A molecular-dynamics code for a colloid suspension times its own force-calculation…

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 molecular-dynamics code for a colloid suspension times its own force-calculation kernel and its decomposed fluid solver. ((a)) A fraction

f=0.88

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

S(32)

on 32 processes and its ceiling. ((b)) Run instead at fixed work per process, with

f'=0.999

; compute Gustafson's scaled speed-up

S(512)

on 512 processes. ((c)) The fluid solver exchanges one halo plane of

262144\,\mathrm{B}

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

\alpha_{\rm lat}=1.0\,\mu\mathrm{s}

and

\beta_{\rm net}=2.0\times10^{10}\,\mathrm{B\,s^{-1}}

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

6.30\,\mathrm{ms}

. ((d)) A triangular pair loop over colloid particles is split into

P=12

equal row ranges. Using

(2P-1)/P^2

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

Browse the problem library