A procedure is described for simulating the behavior of multimode, bolometric, astronomical interferometers. The procedure relies on the use of singular value decomposition to determine the fields on the sky and the fields at the detectors to which the individual elements of an interferometer can couple. The scheme can be used with any configuration of optical components, with a source in any state of coherence, and with a detector of any kind: planar bolometers, waveguide horns, imaging arrays, etc. In the paper we describe the space-domain formulation of the theory, and present simulations of classical Fizeau and Michelson interferometers. We also show that the scheme reproduces correctly the behavior of single-mode radio and highly multimode optical interferometers when the appropriate limits are taken. To conclude, we discuss the many different ways in which the basic technique can be used and extended.