Boundary element dynamical energy analysis: a versatile method for solving two or three dimensional wave problems in the high frequency limit

摘要

Dynamical energy analysis was recently introduced as a new method fordetermining the distribution of mechanical and acoustic wave energy in complexbuilt up structures. The technique interpolates between standard statisticalenergy analysis and full ray tracing, containing both of these methods aslimiting cases. As such the applicability of the method is wide ranging andadditionally includes the numerical modelling of problems in optics and moregenerally of linear wave problems in electromagnetics. In this work we considera new approach to the method with enhanced versatility, enablingthree-dimensional problems to be handled in a straightforward manner. The mainchallenge is the high dimensionality of the problem: we determine the waveenergy density both as a function of the spatial coordinate and momentum (ordirection) space. The momentum variables are expressed in separable (polar)coordinates facilitating the use of products of univariate basis expansions.However this is not the case for the spatial argument and so we propose to makeuse of automated mesh generating routines to both localise the approximation,allowing quadrature costs to be kept moderate, and give versatility in the codefor different geometric configurations.