On the use of a Pseudo-spectral method in the Asymptotic Numerical Method for the resolution of the Ginzburg–Landau envelope equation. (1st July 2022) - Drissi, Mohamed; Mansouri, Mohamed; Mesmoudi, Said; Saadouni, Khalid
Abstract: The present work deals with the resolution of the Ginzburg–Landau envelope equation. It is a nonlinear partial differential equation that requires a robust solver. Nowadays, Newton methods are available in many existing commercial codes. However, the computation of the associated tangent operator and its factorization at each incremental step requires a computational cost. In order to reduce this computational cost, we focus on the use of a high-order solver. This algorithm, named in this work (ANM-SM), is made by associating the Asymptotic Numerical Method (ANM) with the Spectral Method (SM). The efficiency and robustness of the used algorithm are illustrated by numerical results of a simple example of a beam resting on a non-linear Winkler foundation. Highlights: The Spectral Chebyshev was coupled with the Asymptotic Numerical Method to solve nonlinear problems. The Ginzburg–Landau envelope equation was solved by a high order solver based on the Asymptotic Numerical Method with Spectral Method. Nonlinear buckling analysis of beam was investigated. Effects of boundary conditions on the critical buckling loads of a beam were tested. Effect of boundary conditions on the buckling patterns of a beam were analyzed.