An iterative method based upon Padé approximants

Communications in Numerical Methods in Engineering

Volumn 15, Issue 10, 1999, Pages 701-708

  Damil, N ^a   Potier Ferry, M ^b   Najah, A ^a   Chari, R ^a   Lahmam, H ^a  

^a FACULTÉ DES SCIENCES BEN M SIK   (Morocco)

^b UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Asymptotic numerical method; Buckling; Computational strategy; Finite element; Perturbation technique

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ASYMPTOTIC STABILITY; BUCKLING; COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; ITERATIVE METHODS; MATHEMATICAL OPERATORS; NONLINEAR SYSTEMS; PERTURBATION TECHNIQUES; PROBLEM SOLVING; VECTORS;

ASYMPTOTIC NUMERICAL METHODS (ANM); ITERATIVE NEWTON METHODS; PADE APPROXIMANTS; PREDICTION-CORRECTION ALGORITHMS;

MECHANICS;

EID: 0033363961     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-0887(199910)15:10<701::AID-CNM283>3.0.CO;2-L     Document Type: Article

References (12)

1. E. Dale-Martin, 'A technique for accelerating iterative convergence in numerical integration with application in transonic aerodynamics', Lect. Notes Phys., 47, 123-139 (1976).
2. J. M. T. Thompson and A. C. Walker, 'The non-linear perturbation analysis of discrete structure systems', Int. J. Solids Struct., 4, 219-259 (1968).
3. A. Najah, B. Cochelin, N. Damil and M. Potier-Ferry, 'A critical review of asymptotic numerical methods', Arch. Comput. Methods Eng., 5(1), 31-50 (1998).
4. B. Cochelin, N. Damil and M. Potier-Ferry, 'Asymptotic numerical method and Fade approximants for non-linear elastic structures', Int. J. Numer. Methods Eng., 37, 1187-1213 (1994).
5. J. M. Cadou, B. Cochelin and M. Potier-Ferry, 'The asymptotic-numerical method: Application to fluid-structures interaction', Proceedings of the third ECCOMAS Computational Fluid Dynamics Conference, John Wiley & Sons, 1996, pp. 131-138.
6. M. Potier-Ferry, N. Damil, B. Braikat, J. Brunelot, J. M. Cadou, H. L. Cao and A. Elhage-Hussein, 'Treatment of strong non-linearities by the asymptotic numerical method', C. R. Acad. Sci. Paris, Ser. 2, 324, 171-177 (1997).
7. A. Elhage-Hussein, N. Damil and M. Potier-Ferry, 'An asymptotic numerical algorithm for frictionless contact problems', Rev. Eur. Elém. Finis, 7, 119-130 (1998).
8. B. Braikat, N. Damil and M. Potier-Ferry, 'Méthodes asymptotiques numériques en plasticité', Rev. Eur. Elém. Finis, 6, 337-358 (1997).
9. A. K. Noor and J. M. Peters, 'Recent advances in reduction methods for instability analysis of structures', Comput. Struct., 16, 67-80 (1981).
10. L. Azrar, B. Cochelin, N. Damil and M. Potier-Ferry, 'An asymptotic numerical method to compute bifurcating branches', New Advances in Computational Structural Mechanics, P. Ladevèze and O. C. Zienkiewicz (eds), 1992, pp. 117-131.
11. H. De Boer and F. Van Keulen, 'Padé approximant applied to a non-linear finite element solution strategy', Commun. Numer. Meth. Engng, 13, 593-602 (1997).
12. S. Ammar, 'Méthode asymptotique perturbée appliquée à la résolution de problèmes non linéaires en grande rotation et grand déplacement' PhD., Université Laval, Québec, 1996.