Projection techniques to improve high-order iterative correctors

Authors:
J. M. Cadou;N. Damil;M. Potier-Ferry;B. Braikat
Affiliations:
Laboratoire Génie Méanique et Matériaux, Rue de Saint Maudé, B.P. 92116, 56321, Lorient Cedex, France;Laboratoire de Calcul Scientifique en Mécanique, Faculté des Sciences Ben M'Sik, Université Hassan II - Mohammedia, BP 7955 Sidi Othman Casablanca, Maroc;Laboratoire de Physique et Mécanique des Matériaux, I.S.G.M.P., Université de Metz, Ile du Saulcy, 57045, Metz, France;Laboratoire de Calcul Scientifique en Mécanique, Faculté des Sciences Ben M'Sik, Université Hassan II - Mohammedia, BP 7955 Sidi Othman Casablanca, Maroc
Venue:
Finite Elements in Analysis and Design
Year:
2004

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Abstract

High-order iterative algorithms have been proposed recently (Commun. Numer. Methods Eng. 15 (1999) 701; Comput. Methods Appl. Mech. Eng. 190 (2000) 1845-1858). This technique relies on a homotopy transformation and on calculations of series and of Padé approximants. So one can define a high-order Newton algorithm that is efficient, robust and that often converges after a single iteration. Other algorithms denoted as L algorithms do not require any triangulation of a large matrix, but they are not as efficient as the previous one. In this paper, a reduced basis technique is used to improve the latter method, that is a sort of Newton method on the reduced subspace and a sort of L algorithm on the whole space. This new method is evaluated in the finite element analysis of thin shell buckling. So new efficient predictor-correctors are introduced that do not require any matrix triangulation in the correction phase.