A Monte Carlo sweep of a three-dimensional Ising lattice is run on a process pool

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 Monte Carlo sweep of a three-dimensional Ising lattice is run on a process pool, with the field updated on decomposed slabs of spins. ((a)) A fraction

f=0.75

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

S(8)

on 8 processes and its ceiling. ((b)) Run instead at fixed work per process, with

f'=0.95

; compute Gustafson's scaled speed-up

S(16)

on 16 processes. ((c)) Each slab exchanges one halo plane of

16384\,\mathrm{B}

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

\alpha_{\rm lat}=1.5\,\mu\mathrm{s}

and

\beta_{\rm net}=8\times10^{9}\,\mathrm{B\,s^{-1}}

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

1.20\,\mathrm{ms}

. ((d)) A loop over all pairs of spin sites

i<j

, accumulating the spin-spin correlation, is split into

P=5

equal row ranges. Using the fraction

(2P-1)/P^2

held by the first range, find that fraction and the resulting bound on speed-up.

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