MPI  example:

We use overlapping Schwarz method to compute the solution of the boundary value problem

-∆u(x)=1, x∈(0,1)

u(x=0)=0,

u(x=1)=0.

The interval (0,1)  is split in at most 10 overlapping subdomains. We use local computations and local exchange of

information in order to evolve the global computation into the approximation to the true solution.