Ordering Symmetric Sparse Matrices for Small Profile and Wavefront

摘要

The ordering of large sparse symmetric matrices for small profile and wavefrontor for small bandwidth is important for the efficiency of frontal and variable-band solvers. In this report, the authors look at the computation of pseudoperipheral nodes and compare the effectiveness of using an algorithm based on level-set structures with using the spectral method as the basis of the Reverse Cuthill-McKee algorithm for bandwidth reduction. The authors also consider a number of ways of improving the performance and efficiency of Sloan's algorithm for profile and wavefront reduction, including the use of different weights, the use of supervariables, and implementing the priority queue as a binary heap. The authors also examine the use of the spectral ordering in combination with Sloan's algorithm. The design of software to implement the reverse Cuthill-McKee algorithm and a modified Sloan's algorithm is discussed. Extensive numerical experiments that justify the authors' choice of algorithm are reported on.