BibTeX
@ARTICLE{
Bucker2011SoD,
author = "H. M. B{\"u}cker and E. Slusanschi",
title = "Secondorder Derivatives of the Generalpurpose Finite Element Package {SEPRAN} via
Source Transformation",
journal = "Mathematics and Computers in Simulation",
issn = "03784754",
pages = "24312439",
doi = "10.1016/j.matcom.2011.03.008",
abstract = "Secondorder derivatives are crucial ingredients to a variety of numerical methods.
Often, they are difficult to get with numerical differentiation by divided differencing. Automatic
differentiation provides an alternative by a program transformation capable of evaluating Jacobians,
Hessians, or higherorder derivatives of functions given in the form of computer programs. SEPRAN is
a generalpurpose finite element package written in Fortran~77 used in various scientific areas
ranging from fluid dynamics to structural mechanics to electromagnetism. By transforming SEPRAN
twice using the automatic differentiation tool ADIFOR, secondorder derivatives are evaluated
without truncation error. Numerical experiments are reported in which secondorder derivatives of a
flow field with respect to an inflow velocity are computed, demonstrating the feasibility of this
approach.",
year = "2011",
volume = "81",
number = "11",
ad_tools = "ADIFOR",
ad_theotech = "Hessian"
}
