A heat-diffusion simulation of a metal plate updates a binary64 field on a grid using…

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 Graphics processors: kernels, memory and the roofline

Problem

A heat-diffusion simulation of a metal plate updates a binary64 field on a

6144\times6144

grid using two buffers, so that each step moves the perfect-reuse minimum of

16\,\mathrm{B}

per cell update. The run is ported to a GPU whose measured triad bandwidth is

900\,\mathrm{GB\,s^{-1}}

; the host and device are connected by a PCIe 3.0 bus with peak bandwidth

16\,\mathrm{GB\,s^{-1}}

. Every

k

steps the whole field is copied to the host and back (a round trip) for a checkpoint; between round trips the field stays resident on the device. ((a)) Write the fraction of the total wall time spent on this round-trip transfer as a function of

k

, the round-trip transfer time

T_x

and the one-step device time

t_{\rm step}

, defining every symbol used. ((b)) Evaluate

T_x

and

t_{\rm step}

for this grid and this device. ((c)) Find the least integer

k

for which the transfer's share of the wall time falls below

5\%

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