A hybrid SBM-MFS methodology to deal with wave propagation

In this paper, a novel hybrid 2.5D SBM-MFS approach is formulated and developed in the frequency domain. This approach inherits the accuracy of MFS while keeping the robustness presented by the SBM. The MFS is employed to study the smooth portion of the boundary, while the complex segments are analysed through the SBM. For the sake of presenting the potential of the proposed hybrid approach, a square-shaped boundary excited by a unit point load is considered. The performance of the hybrid method is thoroughly assessed against 2.5D BEM, MFS, and SBM methods, in terms of convergence error analysis. Since the considered problem does not have a known analytical solution, the 2.5D FEM-BEM approach with a highly refined mesh is taken as the reference in the error analysis. The convergence error is calculated in terms of receptances at two circular distributions of evaluation points. In the hybrid method, 70 percent of the virtual sources are allocated on an auxiliary virtual boundary (MFS sources) while the remaining 30 percent are allocated on the physical boundary (SBM sources). The convergence plots obtained by four methods show that the accuracy of the hybrid method is significantly higher than the one of MFS and, in some cases, even higher than the one of BEM. While MFS requires a large number of nodes per wavelength to achieve acceptable results, the 2.5D SBM-MFS presents a high convergence rate, even for a small number of nodes per wavelength. The main benefit of the hybrid method is not solely its accuracy, compared with the BEM and SBM methods, but also its computational efficiency is another achievement. Moreover, in contrast to integration-based methods, such as BEM, the implementation of the new procedure is quite simple. It can be concluded that the hybrid 2.5D SBM–MFS is an adequate alternative prediction tool for elastodynamic problems.