Diakoptics or tearing—a mathematical approach

Abstract

The method of diakoptics or tearing was introduced by G. Kron in order to reduce computations in the solution of certain problems arising from large inter-connected power distribution networks. Here the method is given a purely mathematical form which can be used to solve large systems of linear equations by first solving some smaller sub-problems and then combining these solutions into a complete solution. The sub-problems are formed from sets of equations and variables which are strongly connected, within the sub-problem, but only weakly connected to those of another sub-problem.