# Generation of Sparse Antennas and Scatterers Based on Optimal Current Grid Approximation
## 3 Verification of the Modeling Results for Scattering Plate Using MoM with PBF Based on WG Model
The amplitude characterizes the strength of the scattered field created by that wire, while the phase characterizes how the scattered fields created by these wires combine with each other and thus also affect the \(\mathrm{RCS}_{\mathrm{max}}\) value. When GEET is set to 56-100%, \(\mathrm{RCS}_{\mathrm{max}}\) drops to a very low value. This is because most of the segments in the middle of the plate have been removed, leaving only a few segments at the edges. Although the \(\left\lvert\mspace{-1.0 mu }\right\rvert\) in the remaining segments at the edges is large, the number of those segments is clearly insufficient to generate such a substantial scattering field as the field that is contributed by the segments in the middle of the plate. From the above observations, it is clear that the number of wires removed from the WG structure depends on the GEET value: as the GEET value increases, the number of wires removed also increases. This directly impacts the mass and surface of the structure as well as the computational cost required for modeling the scatterer, such as the time and memory needed for subsequent simulations. According to [38], the time cost to solve a linear algebraic system of \(N\) order (using Gaussian elimination) scales with the cube of its order, O(\(N^{3}\)); and the memory cost is O(\(N^{2}\)). Consequently, the reduction in scatterer volume is proportional to \(N/N_{\rm s}\), while the time reduces as \((N/N_{\rm s})^{3}\) and the memory requirement decreases as \((N/N_{\rm s})^{2}\), where \(N\) is the total number segments of the WG structure, and \(N_{\rm s}\)--of sparse structure. The dependence of the reduction in scatterer mass and surface, as well as the time and memory required for subsequent simulations, on GEET is illustrated in Figure 7. As noted, when GEET is very small (1%), the horizontal wires are removed from the structure. Meanwhile, the numbers of horizontal and vertical wires are nearly equal; thus, horizontal wire removal results in approximately a 2-time reduction in the mass and surface of the plate, which corresponds to about 8-time decrease in simulation time and 4-time reduction in memory usage. When GEET increases to 34%, these reductions remain constant, as previously mentioned (the vertical wires are largely retained). When GEET is in the range of 34-55%, these reduction values decrease more rapidly because of the removal of many vertical segments in the middle of the plate. For GEET \(>55\%\), the reduction values still increase but not as rapidly, as the increase in GEET can only eliminate a certain number of vertical segments located at the edges of the plate. However, as previously mentioned, changes in the number of wires in the WG structure directly affect the scattering characteristics of the structure. Therefore, this factor must be carefully analyzed before implementing sparse scatterers in production. The GEET value can be adjusted according to the specific conditions and requirements of the manufacturer. When adjusting GEET, it is necessary to consider the scattering properties and the mass and surface of the model. A higher GEET will help reduce the mass of the structure, but at the same time it may reduce the scattering efficiency. On the contrary, when GEET is low, the scattering properties of the sparse structure will be similar to the original WG but may reduce the effectiveness of mass and surface reduction. Therefore, GEET should be carefully adjusted according to specific practical applications. If the goal is to optimize the structural mass, for example, in designs that require a lightweight structure and are less affected by external factors (such as wind resistance), a GEET value should be high. On the contrary, if the scattering properties of the structure should be similar to the original structure, a low GEET value will be a reasonable choice. In addition, the choice of GEET also affects other factors such as cost, hiding and durability of the structure.