Modeling Low Frequency Magnetic Field Shielding using the Locally Corrected Nyström Method

The problem of magnetic field penetration into a conductive enclosure due to a low frequency loop transmitter is considered using simulations and experiment. The problem is relevant for electromagnetic shielding, through bunker communications, through conductor imaging, and several related problems. The primary difficulty lies in the multiple spatial scales due to the large wavelengths in the exterior and interior air regions in contrast to the short wavelengths in the highly conductive shell region. Although analytical solutions are possible for spherical shields and other specific geometries, determining the penetration through realistic conductive shields requires a numerical approach. Typical finite element methods can be employed to the shielding problem, however, appropriately meshing the enclosure and the air regions can be difficult when the skin-depth and wavelength in the shell are much smaller than the dimensions of the enclosure. To alleviate the multi-scale and near-field nature of the problem, a high-order locally corrected Nyström scheme is utilized to solve a surface integral equation based on an Augmented Müller formulation. The Nyström-SIE method is ideally suited for shield modeling due to the low surface area to volume ratio of the shield and the exponential convergence properties of the code. To validate the theoretical predictions from the model an experiment using two loop antennas inside and outside a 1.2 m aluminum cube of 3 mm thickness is conducted. It is shown that the experimental results agree with numerical predictions.