A hybrid algorithm for reducing matrix bandwidth

A hybrid algorithm for reducing the bandwidth of symmetric matrices is described in terms of a finite element grid. The new algorithm produces significantly lower bandwidths than either the commonly-used Gibbs–Poole-Stockmeyer (GPS) or Cuthill–McKee (CM) algorithms, with run times comparable to the original CM algorithm. The new hybrid algorithm uses the GPS algorithm as a preprocessor to provide a good initial node numbering for the author's node-shuffling algorithm, which accounts for variable degrees-of-freedom per node (DOF/node). The hybrid algorithm was tested on the 30 benchmark problems that were compiled by Everstine, and on 10 supplemental problems with variable DOF/node. Bandwidths and CPU times are presented for all problems.