

Computing sensitivities of the electrostatic potential by automatic differentiation
Article in a journal
  

Area Electrical Engineering 
Author(s)
H. M. Bücker
, B. Lang
, A. Rasch
, C. H. Bischof

Published in
Computer Physics Communications 
Year 2002 
Abstract Given a computer model for the electrostatic potential in an Lshaped region with media of different dielectric permeabilities in two subregions, we are interested in the robustness of the simulation by identifying the rate of change of the potential with respect to a change in the permeabilities. Such sensitivity analyses, assessing the rate of change of certain model outputs implied by varying certain model inputs, can be carried out by computing the corresponding partial derivatives. In largescale computational physics, the underlying computer model is typically available as a complicated computer code in a highlevel programming language such as Fortran, C, or C++. To obtain accurate and efficient derivatives of functions given in this form, we use a technique called automatic or algorithmic differentiation. Unlike numerical differentiation based on divided differences, derivatives generated by automatic differentiation are free of truncation error. Here, the automatic differentiation tool ADIFOR is used to transform the given computer modelimplemented with the general purpose finite element package SEPRANinto a new computer code computing the derivatives of the electrostatic potential with respect to the dielectric permeabilities. In doing so, we automatically translate 400,000 lines of Fortran 77 into a new program consisting of 600,000 lines of Fortran 77. We compare our approach with a traditional approach based on numerical differentiation and quantify its advantages in terms of accuracy and computational efficiency. 
AD Tools ADIFOR 
Related Applications
 Sensitivities of the Electrostatic Potential

BibTeX
@ARTICLE{
Bucker2002Cso,
author = "H. M. B{\"u}cker and B. Lang and A. Rasch and C. H. Bischof",
title = "Computing sensitivities of the electrostatic potential by automatic differentiation",
journal = "Computer Physics Communications",
year = "2002",
volume = "147",
number = "12",
pages = "720723",
doi = "doi:10.1016/S00104655(02)003843",
abstract = "Given a computer model for the electrostatic potential in an Lshaped region with
media of different dielectric permeabilities in two subregions, we are interested in the robustness
of the simulation by identifying the rate of change of the potential with respect to a change in the
permeabilities. Such sensitivity analyses, assessing the rate of change of certain model outputs
implied by varying certain model inputs, can be carried out by computing the corresponding partial
derivatives. In largescale computational physics, the underlying computer model is typically
available as a complicated computer code in a highlevel programming language such as Fortran,
C,~or~C++. To obtain accurate and efficient derivatives of functions given in this form, we use a
technique called automatic or algorithmic differentiation. Unlike numerical differentiation based on
divided differences, derivatives generated by automatic differentiation are free of truncation
error. Here, the automatic differentiation tool Adifor is used to transform the given computer
modelimplemented with the general purpose finite element package SEPRANinto a new computer
code computing the derivatives of the electrostatic potential with respect to the dielectric
permeabilities. In doing so, we automatically translate 400,000 lines of Fortran~77 into a new
program consisting of 600,000 lines of Fortran~77. We compare our approach with a traditional
approach based on numerical differentiation and quantify its advantages in terms of accuracy and
computational efficiency.",
ad_area = "Electrical Engineering",
ad_tools = "ADIFOR"
}
 
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