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We discuss a parallel implementation of the domain
decomposition method based on the macro-hybrid formulation
of a second order elliptic
equation and on an approximation by the mortar element method.
The discretization leads to an algebraic saddle- point problem.
An iterative method with a block- diagonal
preconditioner is used for solving the saddle- point problem.
A parallel implementation of the method is emphasized.
Finally the results of numerical experiments are presented.
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