# On Modeling Antennas Using MoM-Based Algorithms: Wire-Grid versus Surface Triangulation
## 1 Introduction  
Full-wave analysis based on numerical methods is widely used to design antenna arrays and elements. For example, antennas can be analyzed using the finite-difference time-domain method (FDTD) [1, 2], the finite integration technique [3, 4], or the finite element method (FEM) [5, 6]. Using such methods and others, numerous approaches were proposed to model and discretize general structures [7, 8]. However, the most common method for antenna modeling is the method of moments (MoM) [9, 10, 11, 12]. The popularity of the MoM is probably associated with its relatively low computational costs, which are ensured by the need to discretize only the surfaces of the modeled object, rather than the entire solution domain. In the process of antenna modeling by the MoM, usually the conductive structures are replaced by equivalent surface currents, and then, using the reciprocity principle, the radiation problem is solved on the basis of these currents. The most important parts of this process are the discretization of the antenna model and the approximation of surface currents within each discrete section, which are usually performed using two basic algorithms: wire-grid and surface triangulation. In the first widely used algorithm, the conductive surfaces of the antenna are replaced by a grid of thin wires with a radius much smaller than the wavelength of the excitation signal and the length of thewires themselves [13; 14; 15]. This approach enables using a scalar current density function instead of a vector one, which reduces the computational cost of modeling. At the same time, the wire-grid algorithm is relatively poor suited for approximating complex and highly detailed antenna structures and for near-field problems [16]. In the second one, the conductive antenna elements are discretized by triangular surface patches and the vector Rao-Wilton-Glosson (RWG) basis functions are used to approximate the currents [17; 18; 19]. Triangles describe curvilinear surfaces with a high accuracy, allowing one to achieve accurate results of the antenna analysis. However, the triangulation process and vector basis functions significantly increase the computational costs. Without losing the generality, rectangular plates share with wire-grid the same problem of the inability to model a general structure, but they differ in that the former uses surface current densities, while the later uses a fine mesh or grid of crossing wires [20]. Many efforts were paid to develop a technique for modeling nonrectangular plates, since the earlier studies in surface patch modeling were limited only to rectangular ones. Some researchers proposed to expand currents on the problem model as an interconnection of polygonal plates in terms of nonrectangular surface patch modes [21]. While the others decided to deal with the whole problem model at once as a general curved surface, and the nonrectangular surface patches make up a piecewise flat approximation to the surface current density on the surface, which seems to be more general but a slightly more complicated in implementation [22; 23]. The researchers investigated their proposed approaches using polygonal plates of different shapes (square, triangle, octagonal, quadrilateral, and other plate shapes), but among all the nonrectangular patches, triangular patches seem to be more universal in structure description and easier to implement. The researchers noticed that the testing results are still reasonable even in cases where some of the quadrilaterals degenerate to triangles [21; 24]. Therefore, [PERSON] and [PERSON] concentrated their work, which in fact started even earlier than 1978, on using triangular patches [25]. Based on the above, new software codes were developed not only on the wire-grid base, like in the numerical electromagnetic code (NEC) [26], MMANA-GAL [27], CONCEPT-II [28], GEMACS [29], and in AN-SOF [30], but also on the patch surface base like in NEC [31], and in the electromagnetic surface patch code (ESP) [32], and others.