Efficient Delta-Parametrization of 2D Surface-Impedance Solutions

Impedance boundary condition methods (IBCs) are among the most efficient methods for solving time-harmonic eddy-current problems with a small skin depth (delta). However for a wide range of frequencies (or material conductivities) the standard approach is no more efficient, since it requires for each frequency (or conductivity) the computation of a finite element (FE) complex-valued problem. Moreover, the accuracy of IBC decreases dramatically for large delta. As an extension of our previous work, we propose here a more detailed method of parametrization in delta of the 2D small-delta eddy-currents problem. This numerically efficient method gives a very good precision for all the frequencies difficult to address, i.e. from the frequency corresponding to the last good solution obtainable by meshing the conductor up to infinity (perfect conductor solution).