To order an unsymmetric matrix 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:
Here 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 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.