Diakoptics

Gabriel Kron's Diakoptics (Greek dia–through + kopto–cut,tear) or Method of Tearing involves breaking a (usually physical) problem down into subproblems which can be solved independently before being joined back together to obtain a solution to the whole problem.

Gabriel Kron was an unconventional Engineer who worked for GE in the US until his death in 1968. He was responsible for the first load flow (electricity) distribution system in New York.

He was perhaps most famous for his Method of Tearing, a technique for splitting up physical problems into subproblems, solving each individual subproblem and then recombining to give an (unexpectedly) exact overall solution. The technique is efficient on sequential computers, but is particularly so on parallel architectures. Whether this holds for quantum parallelism is as yet unknown. It is peculiar as a decomposition method, in that it involves taking values on the "intersection layer" (the boundary between subsystems) into account. The method has been rediscovered by the parallel processing community recently under the name "Domain Decomposition".

A multilevel hierarchical version of the Method, in which the subsystems are recursively torn into subsubsystems etc., was published by Keith Bowden in 1991.

References

Bowden K, "Kron's Method of Tearing on a Transputer Array", The Computer Journal, Vol 33, No 5, 1990, pp 453–459.

Bowden K, "Hierarchical Tearing: An Efficient Holographic Algorithm for System Decomposition", International Journal of General Systems, 24(1), pp 23–38, 1991.

Kron G, "Diakoptics: The Piecewise Solution of Large Scale Systems", MacDonald, 1963.

Lai C H, "Diakoptics, Domain Decomposition and Parallel Computing", The Computer Journal, Vol 37, No 10, pp. 840–846

See also

• Software componentry