Broadband acoustic lens design using gradient-based optimization and adjusting radii and positions of scatterers

Abstract

In this talk, we present the semi-analytical gradient-based optimization (GBO) technique for an efficient design of the broadband acoustic lens. This idea differs from earlier inverse designs that use topology optimization, shape optimization, and generic algorithms. We derived a formula for the gradients of the absolute pressure at the focal point with respect to positions and radii of a set of cylindrical scatterers. The derived analytic form of gradients of absolute pressure complements the modeling when combined with optimization and parallel computing. The GBO algorithm maximizes the sound amplification at focal point by evaluating pressure derivative with respect to the cylinder positions and radii, and then perturbatively optimizing the position and radius of each cylinder in the lens while considering acoustic multiple scattering between the cylinders. Computations are performed using the MultiStart Global optimization solver with fmincon while supplying the gradient of pressure at the focus and the gradient of nonlinear geometrical constraints. The GBO of the broadband acoustic lens is illustrated performing several performance measures for the dependency on the wavenumber and the incidence angle. The method is presented giving numerical examples for non-uniform configurations of the cylindrical structures of various radii and material submerged in water.