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

Chappell, D. and Tanner, G. and Giani, S. (2012) 'Boundary element dynamical energy analysis : a versatile method for solving two or three dimensional wave problems in the high frequency limit.', Journal of computational physics., 231 (18). pp. 6181-6191.


Dynamical energy analysis was recently introduced as a new method for determining the distribution of mechanical and acoustic wave energy in complex built up structures. The technique interpolates between standard statistical energy analysis and full ray tracing, containing both of these methods as limiting cases. As such the applicability of the method is wide ranging and additionally includes the numerical modelling of problems in optics and more generally of linear wave problems in electromagnetics. In this work we consider a new approach to the method with enhanced versatility, enabling three-dimensional problems to be handled in a straightforward manner. The main challenge is the high dimensionality of the problem: we determine the wave energy density both as a function of the spatial coordinate and momentum (or direction) 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 make use of automated mesh generating routines to both localise the approximation, allowing quadrature costs to be kept moderate, and give versatility in the code for different geometric configurations.

Item Type:Article
Keywords:Statistical energy analysis, High-frequency asymptotics, Perron–Frobenius operator, Boundary element method.
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Publisher statement:Open access under CC BY license. This article is available under the terms of the Creative Commons Attribution License (CC BY). You may distribute and copy the article, create extracts, abstracts, and other revised versions, adaptations or derivative works of or from an article (such as a translation), to include in a collective work (such as an anthology), to text or data mine the article, including for commercial purposes without permission from Elsevier. The original work must always be appropriately credited.
Date accepted:18 May 2012
Date deposited:20 October 2015
Date of first online publication:July 2012
Date first made open access:No date available

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