Efficient analysis of sound propagation in sonic crystals using an ACA–MFS approach

Sonic crystals have been analysed making use of a variety of strategies, such as those based in the multiple-scattering theory (MST) or in the Finite Element Method (FEM). Recently, some works have proposed the use of the Method of Fundamental Solutions (MFS) and of the Boundary Element Method (BEM). However, considering these numerical techniques, the associated memory requirements and CPU times are usually prohibitive when problems with a large number of scatterers are considered, particularly when 3D problems are addressed. A new strategy for the solution of 3D configurations of sonic crystals is proposed here, based on the use of the MFS (formulated in the frequency domain), considering a 2.5D approach to describe the 3D model. The sound field is synthesised as a summation of much simpler 2D problems, drastically reducing the memory requirements and computational effort of the analysis. To allow the solution of very large-scale problems, with a great amount of scatterers, an Adaptive-Cross-Approximation (ACA) approach is incorporated into the MFS algorithm, rendering faster calculations and significant savings in terms of computational requirements. Examples are presented illustrating the good performance of the proposed methodology and its capacity to properly handle complex large-scale models.