Continuum gradient-based shape optimization of conducting shields for power frequency magnetic field mitigation

A shape optimization technique for quasistatic field problems has been developed. The optimization is based on computing the continuum sensitivity function by solving an adjoint problem. We show how this technique can be used to compute, in a very efficient way, the optimal shape of a conducting (or ferromagnetic) shielding structure, in order to minimize the magnetic field in the region of interest. A two-dimensional example of shielding three-phase underground cables is considered.