We consider the retarded potential boundary integral equation, arising from the 3D elastic (vector) wave equation problem, endowed with a Dirichlet condition on the boundary and null initial conditions. For its numerical solution, we employ a weak formulation related to the energy of the system and we discretize it by a Galerkin-type boundary element method (BEM). This approach, called energetic BEM, has been already applied in the context of time-domain acoustic (scalar) wave propagation and it has revealed accurate and stable even on large time intervals of analysis. In particular, when standard (constant) shape functions for time discretization are employed, the double integration in time can be performed analytically. Then, one is left with the task of evaluating double space integrals, whose integration domains are generally delimited by the wave fronts of the primary and the secondary waves. Since the accurate computation of the integrals involved in the numerical scheme is a key issue for the stability of the method, we propose an efficient evaluation strategy, based on the exact detection of the integration domain. The presented numerical tests show the effectiveness of the proposed approach.
A space–time energetic BIE method for 3D elastodynamics: the Dirichlet case
Desiderio L.
Penultimo
Membro del Collaboration Group
;
2023-01-01
Abstract
We consider the retarded potential boundary integral equation, arising from the 3D elastic (vector) wave equation problem, endowed with a Dirichlet condition on the boundary and null initial conditions. For its numerical solution, we employ a weak formulation related to the energy of the system and we discretize it by a Galerkin-type boundary element method (BEM). This approach, called energetic BEM, has been already applied in the context of time-domain acoustic (scalar) wave propagation and it has revealed accurate and stable even on large time intervals of analysis. In particular, when standard (constant) shape functions for time discretization are employed, the double integration in time can be performed analytically. Then, one is left with the task of evaluating double space integrals, whose integration domains are generally delimited by the wave fronts of the primary and the secondary waves. Since the accurate computation of the integrals involved in the numerical scheme is a key issue for the stability of the method, we propose an efficient evaluation strategy, based on the exact detection of the integration domain. The presented numerical tests show the effectiveness of the proposed approach.Pubblicazioni consigliate
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