2. Université de Lorraine, Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (LEM3)UMR CNRS 7239, , Ile du Saulcy, 57045 Metz, France |
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| 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 |
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| Keywords: | asymptotic numerical method bifurcation indicators meshless methods method of particular solutions nonlinear poisson problem padé approximants |
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