## 1 Introduction  
Nowadays, analysis of multi-scale composite transient electromagnetic scattering is an essential part of ocean detection [1], the reconstructing of the microwave imaging of objects [2], etc. A scatterer system with complex geometry, multi-scale and multi-object characteristics requires higher calculation accuracy. Moreover, a large-scale environment, such as a rough sea or land surface, will lead to a sharp increase in computing memory and time, and computers cannot keep up. These problems bring challenges to computational electromagnetism. In order to take into account both accuracy and efficiency, the main method is to mix the full wave method with the high frequency approximation algorithm. In these methods, the full-wave methods, such as the method of moments (MoM), the finite-element time domain (FETD), finite volume time domain (FVTD) and finite-difference time domain (FDTD) calculate the regions with fine structures well. High-frequency algorithms are adopted for the calculation of electrically large areas, so as to improve the calculation speed and reduce the memory costs. Due to the good accuracy of MoM, a class of hybrid methods of MoM and high-frequency approximation algorithms are widely used [3, 4, 5, 6, 7, 8]. However, the MoM has the problem of low frequency breakdown [9, 10, 11]. Simultaneously,as a result of the dense matrix, the MoM is slightly inferior to other time-domain algorithms for solving broadband problems in the time domain. Hence, the hybrid method of FDTD and PO was proposed in [12; 13; 14; 15]. However, due to the ladder error in the calculation of unstructured targets and surface fitting, the accuracy of electromagnetic scattering problem of complex targets had to be improved. Furthermore, the combination of FVTD and PO had also been tried. One paper [16] discussed the 3D radar cross section (RCS) of a sphere over a plate through FVTD/PO. This method achieves good accuracy for an electrically small sphere; and the larger the electrical size of the plate and the further the asymptotic and FVTD regions are, the higher accuracy of this method is. However, the hybrid method only calculates the frequency domain and does not involve the time domain and multi-scale problems. In addition, according to the conclusion in the literature [17], the DGTD method requires more time and memory than the FVTD algorithm, but it is able to handle multi-scale structures well; the FVTD method is not suitable for electrically large problems. In the calculations of the transient scattering of multi-scale targets, a full-wave method named discontinuous Galerkin time domain (DGTD) [18; 19; 20; 21; 22; 23] has more advantages than other methods in solving broadband multi-scale problems. With respect to geometric modeling, the multi-scale structure can be divided into several subdomains through DGTD. Furthermore, the grid density of each subdomain can be adjusted flexibly. As a result of the uneven tetrahedral grid technology, DGTD is much more accurate than FDTD. Moreover, DGTD is able to divide a large system's matrix into a group of smaller matrices, which means DGTD is more efficient than FETD at calculating complex structures. In terms of time integration, DGTD can utilize explicit and implicit hybrid schemes in various subdomains and accelerate the solving process [24]. The flexibility of spatial and temporal discretization makes the DGTD method efficient in multi-scale problems. However, when calculating the complex transient scattering of a complex target above a large area, such as rough sea surface or land through DGTD, the cost in terms of calculations is huge, and the requirement of memory cannot be borne by computers. With the aim of quickly calculating the transient electromagnetic scattering of electrically large targets, time domain high-frequency techniques, such as time domain physical optics (TDPO) and time domain shooting and bouncing ray (TDSBR), have been developed. These techniques can reduce the burden of memory and improve the calculation speed, greatly.