Local Parameterization and the Asymptotic Numerical Method

H. Mottaqui; B. Braikat; N. Damil

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 7, page 16-22
  • ISSN: 0973-5348

Abstract

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The Asymptotic Numerical Method (ANM) is a family of algorithms, based on computation of truncated vectorial series, for path following problems [2]. In this paper, we present and discuss some techniques to define local parameterization [4, 6, 7] in the ANM. We give some numerical comparisons of pseudo arc-length parameterization and local parameterization on non-linear elastic shells problems

How to cite

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Mottaqui, H., Braikat, B., and Damil, N.. Taik, A., ed. "Local Parameterization and the Asymptotic Numerical Method." Mathematical Modelling of Natural Phenomena 5.7 (2010): 16-22. <http://eudml.org/doc/197618>.

@article{Mottaqui2010,
abstract = {The Asymptotic Numerical Method (ANM) is a family of algorithms, based on computation of truncated vectorial series, for path following problems [2]. In this paper, we present and discuss some techniques to define local parameterization [4, 6, 7] in the ANM. We give some numerical comparisons of pseudo arc-length parameterization and local parameterization on non-linear elastic shells problems},
author = {Mottaqui, H., Braikat, B., Damil, N.},
editor = {Taik, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {asymptotic numerical method; continuation methods; local parameterization; parameterization; nonlinear elastic shells},
language = {eng},
month = {8},
number = {7},
pages = {16-22},
publisher = {EDP Sciences},
title = {Local Parameterization and the Asymptotic Numerical Method},
url = {http://eudml.org/doc/197618},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Mottaqui, H.
AU - Braikat, B.
AU - Damil, N.
AU - Taik, A.
TI - Local Parameterization and the Asymptotic Numerical Method
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/8//
PB - EDP Sciences
VL - 5
IS - 7
SP - 16
EP - 22
AB - The Asymptotic Numerical Method (ANM) is a family of algorithms, based on computation of truncated vectorial series, for path following problems [2]. In this paper, we present and discuss some techniques to define local parameterization [4, 6, 7] in the ANM. We give some numerical comparisons of pseudo arc-length parameterization and local parameterization on non-linear elastic shells problems
LA - eng
KW - asymptotic numerical method; continuation methods; local parameterization; parameterization; nonlinear elastic shells
UR - http://eudml.org/doc/197618
ER -

References

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  1. B. Cochelin. A path-following technique via an asymptotic-numerical method. Computers Structures, 53 (1994), No. 5, 1181–1192. Zbl0918.73337
  2. B. Cochelin, N. Damil, M. Potier-Ferry. Méthode asymptotique numérique. Hermès-Lavoisier, Paris, 2007.  
  3. A. Elhage-Hussein, M. Potier-Ferry, N. Damil. A numerical continuation method based on Padé approximants. Int.J. Solids and Structures, 37 (2000), 6981–7001. Zbl0980.74021
  4. J. J. Gervais, H. Sadiky. A new steplength control for continuation with the asymptotic numerical method. IAM, J. Nomer. Anal., 22 (2000), No. 2, 207–229. Zbl1006.65050
  5. H. Mottaqui, B. Braikat, N. Damil.Influence de la paramétrisation dans la méthode asymptotique numérique : Application au calcul de structures. Premier congrès Tunisien de mécanique, (2008), 173–174.  
  6. W. C. Rheinboldt, J. V. Burkadt. A Localy parameterized continuation. Acm Transaction on Mathmatical Software, 9 (1983), No. 2, 215–235. 
  7. R. Seydel. World of bifurcation, online collection and tutorials of nonlinear phenomena, () (1999).  URIwww.bifurcation.de

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