A very general solution has been proposed to the difficult problem of treating instabilities of one-way equation (local) absorbing boundary conditions in time domain electromagnetic simulations. Digital filters have been inserted between the mesh and the absorbing boundaries (as shown in Fig. 1) to filter out the high frequency numerical noise generated by the absorbing boundary interpolation equations. The problem arising out of the finite delay of the digital filters has been solved my making the filter delay equal to the time delay in the longer link lines of the graded mesh. By adopting this technique, instabilities have been eliminated as demonstrated in Figs. 2a and 2b.
Further details can be found in:
C. Eswarappa and W. J. R. Hoefer, "Treatment of instabilities of one-way equation absorbing boundary conditions using digital filters" accepted for presentation at 1995 MTTS Symposium.
Fig. 1 - Two-dimensional graded TLM mesh and digital filters (DF) to filter out the high frequency noise generated by the absorbing boundary interpolation equations. v is computed using absorbing boundary interpolation equations. u is the output of the digital filters.
Fig. 2 - Time domain responses of the waveguide (WR28) discretized with a variable mesh: (a) without digital filters, (b) with digital filters inserted between mesh and absorbing boundaries
