$($a$)$ The execution of a scientific simulation program involves TWO $(2)$ main stages: data

preprocessing and computation. To optimize the program's performance, you, as the

system developer, have parallelized the computation stage, achieving a speedup to $75\%$

in that portion of the program $.$ However, the preprocessing stage remains sequential at

$25\%,$ and its execution time has not improved.

Identify the problems that occurred during the adoption of parallel computing to the

system that lead to the suboptimal performance with four processing elements $($N$=4).$

Calculate the max imum possible improvement in a system's performance and suggest

THREE $(3)$ solutions to overcome the problem.

$[12$ marks$]$

$($b$)$ The institute recently upgraded its computing system with additional processmg

elements to achieve better performance and more accurate results. However, you find

that the overall performance improvement is not proportional to the increase in the

number of processing elements.

Identify the factors that prevent the high$-$performance computing system from achi eving

its full potential, despite the increase in the number of processing elements. Calculate

the potential for scaling the problem size $($serial execution tasks only at $20\%)$ with the

number of processing elements $($N$=8)$ and suggest THREE $(3)$ solutions to overcome

the problem.

$[13$ marks$]$