Diakoptic and generalized hybrid analysis

Two elementary approaches are presented for analyzing large-scale linear resistive networks by first tearing them apart, solving the torn subnetworks separately, and then interconnecting the results to obtain the solution of the overall network. The first approach makes use of elementary graph- and circuit-theoretic concepts and leads to a unified formulation which includes all existing versions of diakoptic analysis based on Kron´s original ideas as special cases. The second approach consists of an appropriate partitioning of the network elements and a manipulation of the linear algebraic equations into the form of a generalized hybrid analysis involving a matrix having a bordered block-diagonal structure. These two distinct approaches are shown to be equivalent in the sense that the first is a special case of the second. The result is then extended to nonlinear networks, where an efficient computational algorithm is presented which takes full advantage of sparse matrix techniques and is compatible with parallel computations.