The inverse source problem in electromagnetics has proved quite relevant for a large class of applications. In antenna diagnostics in particular, Love solutions are often sought at the cost of an increase of the dimension of the linear system to be solved. In this work, instead, we present a reduced-in-size single current formulation of the inverse source problem that obtains one of the Love currents via a stable discretization of the Steklov-Poincar\'e boundary operator leveraging dual functions. The new approach is enriched by theoretical treatments and by a further low-frequency stabilization of the Steklov-Poincar\'e operator based on the quasi-Helmholtz projectors that is the first of its kind in this field. The effectiveness and practical relevance of the new schemes are demonstrated via both theoretical and numerical results.
翻译:电磁学的反源问题已证明与大量应用相当相关,特别是在天线诊断方面,寻求爱的解决方案往往以线性系统范围扩大为代价,而在这个工作中,我们提出了反源问题的缩小规模的单一当前配方,通过Steklov-Poincar\e边界操作员的稳定离散利用双重功能获得一个爱流。新的方法通过理论处理和在准Helmholtz投影器的基础上进一步低频稳定Steklov-Poincar\'e操作器的操作器而得到丰富,这是该领域首个此类投影器,通过理论和数字结果都证明了新方案的有效性和实际相关性。