a$.$ Describe Foster$$s methodology steps which are given below:

$3.$ Partitioning.

$4.$ Communication.

$5.$ Agglomeration or aggregation.

$6.$ Mapping.

b$.$ Apply this methodology for a matrix multiplication algorithm,

i $.$ For shared memory $($if your number is even$)$

ii $.$ For distributed memory $($if your number is odd$)$