%0 Journal Article
%T An Overview of Recent Advances in the Iterative Analysis of Coupled Models for Wave Propagation
%A D. Soares Jr.
%A L. Godinho
%J Journal of Applied Mathematics
%D 2014
%I Hindawi Publishing Corporation
%R 10.1155/2014/426283
%X Wave propagation problems can be solved using a variety of methods. However, in many cases, the joint use of different numerical procedures to model different parts of the problem may be advisable and strategies to perform the coupling between them must be developed. Many works have been published on this subject, addressing the case of electromagnetic, acoustic, or elastic waves and making use of different strategies to perform this coupling. Both direct and iterative approaches can be used, and they may exhibit specific advantages and disadvantages. This work focuses on the use of iterative coupling schemes for the analysis of wave propagation problems, presenting an overview of the application of iterative procedures to perform the coupling between different methods. Both frequency- and time-domain analyses are addressed, and problems involving acoustic, mechanical, and electromagnetic wave propagation problems are illustrated. 1. Introduction The analysis of wave propagation, either involving electromagnetic, acoustic, or elastic waves, has been widely studied by researchers using different strategies and methodologies, as can be seen, for example, in [1¨C10], among many others. In many cases, the interaction between different types of media, such as fluid-solid or soil-structure interaction problems, poses significant challenges that can hardly be tackled by means of a single numerical method, requiring the joint use of different procedures to model different parts of the problem. Indeed, taking into consideration the specificities and particular features of distinct numerical methods, their combined use, as coupled or hybrid models, has been proposed by many authors, in order to explore the individual advantages of each technique. In acoustic and elastodynamic problems, coupled models, including, for example, the joint use of the boundary element method (BEM) and the method of fundamental solutions (MFS) [11] or of the BEM and the meshless Kansa¡¯s method [12], have been successfully applied. Similarly, when modelling dynamic fluid-structure and soil-structure interactions, wave propagation in elastic media with heterogeneities, or the transmission of ground-borne vibration, coupled models using the finite element method (FEM) and the BEM have been extensively documented in the literature [13¨C19], mostly using the FEM to model the structure and the BEM to model the hosting infinite or semiinfinite medium. Although these approaches can be quite useful in addressing many engineering problems, they mostly correspond to standard direct coupling
%U http://www.hindawi.com/journals/jam/2014/426283/