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Foil 3 General Analysis of Parallel ADI Performance -- the Pipeline start-up

From Further PDE Solvers for the NAS Benchmarks CPSP713 Case studies in Computational Science -- Spring Semester 1996. by Geoffrey C. Fox
1 Consider N 3NAS grid decomposed onto P processors
2 We must start each ADI solve at the beginning i,j,k=1 or the end i,j,k= NNAS
3 For each sweep (where elements not all stored in same processor) start half the solves at the beginning and half at the end
  • in each case work towards the middle
4 After at most NNAS/2 steps, we will have "made it" to the middle on the initial solve and all processors will be active.
5 This algorithm is sensitive to latency as in racing to get middle fast(est), we have only performed part of one solve in each processor.
  • We communicate only one (5 component) element
6 Maximizing message size by partial solution of several solves before communication:
  • Decreases communication cost as fewer messages
  • But worsens load balance as delays start of processors near middle
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