### Abstract

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.

Original language | English |
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Place of Publication | Espoo |

Publisher | VTT Technical Research Centre of Finland |

Number of pages | 43 |

ISBN (Print) | 951-38-2050-5 |

Publication status | Published - 1986 |

MoE publication type | D4 Published development or research report or study |

### Publication series

Series | Valtion teknillinen tutkimuskeskus. Tiedotteita |
---|---|

Number | 615 |

ISSN | 0358-5085 |

### Keywords

- sparse matrices
- network simulation
- real time solution
- program modules

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## Cite this

Juslin, K., & Silvennoinen, E. (1986).

*Real time solution approach for sparse network equations*. VTT Technical Research Centre of Finland. Valtion teknillinen tutkimuskeskus. Tiedotteita, No. 615