FRONTAL SOLVERS FOR PROCESS ENGINEERING - LOCAL ROW ORDERING STRATEGIES

The solution of chemical process simulation and optimization problems on today's high performance supercomputers requires algorithms that ca n take advantage of vector and parallel processing when solving the la rge, sparse matrices that arise. The frontal method can be highly effi cient in this context due to its ability to make use of vectorizable d ense matrix kernels on a relatively small frontal matrix in the innerm ost loop of the computation. However, the ordering of the rows in the coefficient matrix strongly affects size of the frontal matrix and thu s the solution time. If a poor row ordering is used it may make the fr ontal method uncompetitive with other methods. We describe here a grap h theoretical framework for identifying suitable row orderings that sp ecifically addresses the issue of frontal matrix size. This leads to l ocal, heuristic methods which aim to limit frontal matrix growth in th e row and/or column dimensions. Results on a wide range of test proble ms indicate that improvements in frontal solver performance can often be obtained by the use of a restricted minimum column degree heuristic , which can be viewed as a variation of the minimum degree heuristic u sed in other contexts. Results also indicate that the natural unit-blo ck structure of process simulation problems provides a quite reasonabl e ordering. (C) 1998 Elsevier Science Ltd. All rights reserved.