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Wave Propagation Problems Treated with Convolution Quadrature and BEM

  • Lehel Banjai
  • Martin Schanz
Chapter
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 63)

Abstract

Boundary element methods for steady state problems have reached a state of maturity in both analysis and efficient implementation and have become an ubiquitous tool in engineering applications. Their time-domain counterparts, however, in particular for wave propagation phenomena, still present many open questions related to the analysis of the numerical methods and their algorithmic implementation. In recent years many exciting results have been achieved in this area. In this review paper, a particular type of methods for treating time-domain boundary integral equations (TDBIE), the convolution quadrature, is described together with application areas and most recent improvements to the analysis and efficient implementation. An important attraction of these methods is their intrinsic stability, often a problem with numerical methods for TDBIE of wave propagation. Further, since convolution quadrature, though a time-domain method, uses only the kernel of the integral operator in the Laplace domain, it is widely applicable also to problems such as viscoelastodynamics, where the kernel is known only in the Laplace domain. This makes convolution quadrature for TDBIE an important numerical method for wave propagation problems, which requires further attention.

Keywords

Boundary Element Method Boundary Integral Equation Multistep Method Laplace Domain Fast Multipole Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Max-Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Institute of Applied MechanicsGraz University of TechnologyGrazAustria

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