Testing a new parallel preconditioner on linear systems arising from flowsheeting simulation

The parallel preconditioner proposed by Paloschi (1996) [12], was intended for almost block diagonal linear systems. While it can be applied to solve flowsheeting problems, its scope is limited. In this paper, we present the application to 4 linear systems, related to problems posed using flowsheeting packages, of an extension to [12] which allows to increase considerably the range of problems capable of tackling. Two of the problems were previously found to be non solvable with iterative methods by Cofer and Stadtherr(1996) [3], and were obtained with the Sequel II flowsheeting package. Both are of small size. The other 2 examples were obtained using the SPEEDUP simulation package and the largest has 11828 equations. Results are presented using the Fujitsu AP1000 parallel machine and a cluster of sparc workstations using MPI.