

Automatic Sensitivity Analysis of DAEsystems Generated from EquationBased Modeling Languages
incollection
  

Area DifferentialAlgebraic Equation 
Author(s)
Atya Elsheikh
, Wolfgang Wiechert

Published in Advances in Automatic Differentiation

Editor(s) Christian H. Bischof, H. Martin Bücker, Paul D. Hovland, Uwe Naumann, J. Utke 
Year 2008 
Publisher Springer 
Abstract This paper aims at sensitivity analysis of differential algebraic equation (DAE) systems, generated from mathematical models, specified in equationbased modeling languages. Modern simulation languages (e.g. Modelica) use an equationbased syntax enriched by facilities for objectoriented modeling, hierarchical system decomposition and code reuse in libraries. Sophisticated compiler tools exist for generating efficient runtime code from a given model specification. These tools rely on powerful algorithms for code optimization and equations rearrangement. Particularly, automatic differentiation (ad) is already used, though for the different task of DAE index reduction. Clearly, the mentioned facilities should be exploited as far as possible in a new ad tool for sensitivity analysis. In this paper, three possible levels at which ad can be applied are discussed. These are given by ad on run time code, flat model and library level. Then the new sourcetosource ad tool (ADModelica) is introduced which takes the second approach. Particularly, it is shown that there are several differences between ad methods for classical procedural languages and equationbased modeling languages. 
CrossReferences Bischof2008AiA 
BibTeX
@INCOLLECTION{
Elsheikh2008ASA,
author = "Atya Elsheikh and Wolfgang Wiechert",
title = "Automatic Sensitivity Analysis of {DAE}systems Generated from EquationBased Modeling
Languages",
doi = "10.1007/9783540689423_21",
pages = "235246",
abstract = "This paper aims at sensitivity analysis of differential algebraic equation (DAE)
systems, generated from mathematical models, specified in equationbased modeling languages. Modern
simulation languages (e.g. Modelica) use an equationbased syntax enriched by facilities for
objectoriented modeling, hierarchical system decomposition and code reuse in libraries.
Sophisticated compiler tools exist for generating efficient runtime code from a given model
specification. These tools rely on powerful algorithms for code optimization and equations
rearrangement. Particularly, automatic differentiation (AD) is already used, though for the
different task of DAE index reduction. Clearly, the mentioned facilities should be exploited as far
as possible in a new AD tool for sensitivity analysis. In this paper, three possible levels at which
AD can be applied are discussed. These are given by AD on run time code, flat model and library
level. Then the new sourcetosource AD tool (ADModelica) is introduced which takes the second
approach. Particularly, it is shown that there are several differences between AD methods for
classical procedural languages and equationbased modeling languages.",
crossref = "Bischof2008AiA",
booktitle = "Advances in Automatic Differentiation",
publisher = "Springer",
editor = "Christian H. Bischof and H. Martin B{\"u}cker and Paul D. Hovland and Uwe
Naumann and J. Utke",
isbn = "9783540689355",
issn = "14397358",
year = "2008",
ad_area = "DifferentialAlgebraic Equation"
}
 
back

