### Abstract

This paper considers direct and iterative solution methods for the
matrix equation Ax=b in the context of large scale dynamic simulation of flow
networks in process industry. The simulation method uses the companion model
approach suggested by Juslin [1]. The study is a part of a semantic plant
modelling framework effort and the automatic generation of simulation models
is discussed. For solving the matrix equation a direct method of Cholesky
factorisation and an iterative method of incompleteCholesky preconditioned
conjugate gradients are considered. The matrices are treated with a minimum
degree reordering permutation and its effects are analysed. The algorithms are
analysed using a set of analytical flow graph topologies and a hydraulic
circuit simulator. The effects of the iterative nature of the simulation
algorithm are considered when using the iterative solver. Promising results
are obtained by using suitable values from previous iterations in the
simulation.

Original language | English |
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Title of host publication | 5th MATHMOD Proceedings |

Editors | Inge Troch |

Place of Publication | Vienna |

Pages | 119 |

Volume | 1 |

Publication status | Published - 2006 |

MoE publication type | Not Eligible |

Event | 5th MATHMOD: Vienna Symposium on Mathematical Modelling - Vienna, Austria Duration: 8 Feb 2006 → 10 Feb 2006 |

### Conference

Conference | 5th MATHMOD |
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Country | Austria |

City | Vienna |

Period | 8/02/06 → 10/02/06 |

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## Cite this

Villberg, A., & Karhela, T. (2006). Solving matrix equations in large-scale dynamic simulation of flow networks. In I. Troch (Ed.),

*5th MATHMOD Proceedings*(Vol. 1, pp. 119).