Design of Acoustic Metamaterials Using Gradient Based Optimization

We derive formulas for the gradients of the total scattering cross section (TSCS) with respect to positions of a set of cylindrical scatterers. Providing the analytic form of gradients enhances modeling capability when combined with optimization algorithms and parallel computing. This results in reducing number of function calls and time needed to converge, and improving solution accuracy for large scale optimization problems especially at high frequencies and with a large number of scatterers. As application of the method we design acoustic metamaterial structure based on a gradient-based minimization of TSCS for a set of cylindrical obstacles by incrementally re-positioning them so that they eventually act as an effective cloaking device. The method is illustrated through examples for clusters of hard cylinders in water. Computations are performed on Matlab using parallel optimization algorithms and a multistart optimization solver, and supplying the gradient of TSCS.