An elastic-wave stencil is decomposed into row slabs of a grid

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

An elastic-wave stencil is decomposed into row slabs of a

N_{\rm g}=2048

grid. A ping-pong test gives

\alpha_{\rm lat}=0.8\,\mu\mathrm{s}

and

\beta_{\rm net}=10\,\mathrm{GB\,s^{-1}}

, and one halo row carries

N_{\rm g}

double-precision values. Each process exchanges two such rows per step, and the time to update one cell on a fully loaded node is

t_{\rm cell}=30\,\mathrm{ns}

. ((a)) Find the slab size

n^*

(in cells owned by a process) at which the two halo messages cost as much as updating

n^*

cells. ((b)) Find the value

t_{\rm cell}

would have to take for that crossover to rise to exactly one row of the grid (

N_{\rm g}=2048

cells). ((c)) State the factor by which

t_{\rm cell}

would have to change from its given value of

30\,\mathrm{ns}

to reach that crossover.

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