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Surface scattering in three dimensions: an accelerated high–order solver

Bruno, Oscar P. and Kunyansky, Leonid A. (2001) Surface scattering in three dimensions: an accelerated high–order solver. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 457 (2016). pp. 2921-2934. ISSN 1364-5021. doi:10.1098/rspa.2001.0882.

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We present a new algorithm for the numerical solution of problems of acoustic scattering by surfaces in three–dimensional space. This algorithm evaluates scattered fields through fast, high–order, accurate solution of the corresponding boundary integral equation. The high–order accuracy of our solver is achieved through use of partitions of unityI together with analytical resolution of kernel singularities. The acceleration, in turn, results from use of high–order equivalent sourceapproximations, which allow for fast evaluation of non–adjacent interactions by means of the three–dimensional fast Fourier transform (FFT). Our acceleration scheme has dramatically lower memory requirements and yields much higher accuracy than existing FFT–accelerated techniques. The present algorithm computes one matrix–vector multiply in O(N^(6/5)logN) to O(N^(4/3)logN) operations (depending on the geometric characteristics of the scattering surface), it exhibits super–algebraic convergence, and it does not suffer from accuracy breakdowns of any kind. We demonstrate the efficiency of our method through a variety of examples. In particular, we show that the present algorithm can evaluate accurately, on a personal computer, scattering from bodies of acoustical sizes (ka) of several hundreds.

Item Type:Article
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Bruno, Oscar P.0000-0001-8369-3014
Additional Information:© 2001 The Royal Society. Received 2 June 2000; revised 19 August 2000; accepted 16 July 2001. Effort sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grant numbers F49620-96-1-0008, F49620-99-1-0010. O.P.B. gratefully acknowledges support from NSF (through an NYI award and through contracts DMS-9523292 and DMS-9816802), and from the Powell Research Foundation. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the US Government.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)F49620-96-1-0008
Air Force Office of Scientific Research (AFOSR)F49620-99-1-0010
Charles Lee Powell FoundationUNSPECIFIED
Subject Keywords:wave scattering; integral equation; fast algorithm; fast Fourier transform; equivalent sources; spherical wave expansion
Issue or Number:2016
Record Number:CaltechAUTHORS:20181106-151356250
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Official Citation:Surface scattering in three dimensions: an accelerated high–order solver. Oscar P. Bruno, Leonid A. Kunyansky. Proc. R. Soc. Lond. A 2001 457 2921-2934; DOI: 10.1098/rspa.2001.0882. Published 8 December 2001
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90680
Deposited By: Tony Diaz
Deposited On:07 Nov 2018 19:36
Last Modified:16 Nov 2021 03:34

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