On the Vanishing Displacement Current Limit for Time-Harmonic Maxwell Equations
- This paper considers a transmission boundary-value problem for the time-harmonic Maxwell equations neglecting displacement currents which is frequently used for the numerical computation of eddy-currents. Across material boundaries the tangential components of the magnetic field H and the normal component of the magnetization müH are assumed to be continuous. this problem admits a hyperplane of solutions if the domains under consideration are multiply connected. Using integral equation methods and singular perturbation theory it is shown that this hyperplane contains a unique point which is the limit of the classical electromagnetic transmission boundary-value problem for vanishing displacement currents. Considering the convergence proof, a simple contructive criterion how to select this solution is immediately derived.