### Generalized Block-Tridiagonal Matrix Orderings for Parallel
Computation in Process Flowsheeting

by

Alan B. Coon and Mark A. Stadtherr

#### ABSTRACT

A new graph partitioning algorithm for use on structurally unsymmetric
systems is presented. Unlike other partitioning algorithms that have been
used to provide reorderings for structurally symmetric matrices, this algorithm
employs a bipartite graph model, and hence, can be used to consider unsymmetric
permutations of structurally unsymmetric matrices. It is shown that the
algorithm can be used in identifying coarse-granular, balanced tasks in
the direct solution of flowsheeting matrices by parallel techniques based
on generalized block-tridiagonal and nested- block-tridiagonal matrix structures.
It is also shown that such reorderings can be obtained inexpensively, in
worst-case running times that increase linearly with the order of the matrix.

Comput. Chem. Eng., 19, 787-805 (1995)