Towards a full higher order AD-based continuation and bifurcation framework

• Published in: Optimization methods & software Vol. 33; no. 4-6; pp. 945 - 962
• Main Authors: Charpentier, Isabelle, Cochelin, Bruno
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.11.2018; Taylor & Francis Ltd
• Subjects: bifurcation analysis; Bifurcation theory; continuation method; Diamant; Engineering Sciences; geometric series; higher order automatic differentiation; Mechanics; nonlinear parametric problems; Nonlinear systems; Diamant AMS Subject Classification: 41A58; geometric series; 68N19; continuation method; 70E60; 65P30; bifurcation analysis; nonlinear parametric problems; higher order automatic differentiation
• ISSN: 1055-6788; 1029-4937
• DOI: 10.1080/10556788.2018.1428604

Some of the theoretical aspects of continuation and bifurcation methods devoted to the solution for nonlinear parametric systems are presented in a higher order automatic differentiation (HOAD) framework. Besides, benefits in terms of generality and ease of use, HOAD is used to assess fold and simple bifurcations points. In particular, the formation of a geometric series in successive Taylor coefficients allows for the implementation of an efficient detection and branch switching method at simple bifurcation points. Some comparisons with the Auto and MatCont continuation software are proposed. Strengths are then exemplified on a classical case study in structural mechanics.