In radio astronomical applications, it may be essential to accurately evaluate the electromagnetic scattering and power dissipation losses of nearby dielectric objects, such as radomes. However, the numerical analysis becomes a burdensome task when the dielectric becomes thin, complex shaped, and electrically large. To mitigate these problems, we propose to employ high-resolution basis functions for accurate modeling of electromagnetic scattering from dielectric objects. Application of these basis functions significantly eases the computational burden of generating the on- and off-diagonal elements of the moment matrix. This method has been hybridized with the Characteristic Basis Function Method (CBFM) and the Adaptive Cross Approximation (ACA) algorithm to reduce both the size and generation time of the moment matrix equation. Furthermore, the proposed method is not only fast and memory efficient but it also generates the accurate solution of scattering problems associated with complex-shaped, thin and electrically large objects.