Abstract
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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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