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Volume 11, Issue 2
Micro-Differential Boundary Conditions Modelling the Absorption of Acoustic Waves by 2D Arbitrarily-Shaped Convex Surfaces

Hélène Barucq, Julien Diaz & Véronique Duprat

DOI: 10.4208/cicp.311209.260411s

Commun. Comput. Phys., 11 (2012), pp. 674-690.

Published online: 2012-12

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  • Abstract

We propose a new Absorbing Boundary Condition (ABC) for the acoustic wave equation which is derived from a micro-local diagonalization process formerly defined by M.E. Taylor and which does not depend on the geometry of the surface bearing the ABC. By considering the principal symbol of the wave equation both in the hyperbolic and the elliptic regions, we show that a second-order ABC can be constructed as the combination of an existing first-order ABC and a Fourier-Robin condition. We compare the new ABC with other ABCs and we show that it performs well in simple configurations and that it improves the accuracy of the numerical solution without increasing the computational burden. 

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@Article{CiCP-11-674, author = {Hélène Barucq, Julien Diaz and Véronique Duprat}, title = {Micro-Differential Boundary Conditions Modelling the Absorption of Acoustic Waves by 2D Arbitrarily-Shaped Convex Surfaces}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {2}, pages = {674--690}, abstract = {

We propose a new Absorbing Boundary Condition (ABC) for the acoustic wave equation which is derived from a micro-local diagonalization process formerly defined by M.E. Taylor and which does not depend on the geometry of the surface bearing the ABC. By considering the principal symbol of the wave equation both in the hyperbolic and the elliptic regions, we show that a second-order ABC can be constructed as the combination of an existing first-order ABC and a Fourier-Robin condition. We compare the new ABC with other ABCs and we show that it performs well in simple configurations and that it improves the accuracy of the numerical solution without increasing the computational burden. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.311209.260411s}, url = {http://global-sci.org/intro/article_detail/cicp/7385.html} }
TY - JOUR T1 - Micro-Differential Boundary Conditions Modelling the Absorption of Acoustic Waves by 2D Arbitrarily-Shaped Convex Surfaces AU - Hélène Barucq, Julien Diaz & Véronique Duprat JO - Communications in Computational Physics VL - 2 SP - 674 EP - 690 PY - 2012 DA - 2012/12 SN - 11 DO - http://doi.org/10.4208/cicp.311209.260411s UR - https://global-sci.org/intro/article_detail/cicp/7385.html KW - AB -

We propose a new Absorbing Boundary Condition (ABC) for the acoustic wave equation which is derived from a micro-local diagonalization process formerly defined by M.E. Taylor and which does not depend on the geometry of the surface bearing the ABC. By considering the principal symbol of the wave equation both in the hyperbolic and the elliptic regions, we show that a second-order ABC can be constructed as the combination of an existing first-order ABC and a Fourier-Robin condition. We compare the new ABC with other ABCs and we show that it performs well in simple configurations and that it improves the accuracy of the numerical solution without increasing the computational burden. 

Hélène Barucq, Julien Diaz and Véronique Duprat. (2012). Micro-Differential Boundary Conditions Modelling the Absorption of Acoustic Waves by 2D Arbitrarily-Shaped Convex Surfaces. Communications in Computational Physics. 11 (2). 674-690. doi:10.4208/cicp.311209.260411s
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