The Gradient of Total Multiple Scattering Cross-Section and Its Application to Acoustic Cloaking

Abstract

We derive a formula for the gradients of the total scattering cross-section (TSCS) with respect to positions of a set of cylindrical scatterers. The analytic form enhances modeling capability when combined with optimization algorithms and parallel computing. As application of the method, we consider a gradient-based minimization of TSCS for a set of cylindrical obstacles by incrementally repositioning them so that they eventually act as an effective cloaking device. The gradient-based optimization algorithm reduces the TSCS by evaluating its derivative with respect to the cylinder positions and then perturbatively optimizing the position of each cylinder in the cloaking device while taking into account acoustic multiple scattering between the cylinders. The method is illustrated for clusters of hard cylinders and sets of elastic thin shells in water.