This study investigates reliable models and methods to be applied in sound field analysis of multi-domain structures. The case structures are two monuments, namely, Süleymaniye Mosque and Hagia Sophia in İstanbul. These are both multi-volume spaces with many smaller sub-volumes coupled to each other by coupling apertures in form of arches. A key concern of the study is to examine energy flow decays and understand the mechanism of multi-slope sound energy decays. The methodology involves diffusion equation model (DEM) application in a finite-element scheme for sound energy flow analysis. Energy flow decays, energy flow dips, and spatial flow vectors are examined for single versus multi-domain DEM solutions. It is concluded that specification of different domains with individual diffusion coefficients is a critical setting such that, if not assigned correctly, may mislead the results. The energy flow vector analysis has enabled us to comprehend the architectural features in relation to such energy flow decay dip occurrence. The computational efficiency of DEM is also discussed. The DEM application in this study has proved to be a powerful and practical method in room acoustics applications, specifically for multi-rate decay investigations.

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