On the DC Loop Modes in the MOT Solution of the Time Domain EFIE

When marching-on-in-time (MOT) method is applied to solve the time domain electric field integral equation (TD-EFIE), DC loop modes are always observed in the solution. In theory these modes should not be observed since they do not satisfy the relaxed initial conditions. Their appearance is attributed to numerical errors. It is shown here that when Rao-Wilton-Glisson basis and Lagrange interpolation functions are used to discretize the TD-EFIE, errors due to this space-time discretization have zero impact on the DC loop modes. Numerical experiments demonstrate that the numerical errors due to approximate solution of the MOT matrix system have more dominant impact on DC loop modes in the MOT solution.