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Finite-Dimensional Approximations of the Steklov–Poincaré Operator in Periodic Elastic Waveguides

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Abstract

For anisotropic elastic waveguides with cylindrical or periodic outlets to infinity, artificial integro-differential conditions are developed at the end face of a truncated waveguide, which simulate the Steklov–Poincaré operator for scalar problems. Asymptotically sharp error estimates are derived in the definition of both the elastic fields themselves in the waveguide and the corresponding scattering coefficients.

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Authors and Affiliations

  1. Faculty of Mathematics and Mechanics, St. Petersburg State University, 198504, Staryi Petergof, St. Petersburg, Russia

    S. A. Nazarov

  2. Peter the Great St. Petersburg State Polytechnic University, 195251, St. Petersburg, Russia

    S. A. Nazarov

  3. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, 199178, St. Petersburg, Russia

    S. A. Nazarov

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  1. S. A. Nazarov
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Correspondence to S. A. Nazarov.

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Translated by I. Nikitin

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Nazarov, S.A. Finite-Dimensional Approximations of the Steklov–Poincaré Operator in Periodic Elastic Waveguides. Dokl. Phys. 63, 307–311 (2018). https://doi.org/10.1134/S1028335818070108

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  • DOI: https://doi.org/10.1134/S1028335818070108

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