Wave Propagation Problems treated with Convolution Quadrature and BEM

Lehel Banjai and Martin Schanz

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Submission date: 18. Oct. 2010 (revised version: October 2010)
Pages: 42
published in: Fast boundary element methods in engineering and industrial applications / U. Langer ... (eds.)
Berlin [u.a.] : Springer, 2012. - P. 145 - 184
(Lecture notes in applied and computational mechanics ; 63) 
DOI number (of the published article): 10.1007/978-3-642-25670-7_5
Bibtex
Keywords and phrases: time domain boundary integral equations, convlution quadrature, convolution quadrature, applications
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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. 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 TBIE an important numerical method for wave propagation problems, which requires further attention.