# A Globally Convergent Method for Generalized Resistive Systems and its Application to Stationary Problems in Gas Transport Networks

### Tanja Clees, Nils Hornung, Igor Nikitin, Lialia Nikitina

#### Abstract

We consider generalized resistive systems, comprising linear Kirchhoff equations and non-linear element equations, depending on the flow through the element and on two adjacent nodal variables. The derivatives of the element equation should possess a special signature. For such systems we prove the global non-degeneracy of the Jacobi matrix and the applicability of globally convergent solution tracing algorithms. We show that the stationary problems in gas transport networks belong to this generalized resistive type. We apply the tracing algorithm to several realistic networks and compare its performance with a generic Newton solver.

#### References

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#### Paper Citation

#### in Harvard Style

Clees T., Hornung N., Nikitin I. and Nikitina L. (2016). **A Globally Convergent Method for Generalized Resistive Systems and its Application to Stationary Problems in Gas Transport Networks** . In *Proceedings of the 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,* ISBN 978-989-758-199-1, pages 64-70. DOI: 10.5220/0005958700640070

#### in Bibtex Style

@conference{simultech16,

author={Tanja Clees and Nils Hornung and Igor Nikitin and Lialia Nikitina},

title={A Globally Convergent Method for Generalized Resistive Systems and its Application to Stationary Problems in Gas Transport Networks},

booktitle={Proceedings of the 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},

year={2016},

pages={64-70},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005958700640070},

isbn={978-989-758-199-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 6th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,

TI - A Globally Convergent Method for Generalized Resistive Systems and its Application to Stationary Problems in Gas Transport Networks

SN - 978-989-758-199-1

AU - Clees T.

AU - Hornung N.

AU - Nikitin I.

AU - Nikitina L.

PY - 2016

SP - 64

EP - 70

DO - 10.5220/0005958700640070