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An efficient high-order algorithm for acoustic scattering from penetrable thin structures in three dimensions

Anand, Akash and Reitich, Fernando (2007) An efficient high-order algorithm for acoustic scattering from penetrable thin structures in three dimensions. Journal of the Acoustical Society of America, 121 (5). pp. 2503-2514. ISSN 0001-4966. https://resolver.caltech.edu/CaltechAUTHORS:ANAjasa07

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Abstract

This paper presents a high-order accelerated algorithm for the solution of the integral-equation formulation of volumetric scattering problems. The scheme is particularly well suited to the analysis of “thin” structures as they arise in certain applications (e.g., material coatings); in addition, it is also designed to be used in conjunction with existing low-order FFT-based codes to upgrade their order of accuracy through a suitable treatment of material interfaces. The high-order convergence of the new procedure is attained through a combination of changes of parametric variables (to resolve the singularities of the Green function) and “partitions of unity” (to allow for a simple implementation of spectrally accurate quadratures away from singular points). Accelerated evaluations of the interaction between degrees of freedom, on the other hand, are accomplished by incorporating (two-face) equivalent source approximations on Cartesian grids. A detailed account of the main algorithmic components of the scheme are presented, together with a brief review of the corresponding error and performance analyses which are exemplified with a variety of numerical results.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1121/1.2714919DOIUNSPECIFIED
Additional Information:©2007 Acoustical Society of America (Received 6 December 2005; revised 10 February 2007; accepted 13 February 2007) F.R. gratefully acknowledges support from AFOSR through Contract No. FA9550-05-1-0019, from NSF through Grant No. DMS-0311763, and from the Army High Performance Computing Research Center (AHPCRC) under Army Research Laboratory Cooperative Agreement No. DAAD19-01-2-0014. The computations for this project were carried out at the Minnesota Supercomputing Institute, whose support is also gratefully acknowledged.
Subject Keywords:acoustic wave scattering; Helmholtz equations; integral equations
Issue or Number:5
Record Number:CaltechAUTHORS:ANAjasa07
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:ANAjasa07
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8473
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:15 Aug 2007
Last Modified:02 Oct 2019 23:51

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