Publication: Computing sensitivities of the electrostatic potential by automatic differentiation
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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 L-shaped 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 large-scale computational physics, the underlying computer model is typically available as a complicated computer code in a high-level 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 model---implemented with the general purpose finite element package SEPRAN---into 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 = "1--2",
       pages = "720--723",
       doi = "doi:10.1016/S0010-4655(02)00384-3",
       abstract = "Given a computer model for the electrostatic potential in an L-shaped 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 large-scale computational physics, the underlying computer model is typically
         available as a complicated computer code in a high-level 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
         model---implemented with the general purpose finite element package SEPRAN---into 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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