We can expect better scaling as we address more complicated problems, which place additional computational work at the highest levels. We divide the execution time for the eigenvalue algorithm, including time spent building the adaptive grid hierarchy, into numerical computation, time lost to load imbalance, communication among grids at the same level of the hierarchy, communication between levels, error estimation, load balancing, and grid generation. Error estimation, load balancing, and grid generation consume only a few percent of the total execution time. As computation times drop with additional processors, communication overheads become a dominant factor in overall performance. Execution time breakdown for the eigenvalue calculation on the Intel Paragon.
Times are in seconds.
It is difficult to assess adaptive mesh library overheads on parallel computers since we do not yet have detailed hardware performance analyzers such as those on the Cray C-90. We can assume that there is little library overhead in computation, since all numerical work is done in Fortran. The remaining contributor of overheads is interprocessor communication.