OpenFVM-v1  1
About: OpenFVM is a general CFD (Computational Fluid Dynamics) solver (developed to simulate the flow in complex 3D geometries).
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OpenFVM-v1 Documentation

reverse Cuthill-McKee algorithm

  • input: an undirected graph G
  • unmask all nodes
  • find a not masked node p
  • for the connected component C rooted by p
    • Find pseudo-peripheral node root in C using fnrooti(). See [3] and [4] for more details, the implementation in [4] is also presented in [2].
    • Find the Cuthill-McKee ordering for the component rooted by root. See [1] for more detils, [2] presents the SPARSPAK implementation .
    • Reverse the ordering (see [5]).


[1] E. Cuthill and J. McKee. Reducing the bandwidth of sparse symmetric matrices. In Proceedings of the 1969 24th national conference, pages 157-172, New York, NY, USA, 1969. ACM Press.

[2] Alan George and Joseph W. H. Liu. Computer solution of large sparse positive definite systems. Prentice-Hall series in computational mathematics. Prentice-Hall, Englewood Cliffs, NJ, USA, 1981.

[3] N. E. Gibbs, W. G. Poole, and P. K. Stockemeyer. An algorithm for reducing the bandwidth and profile of a sparse matrix. SIAM Journal of Numerical Analysis, 13(2):236-250, April 1976.

[4] Alan George and Joseph W. H. Liu. An implementation of a pseudoperipheral node finder. ACM Trans. Math. Softw., 5(3):284-295, 1979.

[5] Wai-Hung Liu and Andrew H. Sherman. Comparative analysis of the Cuthill-McKee and the reverse Cuthill-McKee ordering algorithms for sparse matrices. SIAM Journal on Numerical Analysis, 13(2):198-213, April 1976.