Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The multidimensional stationary-phase method for an asymptotic estimate of edge effects in the multiple Kirchhoff diffraction by curved surfaces


Authors: Edoardo Scarpetta and Mezhlum A. Sumbatyan
Journal: Quart. Appl. Math. 72 (2014), 731-745
MSC (2010): Primary 78A45
DOI: https://doi.org/10.1090/S0033-569X-2014-01365-3
Published electronically: September 25, 2014
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Abstract | References | Similar Articles | Additional Information

Abstract: An analytical approach is proposed to study the contribution of edge effects in the multiple high-frequency diffraction, according to guidelines of classical Kirchhoff theory in (scalar) wave propagation. We start from a suitable asymptotic analysis of the Kirchhoff diffraction integral, here set up in a generalized (iterated) form to describe the multiple reflections from an arbitrary sequence of curved reflecting (smooth) surfaces. The explicit formula obtained for a concrete example of double reflection is compared with the results from direct numerical simulation.


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Additional Information

Edoardo Scarpetta
Affiliation: Department of Industrial Engineering, University of Salerno, 84084 Fisciano (SA), Italy
Email: escarpetta@unisa.it

Mezhlum A. Sumbatyan
Affiliation: Faculty of Mathematics, Mechanics and Computer Science, Southern Federal University, Milchakova Street 8a, 344090 Rostov-on-Don, Russia
Email: sumbat@math.rsu.ru

DOI: https://doi.org/10.1090/S0033-569X-2014-01365-3
Received by editor(s): November 27, 2012
Published electronically: September 25, 2014
Additional Notes: The authors thank the reviewer for his useful suggestions
Article copyright: © Copyright 2014 Brown University

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