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A Fast, High-Order Algorithm for the Solution of Surface Scattering Problems: Basic Implementation, Tests, and Applications

Bruno, Oscar P. and Kunyansky, Leonid A. (2001) A Fast, High-Order Algorithm for the Solution of Surface Scattering Problems: Basic Implementation, Tests, and Applications. Journal of Computational Physics, 169 (1). pp. 80-110. ISSN 0021-9991. doi:10.1006/jcph.2001.6714.

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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 solution of the corresponding boundary integral equation. The high-order accuracy of our solver is achieved through use of partitions of unity together with analytical resolution of kernel singularities. The acceleration, in turn, results from use of a novel approach which, based on high-order “two-face” equivalent source approximations, reduces the evaluation of far interactions to evaluation of 3-D fast Fourier transforms (FFTs). This approach is faster and substantially more accurate, and it runs on dramatically smaller memories than other FFT and k-space methods. The present algorithm computes one matrix-vector multiplication in O(N^(6/5)log N) to O (N^(4/3) logN) operations, where N is the number of surface discretization points. The latter estimate applies to smooth surfaces, for which our high-order algorithm provides accurate solutions with small values of N; the former, more favorable count is valid for highly complex surfaces requiring significant amounts of subwavelength sampling. Further, our approach exhibits super-algebraic convergence; it can be applied to smooth and nonsmooth scatterers, and it does not suffer from accuracy breakdowns of any kind. In this paper we introduce the main algorithmic components in our approach, and we demonstrate its performance with a variety of numerical results. In particular, we show that the present algorithm can evaluate accurately in a personal computer scattering from bodies of acoustical sizes of several hundreds.

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Bruno, Oscar P.0000-0001-8369-3014
Additional Information:© 2001 Academic Press. Received 21 September 2000, Revised 18 December 2000. This effort is sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under Grants F49620-96-1-0008 and F49620-99-1-0010. O.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 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 U.S. Government. The U.S. Government's right to retain a nonexclusive royalty-free license in and to the copyright covering this paper, for governmental purposes, is acknowledged.
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
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Record Number:CaltechAUTHORS:20181101-152903866
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Official Citation:Oscar P. Bruno, Leonid A. Kunyansky, A Fast, High-Order Algorithm for the Solution of Surface Scattering Problems: Basic Implementation, Tests, and Applications, Journal of Computational Physics, Volume 169, Issue 1, 2001, Pages 80-110, ISSN 0021-9991, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90588
Deposited By: George Porter
Deposited On:02 Nov 2018 21:07
Last Modified:16 Nov 2021 03:33

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