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Intensity distributions of linear wave fields are, in the high frequencylimit, often approximated in terms of flow or transport equations in phasespace. Common techniques for solving the flow equations for both time dependentand stationary problems are ray tracing or level set methods. In the context ofpredicting the vibro-acoustic response of complex engineering structures,reduced ray tracing methods such as Statistical Energy Analysis or variantsthereof have found widespread applications. Starting directly from thestationary Liouville equation, we develop a boundary element method for solvingthe transport equations for complex multi-component structures. The method,which is an improved version of the Dynamical Energy Analysis techniqueintroduced recently by the authors, interpolates between standard statisticalenergy analysis and full ray tracing, containing both of these methods aslimiting cases. We demonstrate that the method can be used to efficiently dealwith complex large scale problems giving good approximations of the energydistribution when compared to exact solutions of the underlying wave equation.

Solving the stationary Liouville equation via a boundary element method