An Efficient MFS Formulation for the Analysis of Acoustic Scattering by Periodic Structures

The acoustic behavior of periodic structures has been a subject of intense study in recent years. From the computational point of view, these devices have mostly been analyzed using strategies such as the multiple scattering, theory (MST) or numerical methods such as the finite element method (FEM). Some recent works propose the use of boundary methods, such as the method of fundamental solutions (MFS) or the boundary element method (BEM). However, the geometry and the large number of scatterers of these devices can lead to very large memory requirements and CPU times, which, particularly in the case of 3D problems, can be prohibitive. Here, a new numerical approach based on a frequency domain MFS formulation is proposed for 3D problems, allowing the analysis of very large problems. In this approach, the periodic character of the devices is used to define a matrix with a block structure, in which repeated blocks are only calculated once. In addition, an adaptive-cross-approximation (ACA) approach is incorporated to allow a more efficient memory usage, reducing the global computational requirements, and allowing the analysis of devices with hundreds of scatterers with a minimal memory usage.