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MiS Preprint

Wave Propagation Problems treated with Convolution Quadrature and BEM

Lehel Banjai and Martin Schanz


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.

time domain boundary integral equations, convlution quadrature, convolution quadrature, applications

Related publications

2010 Repository Open Access
Lehel Banjai and Martin Schanz

Wave propagation problems treated with convolution quadrature and BEM

In: Fast boundary element methods in engineering and industrial applications / Ulrich Langer... (eds.)
Berlin [u.a.] : Springer, 2012. - pp. 145-184
(Lecture notes in applied and computational mechanics ; 63)