4.3.2 Time Step Size Correction

After the calculation of each time step the L² norm and the L^$\infty$ norm of the potential update are calculated. If at least one of these norms exceeds a respective threshold the step size of the last time step was too big. Then the step size has to be reduced and the transient simulation has to be continued from the last valid time step.

Figure 4.9: Quadratic step size prediction.

Similar to the time step size prediction a quadratic interpolation of the potential update norm is used to estimate the reduced step size (see Fig. 4.9). The calculations are performed using the L² and the L^$\infty$ norms and the minimum of the resulting estimates is used for repeating the last time step.

Finally the step size has to be compared to a specified minimum step size $\Delta$t_min and corrected in case it is less than this value. This is necessary to make sure that a non-continuous input signal does not cause an infinite repetition of time steps.