# Wire-Grid and Sparse MoM Antennas: Past Evolution, Present Implementation, and Future Possibilities
## Why MoM?
### MoM Antennas  
Historically, MoM has been developed very intensively in relation to the problems of electrostatic and electrodynamic analysis of wire structures [112; 113]. Their analysis is an important task because they are used as antennas [114; 115; 116; 117; 118] in grounding and equipotential bonding systems, in surface approximation [119; 120], and in the development of various electromagnetic field simulators [121]. The analysis of linear (wire) antennas is reduced to the solution of the integral (integro-differential) Pocklington [122] and Hallen [123]equations. The specific features of the solution of these equations are based on the thin-wire approximation and are discussed in detail in several works, e.g., [124; 125; 126; 127; 128]. In this approach, the conductor is assumed to be an ideal conductor in the form of a cylinder located along one of the coordinate axes (one-dimensional problem), with a cross-sectional radius much smaller than the wavelength of the excited signal and the conductor's physical length. It is also assumed that the current is zero at the ends of the wire. This simplification allows one to use a scalar current density function instead of a vector function, which significantly reduces the complexity of the problem. The time required to solve the problem became the determining factor in choosing one or another numerical method [129]. In addition, the required machine memory capacity is important, as it allows the use of relatively weak workstations to solve complex problems [100]. The use of methods for solving SLAE is also strictly associated with the peculiarities of storing its matrices [130; 131; 132]. Reducing the time to form and solve the SLAE to reduce the computational cost of modeling, for example when using MoM, can be achieved by choosing the method of structure discretization, which allows approximating its regions with a smaller number of subdomains, thereby reducing the order of SLAE [133]. In this case, the selection of the sets of basis and test functions most suitable for each specific task is the most important [134]. The choice of basis and test functions, which allow approximating the desired function with a small number of them [135], reduces the time spent on calculations. The choice of similar basis and test functions gives a symmetric matrix [136]. To accelerate MoM, solid-state storage devices (SSDs) [137] and parallel computing on the CPU and/or GPU [138] were also used. Approximation of the SLAE matrix can be achieved by using iterative methods [139], low-rank approximation of matrices [140], zeroing (discarding) the matrix elements of the generated SLAE, whose values are less than a given threshold, and, consequently, transforming the dense matrix into a sparse one, with its further solution by one of the methods for sparse systems [141]. As a result, a general research trend is the reduction of the time required to calculate with the required accuracy and to obtain an optimal structure. Currently there is a growing interest in the optimization of electromagnetic devices. As a consequence, significant efforts have been made to develop competitive optimization methods. However, it should be noted that different optimization algorithms may be used for different applications in order to meet the specifications of the problem [142]. It is also worth noting that the geometric shape plays an important role in changing the characteristics of the design. For example, for a patch antenna, the circular polarization characteristic can be obtained either by placing stubs in proper locations or by placing diagonal connectors in the center of the antenna. In addition, the antenna can be tuned using a powered configuration, or the bandwidth can be increased by adding parasitic elements. It is outstanding that for different types of applications, only a small part of the antenna structure is changed; it is either removing from or adding to the structure's geometry to obtain the desired specification.