Sparse-matrix algorithm for transient analysis of nonlinear electrical networks

Abstract

A sparse-matrix algorithm appropriate to nodal admittance formulation of transient analysis of electrical network is described. The algorithm depends for its efficiency on the splitting of the coefficient matrix into two partitions. These partitions are decomposed sequentially as the LU factorisation of the matrix proceeds. In the decomposition of the first partition, adequate roundoff-error control is shown to be maintained, where pivots are selected from elements in the leading diagonal. In the second part, the algorithm selects suitable pivot elements by means of row reordering as the decomposition of the matrix is carried out. To reduce infill in coefficient matrix, the nodes associated with the first partition are renumbered once-for-all prior to the decomposition of the matrix. The algorithm is particularly suited to small machines having restricted word length and in which floating-point operations are performed by software routines. A comparison is made between the efficiencies of the present algorithm and a full-matrix decomposition method by means of transient analysis of a medium-size circuit.