A cosmological particle-mesh code updates its potential on a decomposed…

PHYSICS · Multi-part · Fermi University Physics · Computational Physics · High-performance and data-driven computational physics · High-performance and data-driven computational physics

Scientific Computing for Physicists, Ch Many processors: speed-up, decomposition and the cost of communication

Problem

A cosmological particle-mesh code updates its potential on a decomposed three-dimensional grid. ((a)) A fraction

f=0.60

of the one-process time parallelises; compute Amdahl's speed-up

S(4)

on 4 processes and its ceiling. ((b)) Run instead at fixed work per process, with

f'=0.99

; compute Gustafson's scaled speed-up

S(64)

on 64 processes. ((c)) The three-dimensional decomposition exchanges one halo plane of

131072\,\mathrm{B}

with each of its six neighbours every step. A ping-pong test gives

\alpha_{\rm lat}=3.0\,\mu\mathrm{s}

and

\beta_{\rm net}=5\times10^{9}\,\mathrm{B\,s^{-1}}

. Find the total time in the six halo messages per step, and its percentage of a step update measured at

9.50\,\mathrm{ms}

. ((d)) A triangular pair loop is split into

P=10

equal row ranges. Using

(2P-1)/P^2

for the first range's share, find that share and the resulting bound on speed-up.

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