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We address in detail the numerical simulations of electromagnetic (EM) wave scattering from a mockup partly coated fighter jet in this presentation. The majority part of the fighter jet surface is considered to be perfect electric conductor (PEC). The horizontal stabilizer, vertical stabilizer and the wings are coated with high-density materials, whereas a hollow dielectric radome is located at the front of the aircraft. Due to the nature of unbounded problem domain, and the desire to avoid a three dimensional discretization, we attempt to compute the numerical approximation using the boundary integral equations (BIEs), or the method of moments (MoM). However, it turns out not to be an easy quest. In the presentation, we shall elucidate difficulties that we have encountered and innovative techniques that we have devised during our journey to solve such a challenging mutli-scale EM application.