# On Modeling Antennas Using MoM-Based Algorithms: Wire-Grid versus Surface Triangulation
## 2 Materials and Methods
### Wire-Grid
#### 2.2.1 Wire-Grid: Overview
However, if the thin wire theory was employed, the circumferential variation of the surface-current density is neglected by the nature of the theory. Among all limitations discussed in each work about wire-grid, the common one is always the solution of electrically large problems [166]. Researchers have always tried to develop new techniques for solving such problems with thousands [167; 168], several thousands [169], and millions [170] of unknowns. However, the dependence of the wire-grid, in general, on MoM makes this approach easier to adapt with other methods to solve its problems. An example is the use of banded matrix iterative solution methods like in the work [171] where the results were compared to the Gaussian elimination. Another approach is the use of LU-decomposition, and the sparse iterative method that provides a faster solution to MoM matrix equations than does LU-decomposition with forward and back substitution [172], and also than the banded Jacobi and CGM [173]. One of the other proposed solutions is the use of parallelization, for example, the parallelization of LU-decomposition [174], and in particular the class of local memory multiple instructions and multiple data. The results obtained in this work were compared and verified using a paralleled CGM. Another example is the parallelization made in NEC based on a bidimensional block-cyclic distribution of matrices on a rectangular processor grid, assuring a theoretically optimal load balance among the processors [175]. In this work, the results were verified experimentally and also by comparing them with the results of other numerical methods, like FDTD and transmission line model. Another NEC parallelization attempt was presented in [176]. The researchers extensively modified the NEC program in order to optimize its performance on a four-processor Cray X-MP computer. As a result, by exploiting judicious use of vectorization and alternative parallelization techniques, they achieved a reduction of run-time by factors of about five or more. In additions, they rewrote the MININEC program into the Occam programming language so that it could be executed directly by a transputer system. However in these efforts, they achieved only a modest reduction in run-time. The result of an additional attempt was the development of the Super-NEC, which is the object-oriented version of NEC that has been modified to execute on a network of distributed memory processors [177]. In this version, the matrix filling, solving and pattern computation routines could run in parallel. The researchers here used the LU-decomposition and an iterative matrix solution scheme to test the code implementation, and verified the obtained results experimentally. On the other hand, one of the most promising approaches in MoM-based wire-grid modeling acceleration is the use of the CUDA-enabled graphics processing unit (GPU). Due to employing the GPU, the researchers achieved a noticeable speedup (about 6 times) of the overall MoM simulation with comparison to CPU results [178].