Abstract:
Transparent artificial boundary conditions and an algorithm for computing the augmented scattering matrix are proposed for finding surface waves in a prescribed range of decay rates. An infinite-dimensional fictitious scattering operator is constructed that determines all waves decaying exponentially with distance from a periodic obstacle.
Key words:
artificial boundary conditions, diffraction by a periodic boundary, search for surface waves.
Citation:
S. A. Nazarov, “Artificial boundary conditions for finding surface waves in the problem of diffraction by a periodic boundary”, Zh. Vychisl. Mat. Mat. Fiz., 46:12 (2006), 2265–2276; Comput. Math. Math. Phys., 46:12 (2006), 2164–2175
\Bibitem{Naz06}
\by S.~A.~Nazarov
\paper Artificial boundary conditions for finding surface waves in the problem of diffraction by a~periodic boundary
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 12
\pages 2265--2276
\mathnet{http://mi.mathnet.ru/zvmmf372}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2344971}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 12
\pages 2164--2175
\crossref{https://doi.org/10.1134/S0965542506120141}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846136735}
Linking options:
https://www.mathnet.ru/eng/zvmmf372
https://www.mathnet.ru/eng/zvmmf/v46/i12/p2265
This publication is cited in the following 15 articles:
S. A. Nazarov, “Almost standing waves in a periodic waveguide with a resonator and near-threshold eigenvalues”, St. Petersburg Math. J., 28:3 (2017), 377–410
D. I. Borisov, “Perturbation of Threshold of Essential Spectrum for Waveguides with Windows. II: Asymptotics”, J Math Sci, 210:5 (2015), 590
Nazarov S.A., Ruotsalainen K.M., “Criteria For Trapped Modes in a Cranked Channel With Fixed and Freely Floating Bodies”, Z. Angew. Math. Phys., 65:5 (2014), 977–1002
S. A. Nazarov, “Scheme for interpretation of approximately computed eigenvalues embedded in a continuous spectrum”, Comput. Math. Math. Phys., 53:6 (2013), 702–720
S. A. Nazarov, “The Mandelstam Energy Radiation Conditions and the Umov–Poynting Vector in Elastic Waveguides”, J Math Sci, 195:5 (2013), 676
G. Cardone, S. A. Nazarov, K. Ruotsalainen, “Asymptotic behaviour of an eigenvalue in the continuous spectrum of a narrowed waveguide”, Sb. Math., 203:2 (2012), 153–182
S. A. Nazarov, “Enforced stability of an eigenvalue in the continuous spectrum of a waveguide with an obstacle”, Comput. Math. Math. Phys., 52:3 (2012), 448–464
Nazarov S.A., “Trapped waves in a cranked waveguide with hard walls”, Acoustical Physics, 57:6 (2011), 764–771
S. A. Nazarov, “On the asymptotics of an eigenvalue of a waveguide with thin shielding obstacle and Wood's anomalies”, J. Math. Sci. (N. Y.), 178:3 (2011), 292–312
Chandler-Wilde S.N., Elschner J., “Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces”, SIAM J. Math. Anal., 42:6 (2010), 2554–2580
Nazarov S.A., “Trapped modes in a T-shaped waveguide”, Acoustical Physics, 56:6 (2010), 1004–1015
S. A. Nazarov, “Gap detection in the spectrum of an elastic periodic waveguide with a free surface”, Comput. Math. Math. Phys., 49:2 (2009), 323–333
S. A. Nazarov, “Concentration of trapped modes in problems of the linearized theory of water waves”, Sb. Math., 199:12 (2008), 1783–1807
S. A. Nazarov, “Trapped modes in a cylindrical elastic waveguide with a damping gasket”, Comput. Math. Math. Phys., 48:5 (2008), 816–833
S. A. Nazarov, “On the concentration of the point spectrum on the
continuous one in problems of the linearized theory of water-waves”, J. Math. Sci. (N. Y.), 152:5 (2008), 674–689
Citation in format AMSBIB
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