Power series analysis as a major breakthrough to improve the efficiency of Asymptotic Numerical Method in the vicinity of bifurcations

Bruno Cochelin (1) , Médale Marc (2)

1 M&S - Matériaux et Structures
2 IUSTI - Institut universitaire des systèmes thermiques industriels

This paper presents the outcome of power series analysis in the framework of the Asymptotic Numerical Method. We theoretically demonstrate and numerically evidence that the emergence of geometric power series in the vicinity of simple bifurcation points is a generic behavior. So we propose to use this hallmark as a bifurcation indicator to locate and compute very efficiently any simple bifurcation point. Finally, a power series that recovers an optimal step length is build in the neighborhood of bifurcation points. The reliability and robustness of this powerful approach is then demonstrated on two application examples from structural mechanics and hydrodynamics

Mots clés: Asymptotic Numerical Method; Path-following; continuation; bifurcation; power series analysis; Asymptotic Numerical Method.

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

Bruno Cochelin, Médale Marc. Power series analysis as a major breakthrough to improve the efficiency of Asymptotic Numerical Method in the vicinity of bifurcations. 2012. ⟨hal-00707513⟩