High Performance Computing 1
Parallel MG
•From this, we can do a
simple complexity analysis of the communication
costs. For simplicity, let p=2^(2*k), so each processor owns a 2^(m-k)-by-2^(m-k) subgrid. Consider a V-cycle starting at level m. Then in levels m
through k of the
V-cycle, each processor will own at least one grid point. After that, in levels k-1 through 1,
fewer than all processors
will own an active grid point, and so some processors will remain idle. Let f be the time per flop, alpha the time for a message startup, and beta the
time per word to send a message.