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In air-packaged surface micromachined devices, drag forces introduce coupling between moving mechanical parts and are an important energy loss mechanism, thus playing an important role in device performance. In these devices, the amount of drag is greatly influenced by the presence of the nearby substrate. In this paper, we present a precorrected fast Fourier transform (pFFT) accelerated boundary element method specialized for calculating the drag force on structures above a substrate. Our method uses the Green's function for Stokes flow bounded by an infinite plane to implicitly represent the device substrate, requiring a number of modifications to the pFFT algorithm. Computational results demonstrate that the use of the implicit representation of the substrate reduces computation time and memory while increasing the solution accuracy. The results demonstrate that surprisingly, and unfortunately, even though representing the substrate implicitly has many benefits, it does not completely decouple discretization fineness from distance to the substrate.