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A Chebyshev-based rectangular-polar integral solver for scattering by geometries described by non-overlapping patches

Bruno, Oscar P. and Garza, Emmanuel (2020) A Chebyshev-based rectangular-polar integral solver for scattering by geometries described by non-overlapping patches. Journal of Computational Physics, 421 . Art. No. 109740. ISSN 0021-9991. doi:10.1016/

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This paper introduces a high-order-accurate strategy for integration of singular kernels and edge-singular integral densities that appear in the context of boundary integral equation formulations for the problem of acoustic scattering. In particular, the proposed method is designed for use in conjunction with geometry descriptions given by a set of arbitrary non-overlapping logically-quadrilateral patches—which makes the algorithm particularly well suited for computer-aided design (CAD) geometries. Fejér's first quadrature rule is incorporated in the algorithm, to provide a spectrally accurate method for evaluation of contributions from far integration regions, while highly-accurate precomputations of singular and near-singular integrals over certain “surface patches” together with two-dimensional Chebyshev transforms and suitable surface-varying “rectangular-polar” changes of variables, are used to obtain the contributions for singular and near-singular interactions. The overall integration method is then used in conjunction with the linear-algebra solver GMRES to produce solutions for sound-soft open- and closed-surface scattering obstacles, including an application to an aircraft described by means of a CAD representation. The approach is robust, fast, and highly accurate: use of a few points per wavelength suffices for the algorithm to produce far-field accuracies of a fraction of a percent, and slight increases in the discretization densities give rise to significant accuracy improvements.

Item Type:Article
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URLURL TypeDescription Paper
Bruno, Oscar P.0000-0001-8369-3014
Garza, Emmanuel0000-0003-1687-8216
Alternate Title:A Chebyshev-based rectangular-polar integral solver for scattering by general geometries described by non-overlapping patches
Additional Information:© 2020 Elsevier Inc. Received 12 July 2019, Revised 24 July 2020, Accepted 24 July 2020, Available online 5 August 2020. The authors gratefully acknowledge support by NSF, AFOSR and DARPA through contracts DMS-1714169 and FA9550-15-1-0043 and HR00111720035, and the NSSEFF Vannevar Bush Fellowship under contract number N00014-16-1-2808. Additionally, the authors thank Dr. Edwin Jimenez and Dr. James Guzman for providing the processing of the CAD geometry used in Section 5.4. CRediT authorship contribution statement: Oscar P. Bruno: Conceptualization, Methodology, Validation, Investigation, Resources, Writing, Supervision, Funding acquisition. Emmanuel Garza: Conceptualization, Methodology, Software, Validation, Investigation, Writing, Visualization. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-15-1-0043
Defense Advanced Research Projects Agency (DARPA)HR00111720035
National Security Science and Engineering Faculty FellowshipN00014-16-1-2808
Vannever Bush Faculty FellowshipUNSPECIFIED
Subject Keywords:Integral equations; Scattering problem; High-order accuracy; CAD representation; Rectangular-polar method; General geometries
Record Number:CaltechAUTHORS:20181102-090626983
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Official Citation:Oscar P. Bruno, Emmanuel Garza, A Chebyshev-based rectangular-polar integral solver for scattering by geometries described by non-overlapping patches, Journal of Computational Physics, Volume 421, 2020, 109740, ISSN 0021-9991, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90609
Deposited By: Tony Diaz
Deposited On:02 Nov 2018 16:24
Last Modified:16 Nov 2021 03:34

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