We present a domain decomposition theory on an interface problemfor the linear transport equation between a diffusive and a non-diffusive region.To leading order, i.e. up to an error of the order of the mean free path in thediffusive region, the solution in the non-diffusive region is independent of thedensity in the diffusive region. However, the diffusive and the non-diffusive regionsare coupled at the interface at the next order of approximation. In particular, ouralgorithm avoids iterating the diffusion and transport solutions as is done in mostother methods — see for example Bal–Maday (2002). Our analysis is based instead on an accurate description of the boundarylayer at the interface matching the phase-space density of particles leaving thenon-diffusive region to the bulk density that solves the diffusion equation.
