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

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.