

From analytic to automated derivatives: a case study of the electrostatic potential
Part of a collection
  

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

Published in Algorithms and Software for Mobile Communications, Proceedings of the 10th Aachen Symposium on Signal Theory, Aachen, Germany, September 2021, 2001

Year 2001 
Publisher VDE Verlag 
Abstract Given a largescale engineering simulation, one is often interested in the derivatives of certain program outputs with respect to certain input parameters, e.g., for sensitivity analysis. From an abstract point of view, the computer program defines a mathematical function whose derivatives are sought. In this note, two cases are investigated where the underlying functions are given by the solution of different twodimensional electrostatic potential problems. For a rectangular region, the function and its derivatives can be derived analytically. For a function based on an Lshaped region, the function is computed by a simulation code and its derivatives are obtained by automatic differentiation. In general, this powerful technique is applicable if a function is given in the form of a computer program in a highlevel programming language such as Fortran, C, or C++. In contrast to numerical differentiation providing approximations based on divided differences, the derivatives computed by automatic differentiation are accurate. Furthermore, automatic differentiation is also shown to be computationally efficient. 
AD Tools ADIFOR 
Related Applications
 Sensitivities of the Electrostatic Potential

BibTeX
@INPROCEEDINGS{
Bucker2001Fat,
author = "H. M. B{\"u}cker and B. Lang and A. Rasch and C. H. Bischof",
title = "From analytic to automated derivatives: a case study of the electrostatic potential",
booktitle = "Algorithms and Software for Mobile Communications, Proceedings of the 10th Aachen
Symposium on Signal Theory, Aachen, Germany, September~2021, 2001",
pages = "255260",
address = "Berlin",
publisher = "VDE~Verlag",
abstract = "Given a largescale engineering simulation, one is often interested in the
derivatives of certain program outputs with respect to certain input parameters, e.g., for
sensitivity analysis. From an abstract point of view, the computer program defines a mathematical
function whose derivatives are sought. In this note, two cases are investigated where the underlying
functions are given by the solution of different twodimensional electrostatic potential problems.
For a rectangular region, the function and its derivatives can be derived analytically. For a
function based on an Lshaped region, the function is computed by a simulation code and its
derivatives are obtained by automatic differentiation. In general, this powerful technique is
applicable if a function is given in the form of a computer program in a highlevel programming
language such as Fortran, C, or C++. In contrast to numerical differentiation providing
approximations based on divided differences, the derivatives computed by automatic differentiation
are accurate. Furthermore, automatic differentiation is also shown to be computationally
efficient.",
ad_area = "Electrical Engineering",
ad_tools = "ADIFOR",
year = "2001"
}
 
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