Optimal design of phononic crystals using higher-order boundary elements and a swarm optimization scheme

The paper deals with an innovative optimization scheme for the design of phononic crystals based on the coupling of a third-order Boundary Element Method (BEM) and a deterministic Particle Swarm Optimization (PSO) algorithm. The band-gap properties of a periodic scattering structure are of paramount interest in many engineering applications. The propagation of acoustic waves can be confined and guided through an appropriate design of the unit cells constituting the crystal, tailored to the specific application at hand. The main difficulty in this process resides in the fact that the topological layout of the periodic structure required to achieve the target cannot be obtained analytically in many practical applications. As a consequence, time-consuming simulation-based approaches must be adopted to obtain the appropriate design. The use of optimization schemes can be a viable and efficient strategy to address the problem from the engineering point of view, provided that accurate and efficient numerical schemes are used. In the present work, the problem is addressed through the coupling of two advanced algorithms for acoustic simulations and optimization. The first is addressed using a high-accuracy BEM solver, capable to capture the details of the acoustic propagation patterns with a relatively low numerical effort. The BEM solver is linked to an optimization scheme based on a cutting-edge original PSO scheme having remarkable properties of efficiency and robustness, especially for optimization problems pertaining to high-dimensional design spaces. The method is applied to the optimization of two-dimensional lattices with specific spectral requirement and/or spatial scattering patterns. Preliminary results show the capability of the method to design periodic structures capable to block the propagation in the prescribed frequency band and confine the scattering within predefined portions of the field.