Version 2.2.0

13th February 2014

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HSL_MC66 Permute an unsymmetric sparse matrix to singly bordered blocked diagonal form

To order an unsymmetric matrix A into singly bordered blocked diagonal (SBBD) form. Given the sparsity pattern of a matrix, this routine generates a row and column ordering that can be used to reorder the matrix into the following SBBD form:

A11 S1 A22 S2 AKKSK .

Here K is the user-defined number of blocks. The aim is to minimize the size of the border in the above matrix, also known as the net-cut, and to achieve load balance by ensuring that the rectangular matrices Aii are of similar sizes.

The MC66 algorithm uses a multilevel approach combined with a Kernighan-Lin type refinement algorithm. Full details are discussed in Hu, Maguire and Blake, Computers and Chemical Engrg. 21 (2000), pp.1631-1647.

MC66 may be used to preorder an unsymmetric matrix for use with the sparse matrix solver HSL_MP43.