Comm -to-comp Ratio

• Surely, there could be many different domain decompositions for a particular problem
  • For grid solver we may have a square block decomposition, block row decomposition or cyclic row decomposition
  • How to determine which one is good? Communication-to-computation ratio

Assume P processors and NxN grid for grid solver

• For block row decomposition
  • Each strip has N/P rows
  • Communication (boundary rows): 2N
  • Computation (area): N 2 /P (same as square block)
  • Comm -to-comp ratio: 2P/N
• For cyclic row decomposition
  • Each processor gets N/P isolated rows
  • Communication: 2N 2 /P
  • Computation: N 2 /P
  • Comm-to-comp ratio: 2
• Normally N is much much larger than P
  • Asymptotically, square block yields lowest comm -to-comp ratio