An ACA-MFS approach for the analysis of sound propagation in sonic crystals

Abstract

Some efficient methods are available in the literature to solve the problem of sound propagation in the presence of sonic crystal structures, such as those based in the Multiple Scattering Theory (MST) or in the Finite Element Method (FEM). More recently, the Method of Fundamental Solutions (MFS) and the Boundary Element Method (BEM) have also been applied for that purpose. In this paper, a new strategy based on the use of the MFS is proposed to tackle problems of sound propagation around 3D sonic crystals with constant geometry along the axis of the scatterers (2.5D). The problem is solved in the frequency domain, and the sound field is synthesized as a summation of simpler 2D problems. To allow the solution of large-scale problems, with a high number of scatterers, an Adaptive-CrossApproximation approach is proposed and incorporated in the MFS algorithm, rendering the calculation much faster and with very significant savings in terms of computational requirements. Examples are presented, and the calculation times and RAM requirements are compared with those provided by a classic MFS formulation.