$($b$)$ A particular finite element model is found to take $5$ hours to run on a computer with $2$ cores, and $2$ hours on

a computer of similar architecture and clock speed which has $8$ cores.

$($i$)$ Estimate the serial and parallel fraction $($as per Amdahl's law$)$ for this job, and the wallclock time

for each computer.

$(3$ marks$)$

$($ii$)$ It is intended to run the job $256$ times with different parameters and dimensions on a cloud$-$based

server which has $128$ cores available. It is proposed either to run $16$ instances of the job, each

using $8$ cores, or $8$ instances of the job, each using $32$ cores. Assuming

that other resources $($memory etc$)$ are sufficient, how long would each option take? $(3$ marks$)$