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Theoretical aspects of the application of convolution quadrature to scattering of acoustic waves

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In this paper we address several theoretical questions related to the numerical approximation of the scattering of acoustic waves in two or three dimensions by penetrable non-homogeneous obstacles using convolution quadrature (CQ) techniques for the time variable and coupled boundary element method/finite element method for the space variable. The applicability of CQ to waves requires polynomial type bounds for operators related to the operator Δ − s 2 in the right half complex plane. We propose a new systematic way of dealing with this problem, both at the continuous and semidiscrete-in-space cases. We apply the technique to three different situations: scattering by a group of sound-soft and -hard obstacles, by homogeneous and non-homogeneous obstacles.

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Authors and Affiliations

  1. Dep. Matemáticas, EUPLA, Universidad de Zaragoza, 50100, La Almunia, Spain

    Antonio R. Laliena

  2. Dep. Matemática Aplicada, CPS, Universidad de Zaragoza, 50018, Zaragoza, Spain

    Francisco-Javier Sayas

  3. School of Mathematics, University of Minnesota, 206 Church St. SE, Minneapolis, MN, 55455, USA

    Francisco-Javier Sayas

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  1. Antonio R. Laliena
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  2. Francisco-Javier Sayas
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Correspondence to Francisco-Javier Sayas.

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Laliena, A.R., Sayas, FJ. Theoretical aspects of the application of convolution quadrature to scattering of acoustic waves. Numer. Math. 112, 637–678 (2009). https://doi.org/10.1007/s00211-009-0220-z

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  • DOI: https://doi.org/10.1007/s00211-009-0220-z

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