Invariant BEM-SIBC formulations for time- and frequency-domain eddy current problems

We demonstrate that frequency- and time-domain boundary integral equation formulations involving the surface impedance boundary conditions (SIBCs) can be transformed to invariant forms that depend only on the geometry of the problem and do not contain temporary parameters of the field. Thus the integral equations have to be solved only once for a given system of conductors and then the results for any source field (steady state or transient) can be easily obtained. We considered both low- and high-order SIBCs so that the formulations obtained can be applied to a wide range of skin effect problems. A numerical example is included to illustrate the theory.