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In this paper, we present our efforts in combating a challenging large multiscale electromagnetic scattering problem, viz. a plane-wave scattering from a mockup partially coated composite jet aircraft at X-band. We first summarize the application of the newly developed integral equation domain decomposition method (IE-DDM) to compute the plane-wave scattering from the jet aircraft, however with neither dielectrics nor lossy thin coatings. We proceed to compute the scattering from the aircraft with dielectrics and lossy thin coatings by employing two additional computational electromagnetics (CEM) techniques: a generalized combined field integral equation (G-CFIE) method to calculate electromagnetics (EM) scatterings from penetrable dielectric targets, and a hybrid finite elements and boundary elements method tailored specifically to address perfect electric conductor (PEC) targets partially coated with lossy thin materials.