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.

中文翻译：

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总多重散射截面梯度及其在声学隐形中的应用

我们推导出总散射截面 (TSCS) 相对于一组圆柱形散射体位置的梯度公式。当与优化算法和并行计算相结合时，解析形式增强了建模能力。作为该方法的应用，我们考虑对一组圆柱形障碍物进行基于梯度的 TSCS 最小化，方法是通过增量重新定位它们，使它们最终充当有效的隐形装置。基于梯度的优化算法通过评估其相对于圆柱体位置的导数，然后在考虑圆柱体之间的声学​​多重散射的同时，微扰优化隐身装置中每个圆柱体的位置，从而降低了 TSCS。