4 are extrapolations of execution time relative to the performance of the SGI Origin 2000 on this problem. Note that the IBM SP is considerably slower than the other two machines. The parallel speedup is given in Fig. 5. The parallel efficiency is given in Fig. 6. Note that, for all machines, efficiency deteriorates for larger numbers of processors.
Reasonable efficiency is maintained until about twelve processors.
In order to examine the impact of increased problem size on parallel performance, a grid with size 200x200x200 was run on the Origin 2000 and compared with the results from the 100x100x100 grid. The results are presented in Fig. 7. These results clearly demonstrate that large problem sizes allow the efficient use of greater numbers of processors. Note that it was impossible to run the sequential case on the Origin 2000 for the large grid. Therefore, the sequential times for smaller grids were obtained on the Origin 2000 and extrapolated via curve fitting, as shown in Fig. 8.