An Overview of Recent Advances in the Iterative Analysis of Coupled Models for Wave Propagation

Abstract

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.

Inelastic 2D analysis by adaptive iterative BEM–FEM coupling procedures

“…(20) and if a R ½0:01; 1:00 the previous iterative-step relaxation parameter is adopted. For the first iterative step, a ¼ 0:5 is selected.…”

“…As one can observe, the relaxation parameter is characterized by an intricate evolution. In fact, since expression (20) is based on residuals (see Eq. (18)), a very dynamic behavior is expected for this parameter.…”

“…In fact, it did not take long until some researchers started to combine the BEM and the FEM in order to profit from their respective advantages, trying to evade their disadvantages, and nowadays several works dealing with BEM-FEM coupling are available [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. However, standard coupling procedures of BEM/FEM can lead to several problems with respect to efficiency, accuracy and flexibility.…”

“…Initially, static problems were studied considering iterative coupling approaches, and linear and nonlinear behavior have been simulated [5][6][7][8][9][10][11]. Later on, dynamic problems were focused, and time [12][13][14][15] and frequency domain [16][17][18][19] iterative analyses have been implemented (in this case, an overview is presented by Soares and Godinho [20]). …”

“…For both coupling approaches, optimal relaxation parameters are employed to speed up and/or to ensure the convergence of the iterative coupling analysis. As it has been previously remarked [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], this procedure is highly important to guarantee the effectiveness of the technique.…”