Assignment #2:

This is an optimization project.  We want a faster program.

Select one of the MPI versions of the Stommel programs, stf_01.f90
or stc_01.c, for examples.

(a) Modify it so that the copy in do_jacobi from new_psi to
psi is not required.  That is eliminate the following lines:

##Fortran Version 
    psi(i1:i2,j1:j2)=new_psi(i1:i2,j1:j2)

##C Version:
    for( i=i1;i<=i2;i++)
        for(j=j1;j<=j2;j++)
           psi[i][j]=new_psi[i][j];

(b) Modify the program so that it quits when the solution
has converged, instead of continuing for a fixed number of
iterations.

(c) Convert this program to a multigrid type application.  We
currently start with an initial grid size of (N x N) and an
initial guess of the solution of the constant 1.0.  

We want to start with a smaller grid size say (N1 x N1) and 
the initial guess of 1.0.  Run the calculation allowing it to
converge.  The use this solution as an initial guess for a
second grid (N2 x N2) and run to convergence.  Continue this
process with increasing grid sizes until you reach your desired
size.  Typically N(n+1) = 2*N(n).  Do this for a final grid size
of 512 x 512 and compare the total number of iterations required
and the run times to the original program on the same grid size.