Computational cost estimations and comparisons for three methods of applied electromagnetics (MoM, MAS, MMAS)

The computational costs of three numerical techniques used in electromagnetics, namely the Moment Method (MoM), the Method of Auxiliary Sources (MAS), and its modified version (MMAS), are estimated for various calculation schemes and configurations. Both surface and volumetric problems are considered. The number of multiplications required for the system-matrix fill is calculated and added to the algorithmic cost of the matrix inversion. The Green's function singularity extraction is also taken into account, particularly for the MoM. The original integrals are transformed into the local (area or volume) coordinate systems, and are subsequently evaluated on the basis of standard numerical quadrature schemes. For the surface integral equation (SIE), some calculations using either the well-known Duffy Transformations or some analytical-numerical integration schemes are also presented (expressions are available only for the scalar potential integral case). For the MAS and MMAS, the matrix fill is shown to be much faster, since no time-consuming integrations are involved. The analysis is applied to various objects, such as a perfectly conducting (PEC) parallelepiped, a PEC sphere, and a microstrip patch antenna, and useful conclusions are drawn on the relative efficiency of the three methods.