Surface integral equations for electromagnetic testing: The low-frequency and high-contrast case

This paper concerns boundary element methods applied to electromagnetic testing for a wide range of frequencies, conductivities and permeabilities. The eddy-current (EC) approximation cannot handle all configurations, while numerical instabilities at low-frequency or for highly contrasted media affect the Maxwell formulation. We examine on a test example how the performance of several Maxwell and EC formulations is affected by frequency, conductivity, and permeability. Among those tested, we propose a weighted loop-tree Maxwell formulation, which is found to be the only one yielding satisfactory results in all considered configurations.