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Numerische Mathematik

, Volume 112, Issue 4, pp 637–678 | Cite as

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

  • Antonio R. Laliena
  • Francisco-Javier SayasEmail author
Article

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.

Mathematics Subject Classification (2000)

65N30 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Dep. MatemáticasEUPLA, Universidad de ZaragozaLa AlmuniaSpain
  2. 2.Dep. Matemática Aplicada, CPSUniversidad de ZaragozaZaragozaSpain
  3. 3.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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