An integral representation of the Green’s function for a linear array of acoustic point sources

Peer reviewed: 
Yes, item is peer reviewed.
Scholarly level: 
Faculty/Staff
Date created: 
2010
Keywords: 
Green’s function periodic domain
rough-surface
high-frequency
free-space
Helmholtz equation
Abstract: 

We present a new algorithm for the evaluation of the periodized Green’s function fora linear array of acoustic point sources such as those arising in the analysis of linearray loudspeakers. A variety of classical algorithms (based on spatial and spectralrepresentations, Ewald transformation, etc.) have been implemented in the past toevaluate these acoustic fields. However as we show, these methods become unstableand/or impractically expensive as the frequency of use of the sources increases. Herewe introduce a new numerical scheme that overcomes some of these limitations allowingfor simulations at unprecedentally large frequencies. The method is based ona new integral representation derived from the classic spatial form, and on suitablefurther manipulations of the relevant integrands to render the integrals amenable toefficient and accurate approximations through standard quadrature formulas. Weinclude a variety of numerical results that demonstrate that our algorithm comparesfavorably with several classical method both for points close to the line where thepoles are located and at high-frequencies while remaining competitive with them inevery other instance.

Language: 
English
Document type: 
Article
Rights: 
You are free to copy, distribute and transmit this work under the following conditions: You must give attribution to the work (but not in any way that suggests that the author endorses you or your use of the work); You may not use this work for commercial purposes; You may not alter, transform, or build upon this work. Any further uses require the permission of the rights holder (or author if no rights holder is listed). These rights are based on the Creative Commons Attribution-NonCommercial-NoDerivatives License.
Citation: 
Kurkcu, H., Nigam, N., & Reitich, F. (2011). An integral representation of the green function for a linear array of acoustic point sources. Journal of Computational Physics, 230(8), 2838-2856. doi:10.1016/j.jcp.2010.12.034
Statistics: