There is one last detail; this replacement of xnew with the average of the values around it is applied only in the interior; the boundary values are left fixed. In practice, this means that if the mesh is n by n, then the values
are left unchanged. Of course, these refer to the complete mesh; you'll have to figure out what to do with for the decomposed data structures (xlocal).
Because the values are replaced by averaging around them, these techniques are called relaxation methods.
We wish to compute this approximation in parallel. Write a program to apply this approximation.