A gradient-based optimization (GBO) method is presented for acoustic lens design and sound localization. GBO uses a semi-analytical optimization combined with the principle of acoustic reciprocity. The idea differs from earlier inverse designs that use topology optimization tools and generic algorithms. We first derive a formula for the gradients of the pressure at the focal point with respect to positions of a set of cylindrical scatterers. The analytic form of the gradients enhances modeling capability when combined with optimization algorithms and parallel computing. The GBO algorithm maximizes the sound amplification at the focal point and enhances the sound localization by evaluating pressure derivatives with respect to the cylinder positions and then perturbatively optimizing the position of each cylinder in the lens while incorporating multiple scattering between the cylindrical scatterers. The results of the GBO of the uni-and multi-directional broadband acoustic lens designs are presented including several performance measures for the frequency dependence and the incidence angle. A multi-directional broadband acoustic lens is designed to localize the sound and to focus acoustic incident waves received from multiple directions onto a predetermined localization region or focal point. The method is illustrated for configurations of sound hard and sound soft cylinders as well as clusters of elastic thin shells in water.
San José State University
Acoustic lens, Acoustic reciprocity, Broadband metamaterials, Gradient-based optimization, Helmholtz equations, Inverse design, Multiple scattering, Multipole expansions, Sound localization
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Feruza Amirkulova, Samer Gerges, and Andrew Norris. "Sound localization through multi-scattering and gradient-based optimization" Mathematics (2021). https://doi.org/10.3390/math9222862