Effective Ordering of Sparse Matrices Arising from Nonlinear Electrical Networks

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Abstract
Hachtel et al. [1], [2] have recently proposed sparse matrix methods for nonlinear analysis incorporating an algorithm that generates symbolic code which, when executed, solves a system of linear equations of arbitrary, but particular, sparseness structure. They point out that the execution time and storage requirements of this code are critically dependent upon the ordering selected for processing the network equations and variables, and have themselves developed ordering methods. An efficient ordering algorithm is presented which tends to minimize the length and execution time of this symbolic code. Although the algorithm takes full advantage of the unique character of the sparse system that arises from a certain nonlinear circuit analysis representation, it is flexible enough to be used efficiently for ordering sparse matrices with different characteristics. In particular, it is especially appropriate when solving repetitively the large sparse systems which appear in circuit analysis in general, nonlinear differential and discrete system analysis, and in systems of linear or nonlinear algebraic equations. These problems are often part of larger problems or simulations. The algorithm contains parameters that may be easily adjusted to vary the tradeoff between ordering time and ordering efficiency. The method can (and should) be generalized to include some pivoting for numerical accuracy. Results for a typical nonlinear network indicate considerable improvement over previously published ordering schemes.