Diakoptics or tearing--a mathematical approach

Author:
P. W. Aitchison

Journal:
Quart. Appl. Math. **41** (1983), 265-272

MSC:
Primary 65F30

DOI:
https://doi.org/10.1090/qam/721417

MathSciNet review:
721417

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[1]**Adi Ben-Israel and T. N. E. Greville,*Generalized inverses: Theory and applications*, Wiley, New York, 1974, reprinted by Krieger, Huntington, New York, 1980 MR**0396607****[2]**A. Brameller, M. N. John and M. R. Scott,*Practical diakoptics for electrical networks*, Chapman and Hall, London, 1969**[3]**F. H. Branin Jr.,*The relations between Kron's method and the classical methods of network analysis*, IRE Wescon Convention Record,**8**, 3-28 (1959)**[4]**H. H. Happ,*The applications of diakoptics to the solutions of power system problems*, Electric Power Problems: The Mathematical Challenge, SIAM, Philadelphia, pp. 69-103, 1980**[5]**H. H. Happ,*Piecewise methods and applications to power systems*, John Wiley, New York, 1980**[6]**H. K. Kesavan and J. Dueckman,*Multi-terminal representations and diakoptics*, University of Waterloo, Waterloo. Canada, 1981 (a report)**[7]**G. Kron,*Diakoptics--piecewise solutions of large scale systems*, Elect. J. (London) Vol. 158-Vol. 162 (JUne 1957-Feb. 1959)**[8]**G. Kron,*Diakoptics*, Macdonald, London 1963**[9]**J. S. Przemieniecki,*Matrix structural analysis of substructures*, AIAA Journal,**1**, 138-147 (1963)**[10]**J. K. Reid,*A survey of sparse matrix computation*, Electric Power Problems: The Mathematical Challenge, SIAM, pp. 47-68, 1980 MR**606417****[11]**J. P. Roth,*An application of algebraic topology: Kron's method of tearing*, Quarterly of Appl. Math.,**17**, 1-24 (1959) MR**0104337****[12]**D. V. Steward.*Partitioning and tearing systems of equations*, SIAM J. Numer. Anal., Ser. B,**2**, 345-365 (1965) MR**0219224**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
65F30

Retrieve articles in all journals with MSC: 65F30

Additional Information

DOI:
https://doi.org/10.1090/qam/721417

Article copyright:
© Copyright 1983
American Mathematical Society