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The application of the Method of Moments to the analysis of large PEC structures is difficult due to the computational requirements when the structure is discretized in a high number of unknowns. To solve this problem we propose the Multilevel Field Interpolation Algorithm (MLFIA) based on a source domain decomposition that permits a fast matrix-vector multiplication within the iterative solution that reduces the computational complexity and the memory requirements to O(NlogN). The execution of the algorithm is composed of five steps that follow the computation of the field evaluated at a set of evaluation points within the observation domain, the extraction of the Green's function, the interpolation of the fields, the restoration of the Green's function and finally the aggregation of the fields. The algorithm is applied to the fast solution of 2D problems. The generalization to 3D problems is straightforward.