Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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
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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.


References [Enhancements On Off] (What's this?)

  • [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

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DOI: https://doi.org/10.1090/qam/721417
Article copyright: © Copyright 1983 American Mathematical Society

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