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Foil 10 Ideas behind Wavefront or Hyperplane Parallelization of LU NAS Benchmark

From Further PDE Solvers for the NAS Benchmarks CPSP713 Case studies in Computational Science -- Spring Semester 1996. by Geoffrey C. Fox
1 Let us discuss parallelization of first (D + Lo) DU1 Lower Triangular equation as Upper triangular case is trivially the same by reversing order of indices
2 RNR-93-007 distinguishs Wavefront (2D) and hyperplane(3D) methods and concludes hyperplane best.
  • We agree but will draw all pictures in two dimensions -- they have obvious three dimensional extensions
3 Key observation is that:
  • After Processor 1 has finished case i=j=k=1
  • Processor 1 can proceed with case i=2 j=k=1 while
  • Processor 2 can compute i=1 k=2 and j=1
  • This (only taking k=1 for Processor 1 and k=2 for Processor 2) gives a pipeline with Processor 2 following one grid point behind Processor 1.
in Table To:

Northeast Parallel Architectures Center, Syracuse University, npac@npac.syr.edu

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