The aim of the present contribution is the analysis of one-dimensional wave propagation problems, rewritten as BIEs directly in space-time domain, thus avoiding the use of the Laplace transform and of its inversion: the transformation back to time domain employs particular procedure corresponding to a linear multi-step method for ordinary differential equations [Becache, 1993, Lubich, 1988a, Lubich, 1988b, Bamberger and Duong, 1986a]. Some different approximation techniques will be used, analyzing and comparing the numerical properties of the derived linear systems: the first comes from a classical weak formulation of the corresponding BIE, the second from a new energetic weak formulation which has a more robust theoretical background. An alternative weak formulation of the BIEs is the one presented in [Bamberger and Duong, 1986a], [Bamberger and Duong, 1986b], which is based on the Laplace-Fourier transform of the differential problem and its inversion.
Numerical results for the wave propagation problem with space-time boundary element method / A. Aimi, M. Diligenti, C. Guardasoni - In: Atti del XVIII congresso dell’Associazione Italiana di Meccanica Teorica e Applicata / [a cura di] A. Carini, G. Mimmi, R. Piva. - Brescia : Starrylink, 2007. - ISBN 9788889720691. - pp. 393-404 (( Intervento presentato al 18. convegno AIMETA Congress tenutosi a Brescia nel 2007.
Numerical results for the wave propagation problem with space-time boundary element method
C. GuardasoniUltimo
2007
Abstract
The aim of the present contribution is the analysis of one-dimensional wave propagation problems, rewritten as BIEs directly in space-time domain, thus avoiding the use of the Laplace transform and of its inversion: the transformation back to time domain employs particular procedure corresponding to a linear multi-step method for ordinary differential equations [Becache, 1993, Lubich, 1988a, Lubich, 1988b, Bamberger and Duong, 1986a]. Some different approximation techniques will be used, analyzing and comparing the numerical properties of the derived linear systems: the first comes from a classical weak formulation of the corresponding BIE, the second from a new energetic weak formulation which has a more robust theoretical background. An alternative weak formulation of the BIEs is the one presented in [Bamberger and Duong, 1986a], [Bamberger and Duong, 1986b], which is based on the Laplace-Fourier transform of the differential problem and its inversion.Pubblicazioni consigliate
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