Boundary conditions

• Boundary conditions (global) often cause special problems for parallel programming with distributed data.

• Periodic boundary conditions for finite difference example:
  • Data parallel
    • In absence of CSHIFT, need extra serial statements

               fdprime(2) = c0*(-f(nx-1) + 16*f(nx) -
                              30*f(2) + 16*f(3) - f(4))
               fdprime(1) = c0*(-f(nx-1) + 16*f(nx) -
                              30*f(2) + 16*f(3) - f(4))
               fdprime(nx-1) = c0*(-f(nx-3) +16*f(nx-2) -
                                30*f(nx-1) +16*f(nx) -
                                   f(1))
               fdprime(nx) = c0*(-f(nx-2) +16*f(nx-1) -
                               30*f(nx) +16*f(1) - f(2))
      

  • Message passing
    • PE's at ends of global box have guard points that wrap around periodically.
      • No extra statements needed in loop.

• Which parts of calculation are parallel?
  • Data parallel: non-boundary points.

  • Message passing: all points

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