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Convergence analysis of a high-order Nyström integral-equation method for surface scattering problems

Bruno, Oscar P. and Domínguez, Víctor and Sayas, Francisco-Javier (2013) Convergence analysis of a high-order Nyström integral-equation method for surface scattering problems. Numerische Mathematik, 124 (4). pp. 603-645. ISSN 0029-599X. doi:10.1007/s00211-013-0525-9.

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In this paper we present a convergence analysis for the Nyström method proposed in [J Comput Phys 169 (1):80–110, 2001] for the solution of the combined boundary integral equation formulations of sound-soft acoustic scattering problems in three-dimensional space. This fast and efficient scheme combines FFT techniques and a polar change of variables that cancels out the kernel singularity. We establish the stability of the algorithms in the L^2 norm and we derive convergence estimates in both the L^2 and L^∞ norms. In particular, our analysis establishes theoretically the previously observed super-algebraic convergence of the method in cases in which the right-hand side is smooth.

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Bruno, Oscar P.0000-0001-8369-3014
Additional Information:© 2013 Springer-Verlag Berlin Heidelberg. Received: 27 September 2011; Revised: 8 July 2012; Published online: 6 March 2013. OB gratefully acknowledges support from AFOSR and NSF. VD is partially supported by Project MTM2010-21037. FJS is partially supported by the NSF-DMS 1216356 grant. A portion of this research was carried out when FJS was visiting professor at the University of Minnesota and during short visits of FJS and VD to the California Institute of Technology.
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Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Ministerio de Ciencia e Innovación (MICINN)MTM2010-21037
Issue or Number:4
Classification Code:Mathematics Subject Classification: 65N38; 65N35; 65T40
Record Number:CaltechAUTHORS:20130816-112500114
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Official Citation:Bruno, O.P., Domínguez, V. & Sayas, FJ. Numer. Math. (2013) 124: 603. doi:10.1007/s00211-013-0525-9
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:40708
Deposited By: Tony Diaz
Deposited On:16 Aug 2013 19:46
Last Modified:10 Nov 2021 00:07

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