  Standard methods for describing the intensity distribution of mechanical and
acoustic wave fields in the high frequency asymptotic limit are often based on
flow transport equations. Common techniques are statistical energy analysis,
employed mostly in the context of vibro-acoustics, and ray tracing, a popular
tool in architectural acoustics. Dynamical energy analysis makes it possible to
interpolate between standard statistical energy analysis and full ray tracing,
containing both of these methods as limiting cases. In this work a version of
dynamical energy analysis based on a Chebyshev basis expansion of the
Perron-Frobenius operator governing the ray dynamics is introduced. It is shown
that the technique can efficiently deal with multi-component systems overcoming
typical geometrical limitations present in statistical energy analysis. Results
are compared with state-of-the-art hp-adaptive discontinuous Galerkin finite
element simulations.
