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A multiresolution (MR) (wavelet) basis is employed in the method of moments (MoMs) analysis to achieve an efficient evaluation of the electromagnetic wave coupling inside metallic enclosures with arbitrary-shape openings. In this method, the electric field integral equation is solved on the surface of the enclosure discretized by triangular meshes. Using the MR meshing, different scales of the problem such as small apertures and narrow slots are represented directly into basis functions constructed by hierarchical sets of Rao-Wilton-Glisson expansion functions on a group of meshes yielded from subsequent refinements. As will be shown, the method results in highly sparse MoM matrices, which lead to fast convergence of iterative solvers. Hence, a remarkable reduction in the computational burden is achieved compared to the conventional RWG basis solution especially for the realistic enclosures with large number of apertures, used in the discipline of electromagnetic compatibility. Besides efficiency, the accuracy of the presented method is validated by a set of measurements conducted in an anechoic chamber.