We discuss a parallel implementation of the domain decomposition method bas
ed on the macro-hybrid formulation of a second order elliptic equation and
on an approximation by the mortar element method. The discretization leads
tc, an algebraic saddle-point problem. An iterative method with a block-dia
gonal preconditioner is used far solving the saddle-point problem. A parall
el implementation of the method is emphasized. Finally the results of numer
ical experiments are presented.