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Structural Engineering and Mechanics Volume 27, Number 6, December10 2007 , pages 683-696 DOI: https://doi.org/10.12989/sem.2007.27.6.683 |
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A step-by-step approach in the time-domain BEM formulation for the scalar wave equation |
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J. A. M. Carrer and W. J. Mansur
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| Abstract | ||
| This article is concerned with the presentation of a time-domain BEM approach applied to the solution of the scalar wave equation for 2D problems. The basic idea is quite simple: the basic variables of the problem at time tn (potential and flux) are computed with the results related to the potential and to its time derivative at time tn.1 playing the role of ?initial conditions?. This time-marching scheme needs the computation of the potential and its time derivative at all boundary nodes and internal points, as well as the entire discretization of the domain. The convolution integrals of the standard timedomain BEM formulation, however, are not computed; the matrices assembled, only at the initial time interval, are those related to the potential, flux and to the potential time derivative. Two examples are presented and discussed at the end of the article, in order to verify the accuracy and potentialities of the proposed formulation. | ||
| Key Words | ||
| time-domain BEM; scalar wave equation; step-by-step BEM analysis. | ||
| Address | ||
| J. A. M. Carrer; Programa de Pos-Graduacao em Metodos Numericos em Engenharia, Universidade Federal do Parana, CEP 81531-990, Curitiba, PR, Brasil W. J. Mansur; Programa de Engenharia Civil, COPPE/UFRJ, Caixa Postal 68506, CEP 21945-970, Rio de Janeiro, RJ, Brasil | ||