Publication: Towards a full higher order AD-based continuation and bifurcation framework
Introduction
Applications
Tools
Research Groups
Workshops
Publications
   List Publications
   Advanced Search
   Info
   Add Publications
My Account
About

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

- Article in a journal -
 

Author(s)
Isabelle Charpentier , Bruno Cochelin

Published in
Special issue of Optimization Methods & Software: Advances in Algorithmic Differentiation Optimization Methods & Software

Editor(s)
Bruce Christianson, Shaun A. Forth, Andreas Griewank

Year
2018

Publisher
Taylor & Francis

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.

Cross-References
Christianson2018Sio

BibTeX
@ARTICLE{
         Charpentier2018Taf,
       crossref = "Christianson2018Sio",
       author = "Isabelle Charpentier and Bruno Cochelin",
       title = "Towards a full higher order {AD}-based continuation and bifurcation framework",
       journal = "Optimization Methods \& Software",
       volume = "33",
       number = "4--6",
       pages = "945--962",
       year = "2018",
       publisher = "Taylor \& Francis",
       doi = "10.1080/10556788.2018.1428604",
       url = "https://doi.org/10.1080/10556788.2018.1428604",
       eprint = "https://doi.org/10.1080/10556788.2018.1428604",
       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.",
       booktitle = "Special issue of Optimization Methods \& Software: Advances in
         Algorithmic Differentiation",
       editor = "Bruce Christianson and Shaun A. Forth and Andreas Griewank"
}


back
  

Contact:
autodiff.org
Username:
Password:
(lost password)