Towards a full higher order AD-based continuation and bifurcation framework. (2nd November 2018)

• Record Type: Journal Article
• Authors: Charpentier, Isabelle; Cochelin, Bruno
• Is Part Of: Optimization methods and software. Volume 33:Number 4/6(2018)
• Page Start: 945
• Page End: 962
• Publication Date: 2018-11-02
• Subjects: nonlinear parametric problems -- continuation method -- bifurcation analysis -- geometric series -- higher order automatic differentiation -- Diamant; 41A58 -- 65P30 -- 68N19 -- 70E60; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2018.1428604
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : 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.