Review Dynamic analysis of fluid–soil–structure interaction problems by the boundary element method D. Soares Jr. a,b, * , W.J. Mansur a a Department of Civil Engineering, COPPE – Federal University of Rio de Janeiro, CP 68506, CEP 21945-970, Rio de Janeiro, RJ, Brazil b Structural Engineering Department, Federal University of Juiz de Fora, Cidade Universita ´ ria, CEP 36036-330, Juiz de Fora, MG, Brazil Received 7 September 2005; received in revised form 19 April 2006; accepted 20 April 2006 Available online 19 June 2006 Abstract The present paper describes an iterative procedure for BEM–BEM coupling. The paper presents suitable interface conditions and algorithms for iteratively coupling sub-domains modeled by three different boundary element time-domain formulations, namely: acoustic and elastodynamic BEM formulations based on time-dependent Green’s functions and non-linear time-domain approach which employs elastostatic Green’s functions and therefore requires domain discretiza- tion. Two examples are analyzed and at the end of the paper conclusions of the study are presented. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Time-domain BEM; Iterative BEM–BEM coupling; Acoustics; Elastodynamics; Plasticity 1. Introduction Numerical solution algorithms for wave propagation analysis may give inaccurate results or else become unstable when the medium being considered is composed of sub-domains with too different physical proper- ties, when different media interact either through common interfaces, as is the case of soil–fluid–structure interaction analyses, or by forming a mixture, e.g. poroelastic media. Inaccurate and unstable time-domain algorithms may also occur when two different numerical methods are coupled, e.g. the boundary element method (BEM) and the finite element method (FEM); this problem may become even more serious when cou- pled algorithms and different physical media are considered simultaneously in the same analysis. There are many strategies in the FEM literature concerning the subject described in the last paragraph [1,2], one simple but efficient approach being subcycling [3–5]. Researchers dealing with the finite difference method (FDM) also proposed strategies to deal with interaction between different media; robust strategies have been proposed, some of them are widely used [6–8]. When no special procedure is employed to deal with this problem, e.g. assemble of the global matrix follows standard FEM procedures for homogeneous media, the 0021-9991/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2006.04.006 * Corresponding author. E-mail addresses: delfim@coc.ufrj.br (D. Soares Jr.), webe@coc.ufrj.br (W.J. Mansur). Journal of Computational Physics 219 (2006) 498–512 www.elsevier.com/locate/jcp