## 3 Numerical Results
### Multi-Scale Object and Plate  
The second scatterer was a multi-scale object above a PEC plate in Figure 7. The overall length of the object was 3.3 m, the tail size was 0.3 m and the thickness was 0.01 m. For the frequency range of the incident wave from 0.5 to 1 GHz, the object body was electrically large, but the tail was equivalent to an electrically small structure. Consequently, the scatterer can be considered as a multi-scale electromagnetic scattering problem.  
As shown in the Figure 8a,b, the bistatic RCS results of an object at 0.5 GHz and 1 GHz through DGTD agree well with MoM, and the NRMSD values were 0.0427 and 0.0452 respectively. Meanwhile, in Figure 9a,b, the electric field in the time domain and frequency domain from 0.5 to 1 GHz was calculated by DGTD, and the result is almost consistent with that of HFSS; the resulting NRMSD values were 0.0112 and 0.0053 respectively. These results show that DGTD method can be used to calculate the multi-scale problem very well. At the same time, the accuracy of the above results is also an important guarantee for the hybrid algorithm's accuracy.  
Figure 5: Bistatic radar cross section (RCS) of a perfect electrically conducting (PEC) sphere computed through DGTD and Mie at (**a**) 0.3004 GHz, and (**b**) the electric field of a PEC sphere computed through DGTD and Mie at range of frequencies from 0.1 to 500 MHz.  
Figure 6: The RCS of a PEC sphere-plate computed at (**a**) 0.3004 GHz and (**b**) 0.5 GHz from the solutions of the DGTDPO method and Method of Moment (MoM).  
Figure 10 indicates the superiority of the DGTD method in multiples scales over the time domain, high-frequency approximation methods, including TDPO, and the timed  
Figure 8: The RCS of a multi-scale object above a PEC plate computed at **(a)** 0.5 GHz and **(b)** 1 GHz from the solutions of the DGTD method and MoM.  
Figure 7: Multi-scale object-plate composite object.  
Figure 9: (**a**) The transient scattered electric field of a multi-scale object computed at theta = 0\({}^{\circ}\), phi = 0\({}^{\circ}\). (**b**) The RCS of a PEC object computed from 0.5 to 1 GHz (theta = 0\({}^{\circ}\), phi = 0\({}^{\circ}\)) from the solutions of the DGTD method and MoM.  
main shooting and bouncing ray (TDSBR). The NRMSD of DGTD, TDPO and TDSBR are shown in Table 3.  
Compared with time domain high-frequency technique, Table 3 shows that DGTD has higher accuracy when solving multi-scale complex problems.  
As shown in Figure 11a,b, these are the bistatic RCS results of the PEC sphere plate composite object at 1 and 1.5 GHz. In addition to the scattering field in the angle range below the rough sea surface, the DGTDPO results are similar to MoM.  
Figure 11: The RCS of a multi-scale object above a plate computed at (**a**) 1 GHz and (**b**) 1.5 GHz from the solutions of the DGTDPO method and MoM.  
Figure 10: Accuracy comparison of DGTD, TDPO and TDSBR methods for RCS calculation at 1 GHz of multi-scale structural objects.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **DGTD** & **TDPO** & **TDSBR** \\ \hline NRMSD & 0.0348 & 0.2360 & 0.1028 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The NRMSD of DGTD, TDPO and TDSBR for the multi-scale object at 1.5 GHz.  
Compared with time domain high-frequency technique, Table 4 shows that DGTDPO has higher accuracy when solving for a multi-scale object than for plate composite objects.  
As shown in Table 5, the complex multi-scale structure leads CPU time and memory both to get higher than the sphere-plate composited scatter. In addition, the calculation time and memory consumption of DGTDPO method were reduced by 99.54% and 72.56% respectively.