Solving matrix equations in large-scale dynamic simulation of flow networks

Antti Villberg, Tommi Karhela

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientific


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 languageEnglish
Title of host publication5th MATHMOD Proceedings
EditorsInge Troch
Place of PublicationVienna
ISBN (Print)3-901608-30-3
Publication statusPublished - 2006
MoE publication typeNot Eligible
Event5th MATHMOD: Vienna Symposium on Mathematical Modelling - Vienna, Austria
Duration: 8 Feb 200610 Feb 2006


Conference5th MATHMOD


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