Basic HTML version of Foils prepared August 7 98

Foil 16 Gaussian Elimination: Agglomeration

From DoD HPF Training -- 5. Parallel Programming in HPF DoD Training and Others -- 1995-98. by Chuck Koelbel -- Rice University


Pivot selection requires a 1-D reduction
  • Distribute rows Þ parallel, with communication
  • Distribute columns Þ sequential, but no communication
Element updates require the old value and elements from the pivot row and column
  • Distribute rows Þ parallel, but broadcast the pivot row
  • Distribute columns Þ parallel, but broadcast the pivot column
Each stage works on a smaller contiguous region of the array
  • BLOCK Þ processors drop out of the computation
  • CYCLIC Þ work stays (fairly) evenly distributed until the end
The bottom line
  • (*,CYCLIC) if broadcast > pivoting one column
  • (CYCLIC,*) if broadcast < one column, synchronous comm.
  • (CYCLIC,CYCLIC) if broadcast < one col., overlapped comm.



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