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This article combines the equivalence principle with multiple-pass finite-difference time-domain (FDFD) techniques to compute fields behind a cavity-backed aperture. On the first pass, the electromagnetic response of the target is externally determined with the aperture foiled over. The current flowing on the foil is recorded and used to illuminate the aperture on the second pass. Almost no detail of the target external to the aperture need be supplied for the second-pass computation. This makes possible very efficient use of available clomputer memory for concentrating on cavity details. The technique can treat electrically large apertures. The example used here is a fighter aircraft where the cavity is the cockpit and thLe cockpit bubble is the aperture. There is no appeal to superposition inside the cavitykockpit, so nonlinear electromagnetic phenomena may be included there in the model.