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

卷:231

Article

Chappell, David J.¹  Tanner, Gregor¹  Giani, Stefano¹ 

[1] Univ Nottingham, Sch Math Sci, Nottingham NG7 2RD, England

关键词: Statistical energy analysis;    High-frequency asymptotics;    Perron-Frobenius operator;    Boundary element method;   

DOI  :  10.1016/j.jcp.2012.05.028

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free