Fast multipole boundary element method for the acoustic analysis of finite periodic structures

In this work, two fast multipole boundary element formulations for the linear time-harmonic acoustic analysis of finite periodic structures are presented. Finite consist a bounded number unit cell replications in one or more directions periodicity. Such can be designed to efficiently control and manipulate sound waves referred as metamaterials sonic crystals. Our methods subdivide geometry into boxes which correspond cell. A discretization is applied interactions between well separated approximated by expansion. Due periodicity underlying geometry, certain operators expansion become block Toeplitz matrices. This allows express matrix-vector products circular convolutions significantly reduces computational effort overall memory requirements. The efficiency presented techniques shown based on an scattering problem. addition, study design barriers where performance wall-like barrier compared crystal barriers.