Diakoptics

In systems analysis, Diakoptics (Greek dia–through + kopto–cut,tear) or the "Method of Tearing" involves breaking a (usually physical) problem down into subproblems which can be solved independently before being joined back together to obtain an exact solution to the whole problem. The term was introduced by Gabriel Kron in a series "Diakoptics — The Piecewise Solution of Large-Scale Systems" published in London, England by The Electrical Journal between June 7, 1957 and February 1959. The twenty-one installments were collected and published as a book of the same title in 1963. The term diakoptics was coined by Philip Stanley of the Union College Department of Philosophy.

According to Kron, "Diakoptics, or the Method of Tearing, is a combined theory of a pair of storehouses of information, namely equations+graph, or matrices+graph, associated with a given physical or economic system.". What Kron was saying here is that in order to carry out the Method of Tearing, not only were the system equations needed, but also the topology of the system.

Diakoptics was explained in terms of algebraic topology by J. Paul Roth. Roth describes how Kirchhoff's circuit laws in an electrical network with a given impedance matrix or admittance matrix can be solved for currents and voltages by using the circuit topology. Roth translates Kron’s "orthogonality conditions" into exact sequences of homology or cohomology. Roth’s interpretation is confirmed by Raoul Bott in reports in Mathematical Reviews. Roth says, "tearing consists essentially in deducing from the solution of one (easier to solve) network K^~ the solution of a network K having the same number of branches as K^~ and having the same isomorphism L between the groups of 1-chains and 1-cochains."

...
Wikipedia