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


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)



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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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