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9.6.6 Conclusions

We have developed a high-quality concurrent code, Concurrent DASSL, for the solution of ordinary differential-algebraic equations  of low index. This code, together with appropriate linear algebra and simulation layers, allows us to explore the achievable concurrent performance of nontrivial problems. In chemical engineering,  we have applied it thus far to a reasonably large, simple model of coupled distillation columns. We are able to solve this large problem, which is quite demanding on even a large mainframe because of huge memory requirements and nontrivial computational requirements; the speedups achieved thus far are legitimately at least five, when compared to an efficient sequential implementation. This illustrates the need for improvements to the linear algebra code, which are feasible because sparse matrices will admit multiple pivots heuristically. It also illustrates the need to consider hidden sources of additional timelike concurrency in Concurrent DASSL, perhaps allowing multiple right-hand sides to be attacked simultaneously by the linear algebra codes, and amortizing their cost more efficiently. Furthermore, the performance points up the need for detailed research into novel numerical techniques, such as waveform relaxation, which we have begun to do as well [Skjellum:88a].

Guy Robinson
Wed Mar 1 10:19:35 EST 1995