Diagnosis of singular points of structured DAEs using automatic differentiation

At a singular point of a DAE, the IVP fails to have a unique solution. Hence, numerical integration methods cannot provide reasonable results. Unfortunately, common error control strategies do not always detect these circumstances and arbitrary solutions may be given to the user without warnings of...

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Bibliographic Details
Published in:Numerical algorithms 2015-08, Vol.69 (4), p.667-691
Main Authors: Estévez Schwarz, Diana, Lamour, René
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Automation
Circuits
Computer Science
Diagnosis
Differentiation
Electric circuits
Initial value problems
Mathematical models
Monitors
Numeric Computing
Numerical Analysis
Numerical integration
Numerical methods
Original Paper
Strategy
Theory of Computation
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Summary:At a singular point of a DAE, the IVP fails to have a unique solution. Hence, numerical integration methods cannot provide reasonable results. Unfortunately, common error control strategies do not always detect these circumstances and arbitrary solutions may be given to the user without warnings of any kind. Automatic (or Algorithmic) Differentiation (AD) opens new possibilities to realize an analysis of DAEs and to monitor assumptions required for the existence and uniqueness of IVPs. We show how the diagnosis of singular points can be performed for structured quasi-linear DAEs up to index 2. Our approach uses the projector based analysis for DAEs employing AD. The resulting method is illustrated by several examples, with particular emphasis on simple electrical circuits containing controlled sources.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-014-9919-8