Modeling late reverberation at interactive speeds is a challenging task when multiple sound sources and listeners are present in the same environment. This is especially problematic when the environment is geometrically complex and/or features uneven energy absorption (e.g. coupled volumes), because in such cases the late reverberation is dependent on the sound sources' and listeners' positions, and therefore must be adapted to their movements in real time. We present a novel approach to the task, named modal decomposition of Acoustic Radiance Transfer (MoD-ART), which can handle highly complex scenarios with efficiency. The approach is based on the geometrical acoustics method of Acoustic Radiance Transfer, from which we extract a set of energy decay modes and their positional relationships with sources and listeners. In this paper, we describe the physical and mathematical meaningfulness of MoD-ART, highlighting its advantages and applicability to different scenarios. Through an analysis of the method's computational complexity, we show that it compares very favourably with ray-tracing. We also present simulation results showing that MoD-ART can capture multiple decay slopes and flutter echoes.

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