Row ordering for frontal solvers in chemical process engineering

The solution of chemical process engineering problems often requires the re peated solution of large sparse linear systems of equations that have a hig hly asymmetric structure. The frontal method can be very efficient for solv ing such systems on modern computer architectures because, in the innermost loop of the computation, the method exploits dense linear algebra kernels, which are straightforward to vectorize and parallelize. However, unless th e rows of the matrix can be ordered so that the frontsize is never very lar ge, frontal methods can be uncompetitive with other sparse solution methods . We review a number of row ordering techniques that use a graph theoretica l framework and, in particular, we show that a new class of methods that ex ploit the row graph of the matrix can be used to significantly reduce the f ront sizes and greatly enhance frontal solver performance. Comparative resu lts on large-scale chemical process engineering matrices are presented. (C) 2000 Elsevier Science Ltd. All rights reserved.