Imagine that you have a physical domain that looks like two 8x8 checker boards overlapping at one corner by N squares along the diagonal. (where...

Imagine that you have a physical domain that looks like two 8x8 checker boards overlapping at one corner by N squares along the diagonal. (where 1<= N <= 7, pictured below are N=3 and N= 5).  It is desired to solve some equation over this domain on a parallel computer with 3 nodes, a head node and 2 slave nodes using a direct method on each subdomain (checkerboard). Generate a table that shows as a function of all accepted values of N the memory allocation requirements on each slave and on the head node, the size of data being transferred from the slaves to the head node and from the head to the slave nodes. Would you always recommend that the head node run a small number of Jacobi iterations on the updated solution or only sometimes or never? What direct solver would you use on the subdomains? Justify your answers.