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  4. Making network solvers globally convergent
 
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2018
Conference Paper
Titel

Making network solvers globally convergent

Abstract
Stationary network problems are considered, unifying linear Kirchhoff equations and non-linear element equations, possessing a proper signature of the derivatives. The global non-degeneracy of the Jacobi matrix is proven, providing the applicability of globally convergent tracing algorithms for such systems. It is shown that stationary problems in gas transport networks can be written in the form necessary for the global convergence. Two stabilized algorithms for the solution of these problems are implemented. The algorithms outperform a standard Newtonian solver for a number of realistic networks. The algorithms do not depend on the staring point, are stable, converge for all scenarios and, additionally, provide feasibility indicator for the problem statement.
Author(s)
Clees, Tanja
Fraunhofer-Institut für Algorithmen und Wissenschaftliches Rechnen SCAI
Nikitin, Igor
Fraunhofer-Institut für Algorithmen und Wissenschaftliches Rechnen SCAI
Nikitina, Lialia
Fraunhofer-Institut für Algorithmen und Wissenschaftliches Rechnen SCAI
Hauptwerk
Simulation and Modeling Methodologies, Technologies and Applications. International Conference, SIMULTECH 2016
Konferenz
International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH) 2016
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DOI
10.1007/978-3-319-69832-8_9
Language
English
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Fraunhofer-Institut für Algorithmen und Wissenschaftliches Rechnen SCAI
Tags
  • non-linear system

  • globally convergent m...

  • stationary network pr...

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