On the use of a Pseudo-spectral method in the Asymptotic Numerical Method for the resolution of the Ginzburg-Landau envelope equation

被引：17

作者：

Drissi, Mohamed ^{[1
]}

Mansouri, Mohamed ^{[1
]}

Mesmoudi, Said ^{[2
]}

Saadouni, Khalid ^{[2
]}

机构：

[1] Hassan First Univ Settat, LAMSAD Lab, Ecole Natl Sci Appl, Berrechid 26100, Morocco

[2] Hassan First Univ Settat, LISA Lab, Ecole Natl Sci Appl, Berrechid 26100, Morocco

来源：

ENGINEERING STRUCTURES | 2022年 / 262卷

关键词：

Buckling; Landau-Ginzburg equation; Bifurcation; Pseudo-spectral; SPECTRAL COLLOCATION METHOD; GENERALIZED CONTINUUM APPROACH; FUNDAMENTAL-SOLUTIONS; SIMULATION;

D O I：

10.1016/j.engstruct.2022.114236

中图分类号：

TU [建筑科学];

学科分类号：

0813 ;

摘要：

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.

引用

页数：8

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