A critical review of asymptotic numerical methods

SummaryVarious sorts of asymptotic-numerical methods have been propsed in the literature: the reduced basis technique, direct computation of series or the use of Padé approximants. The efficiency of the method may also depend on the chosen path parameter, on the order of truncature and on alternative parameters. In this paper, we compare the three classes of asymptotic-numerical method, with a view to define the “best” numerical strategy.

[1]  P. Vannucci,et al.  An asymptotic-numerical method to compute bifurcating branches , 1998 .

[2]  J. M. T. Thompson,et al.  The non-linear perturbation analysis of discrete structural systems , 1968 .

[3]  M V Dyke.  Computer-Extended Series , 1984 .

[4]  B. Cochelin.  A path-following technique via an asymptotic-numerical method , 1994 .

[5]  Michel Potier-Ferry,et al.  Traitement des fortes non-linarits par la mthode asymptotique numrique , 1997 .

[6]  E. Riks.  Some computational aspects of the stability analysis of nonlinear structures , 1984 .

[7]  A. Noor.  Recent advances in reduction methods for nonlinear problems. [in structural mechanics , 1981 .

[8]  Michel Potier-Ferry,et al.  A New method to compute perturbed bifurcations: Application to the buckling of imperfect elastic structures , 1990 .

[9]  Ahmed K. Noor,et al.  Tracing post-limit-point paths with reduced basis technique , 1981 .

[10]  H. Padé.  Sur la représentation approchée d'une fonction par des fractions rationnelles , 1892 .

[11]  Bruno Cochelin,et al.  Asymptotic-numerical methods and pade approximants for non-linear elastic structures , 1994 .

[12]  M. Potier-Ferry,et al.  Résolution des équations de Navier-Stokes et Détection des bifurcations stationnaires par une Méthode Asymptotique-Numérique , 1996 .

[13]  Katsuya Nakagawa,et al.  STEADY AND UNSTEADY FINITE ELEMENT ANALYSIS OF INCOMPRESSIBLE VISCOUS FLUID. , 1976 .

[14]  Bruno Cochelin,et al.  An asymptotic‐numerical method to compute the postbuckling behaviour of elastic plates and shells , 1993 .

[15]  Ahmed K. Noor,et al.  Recent advances in reduction methods for instability analysis of structures , 1983 .

[16]  Bruno Cochelin,et al.  The asymptotic-numerical method: an efficient perturbation technique for nonlinear structural mechanics , 1994 .

[17]  Ted Belytschko,et al.  Buckling of structures with finite prebuckling deformations—a perturbation, finite element analysis , 1975 .