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A two-step expansion technique has been developed for finite-difference codes that can increase the spectral resolution of such codes over selected subvolumes of the original problem space. The utility of this technique is demonstrated by predicting the responses arising from the coupling of an incident exterior field across an aperture in a hollow cylinder to an interior wire. Expansions on the order of fourfold or more are possible. The cost of such increased resolution is a second computer run, doubling the cost as opposed to a cost increase of a factor of 64 if the resolution equivalent to a fourfold expansion were sought from a single run. Possible applications extend to many diverse areas, but most importantly, interior coupling problems may be treated using this technique. For example, this technique may provide a useful method for estimating the responses of cables interior to an aircraft.