This report is a sequel to several publications in which a {\em Multiple-Gradient Descent Algorithm (MGDA)} has been proposed and tested for the treatment of multi-objective differentiable optimization. The method was originally introduced in \cite{JAD09:MGDA}, and again formalized in \cite{JAD12:MGDA-CRAS}. Its efficacy to identify the Pareto front has been demonstrated in \cite{JAD11:MGDA-PAES}, in comparison with an evolutionary strategy. Finally, recently, a variant, {\em MGDA II}, has been proposed in which the descent direction is calculated by a direct procedure \cite{JAD12:MGDA2}. In this new report, the efficiency of the algorithm is tested in the context of a simulation by domain partitioning, as a technique to match the different interface components concurrently. For this, the very simple testcase of the finite-difference discretization of the Dirichlet problem over a square is considered. The study aims at assessing the performance of {\em MGDA} in a discretized functional setting. One of the main teachings is the necessiy, here found imperative, to normalize the gradients appropriately.
