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Bifurcation indicator based on meshless and asymptotic numerical methods for nonlinear poisson problems
Author(s) -
Tri Abdeljalil,
Zahrouni Hamid,
PotierFerry Michel
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21851
Subject(s) - mathematics , regularized meshless method , discretization , nonlinear system , bifurcation , partial differential equation , robustness (evolution) , meshfree methods , numerical analysis , poisson's equation , work (physics) , mathematical analysis , singular boundary method , finite element method , mechanical engineering , biochemistry , chemistry , physics , quantum mechanics , boundary element method , gene , engineering , thermodynamics
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