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A novel approach of dual GPOF (general pencil of functions) combined with the DCIM (the discrete complex image method) is developed to accelerate the Sommerfeld integral evaluation, when the mixed potential integral equation (MPIE) is applied to numerically calculate scattering from a conductive object partially embedded in a dielectric half-space, where the field and source points are located in different media. Firstly, the factors related with the field point are separated from the spectrum function, and the GPOF is used to find the complex image parameters at finite discrete source points. Secondly, the GPOF is used again to fit the functional relationship of each complex image parameter with the source positions to evaluate the complex image parameters for any source position in a closed functional summation. Comparing numerical results of dual GPOF and direct numerical integration, this dual GPOF process is proved highly effective. Finally, dual GPOF/DCIM is applied to computation of electromagnetic scattering from a PEC spherical object partially embedded in a dielectric half-space medium, and numerical scattering results upon different model parameters are presented and analyzed.