A new approach to Kron's method of analysing large systems

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Abstract
Generally an electrical network is used as a model circuit for a physical field. This circuit is most complicated and the analysis of it is frequently difficult. ‘Diakoptics’, introduced by Kron, is very effective for analysis of the network. The method entails the operation of ‘cutting’, which is generally classified into open-circuiting and short-circuiting. The latter operation is the dual of the former, but, as far as the author is aware, has not yet been reported in any of the literature. A method is described, based on Kron's diakoptics, which uses the operation of open-circuiting, and is further extended to dual diakoptics treated by the operation of short-circuiting. Here a simplification of Kron's diakoptics is attempted and a dual method is introduced. It seems that this attempt goes backwards in tensor geometry, but forward in combinatorial topology. The first intention of the paper is to show the duality between diakoptics and codiakoptics.

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  • Topology
    Published by American Mathematical Society (AMS) ,1930