GS510

Assignment 6 -- Fall 2000

Consider the (Laplace) Finite Difference Equation:

        -U_i-1,j - U_i,j-1 + 4U_i,j - U_i+1,j - U_i,j+1 = 0   for i,j = 1,2, ... N-2

To begin, take N = 12.

Let x_i = 1/(N+1) = y_j and set the boundary cells (i = 0, i = N-1 for j = 0,...,N-1 and
j = 0, j=N-1 for i = 0,...,N-1) to the values consistent with the exact solution

                        E_ij = (x_i)² - (y_j)²

On the interior cells, initialize the numerical solution to be zero.

1.  Use the example MPI code as a starting point to construct a four process  Jacobi iteration method that terminates when the maximum difference between the numerical solution and the exact solution is less that .0005.

2.  Replace N by 144 in your code and use calls to MPI_WTIME() to determine the megaflop rate of your four processor Jacobi method on the grid with N = 144.