$($a$)$ Write down and explain Amdahl's law. Comment on its ability and limitations in describing the speedup

obtainable due to parallel processing.

$(4$ marks$)$

$($b$)$ A computer simulation is observed to take $40$ hours to execute on a PC with a single quad$-$core processor, and

$22\mathrm{.}5$ hours on a similar computer with $12$ cores.

$($i$)$ Using Amdahl's law, estimate the parallel and serial fractions, and the total compute time for

this problem.

$(3$ marks$)$

$($ii$)$ It is proposed to lease time on a $48-$core machine of similar architecture to run this problem.

Estimate the time that the problem would take on this machine.

$(2$marks$)$

$($iii$)$ If the problem is made $10$ times larger, give a best$-$case estimate of the speedup, and wallclock

time, for this larger problem on the $48$ core and $12$ core machines.

$(3$ marks$)$

$($c$)$ Explain the terms validation and verification as they apply to finite element modelling, stating what each

involves, when they are done and what best practice would be for validation.

$(8$ marks$)$