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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.; Tanner, G.; Giani, S.

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


Authors

D. Chappell

G. Tanner



Abstract

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.

Citation

Chappell, D., Tanner, G., & 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), 6181-6191. https://doi.org/10.1016/j.jcp.2012.05.028

Journal Article Type Article
Acceptance Date May 18, 2012
Publication Date Jul 15, 2012
Deposit Date Feb 12, 2013
Publicly Available Date Mar 29, 2024
Journal Journal of Computational Physics
Print ISSN 0021-9991
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 231
Issue 18
Pages 6181-6191
DOI https://doi.org/10.1016/j.jcp.2012.05.028
Keywords Statistical energy analysis, High-frequency asymptotics, Perron–Frobenius operator, Boundary element method.
Related Public URLs http://arxiv.org/pdf/1202.4416v1.pdf

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http://creativecommons.org/licenses/by/4.0/

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