A unified time domain surface impedance concept for both linear and non-linear skin effect problems

A new time-domain boundary element technique for calculation of the magnetic field and temperature distribution in the skin layer of conductors of isotropic material with general BH-curve and σ(T) relationship is proposed. The formulation consists of the surface integral equation for the scalar magnetic potential and the time-domain surface impedance boundary condition (SIBC) for the normal component of the magnetic field. The SIBC is obtained in the form of 1-D nonlinear diffusion equations for the magnetic field and temperature inside the conductor normal to its surface. The number of integral equations is the same for 2-D and 3-D problems. The technique requires the same computational expenses as solving the problem in the well-known perfect electrical conductor limit. Numerical examples are also considered