Bifurcation Indicator Based on Meshless and Asymptotic Numerical Methods for Nonlinear Poisson Problems

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, Pade approximants, and analytical bifurcation indicator are proposed. Numerical applications show the robustness and the effectiveness of the proposed algorithms.
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Numerical Methods for Partial Differential Equations, Wiley, 2014, 30 (3), pp.978-993. 〈10.1002/num.21851〉
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https://hal.univ-lorraine.fr/hal-01503448
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Soumis le : vendredi 7 avril 2017 - 10:24:13
Dernière modification le : jeudi 11 janvier 2018 - 06:23:43

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Abdeljalil Tri, Hamid Zahrouni, Michel Potier-Ferry. Bifurcation Indicator Based on Meshless and Asymptotic Numerical Methods for Nonlinear Poisson Problems. Numerical Methods for Partial Differential Equations, Wiley, 2014, 30 (3), pp.978-993. 〈10.1002/num.21851〉. 〈hal-01503448〉

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