Projection techniques to improve high-order iterative correctors
High-order iterative algorithms have been proposed recently (Commun. Numer. Methods Eng. 15 (1999) 701; Comput. Methods Appl. Mech. Eng. 190 (2000) 18451858). This technique relies on a homotopy transformation and on calculations of series and of Pad 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* 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* L * algorithm on the whole space. This new method is evaluated in the finite element analysis of thin shell buckling. So new efficient predictorcorrectors are introduced that do not require any matrix triangulation in the correction phase.
projection iterative correctors homotopy pad approximants asymptotic numerical method high order reduction splitting