%0 Journal Article
%T An improved multimodal approach for non-uniform acoustic waveguides
%+ Propagation des Ondes : Étude Mathématique et Simulation (POEMS)
%A Hazard, Christophe
%A Lunéville, Éric
%< avec comité de lecture
%@ 0272-4960
%J IMA Journal of Applied Mathematics
%I Oxford University Press (OUP)
%V 73
%N 4
%P 668-690
%8 2008
%D 2008
%R 10.1093/imamat/hxn006
%Z Mathematics [math]/Numerical Analysis [math.NA]
%Z Physics [physics]/Mechanics [physics]/Acoustics [physics.class-ph]
%Z Engineering Sciences [physics]/Acoustics [physics.class-ph]Journal articles
%X This paper explores from the point of view of numerical analysis a method for solving the acoustic time-harmonic wave equation in a locally non-uniform 2D waveguide. The multimodal method is based on a spectral description of the acoustic field in each transverse section of the guide, using Fourier-like series. In the case of sound-hard boundaries, the weak point of the method lies in the poor convergence of such series due to a poor approximation of the field near the boundaries. A remedy was proposed by Athanassoulis & Belibassakis (1999, J. Fluid Mech., 389, 275-301), where the convergence is improved thanks to the use of enhanced series. The present paper proposes a theoretical analysis of their idea and studies further improvements. For a general model which includes different kinds of non-uniformity (varying cross section, bend and inhomogeneous medium), a hybrid spectral/variational formulation is introduced. Error estimates are provided for a semi-discretized problem which concerns the effect of spectral truncation. These estimates are confirmed by numerical results. © The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
%G English
%L hal-00873082
%U https://hal-ensta-paris.archives-ouvertes.fr//hal-00873082
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