Real time solution approach for sparse network equations

A set program modules for solving linear equation systems in real time simulation of processes structured as sparse networks has been developed. The solution principles are described including network structure definition, forming of matrix equation, dynamic sparse matrix storage, factorization order optimization, fast bifactorization, and the calcu-lation of the unknown vector element values. The user interface of the various program modules is realized with their parameter lists. The parameter lists are described in detail for the main user level subroutines. An application of the modules on solving an example network is described. Execution time comparisons are presented for the different versions of the modules developed: the general purpose matrix and network equation solvers and the tailored network equation solvers for networks with fixed structure. The ex-ecution times measured on a minicomputer for the tailored solvers are of the same magnitude as those of vectored solvers for dense matrices on supercomputers. The network oriented parameter list is more comfortable to use than the matrix oriented parameter list for simulation of networks. Using the network approach it is further easier to ensure positive definiteness of the resulting matrix and to get a numerically stable solution. The modules have been used for simulation of both electrical networks and pipe networks. The applications include training simulators and engin-eering simulators.