We study inverse problems of magnetostatics that arise when designing two-dimensional multilayered shielding and cloaking devices. It is assumed that the device to be designed has the form of a circular shell consisting of finitely many layers, each filled with a homogeneous isotropic medium. Using an optimization method, the inverse problems under consideration are reduced to finite-dimensional control problems in which the constant permeabilities of the layers play the role of control parameters. A numerical algorithm based on the particle swarm method is proposed for solving the control problems. Some properties of the algorithm proposed and of the resulting optimal solutions are established. Results of computational experiments are discussed.

中文翻译：

---

基于优化方法的二维磁隐身问题数值分析

我们研究设计二维多层屏蔽和隐形装置时出现的静磁反问题。假设要设计的设备具有由有限多层组成的圆形壳的形式，每一层都填充有均匀的各向同性介质。使用优化方法，所考虑的逆问题被简化为有限维控制问题，其中层的恒定渗透率起到控制参数的作用。提出了一种基于粒子群方法的数值算法来解决控制问题。建立了所提出的算法和由此产生的最优解的一些性质。讨论了计算实验的结果。