On the testing of the magnetic field integral equation with RWG basis functions in method of moments

Abstract

Abstract-For electromagnetic analysis using Method of Moments (MoM), three-dimensional (3-D) arbitrary conducting surfaces are often discretized in Rao, Wilton and Glisson basis functions. The MoM Galerkin discretization of the magnetic field integral equation (MFIE) includes a factor 0 equal to the solid angle external to the surface at the testing points, which is 2 everywhere on the surface of the object, except at edges or tips that constitute a set of zero measure. However, the standard formulation of the MFIE with 0 = 2 leads to inaccurate results for electrically small sharp-edged objects. This paper presents a correction to the 0 factor that, using Galerkin testing in the MFIE, gives accuracy comparable to the electric field integral equation (EFIE), which behaves very well for small sharp-edged objects and can be taken as a reference.

Improving the accuracy of the magnetic field integral equation with the linear‐linear basis functions

“…This approach is known to provide accurate results for the EFIE and therefore is also employed for the discretization and solution of the MFIE and CFIE [Hodges and RahmatSamii, 1997;Song et al, 1998;Shanker et al, 2000;Rius et al, 2001]. Unfortunately, compared to the EFIE results, the MFIE results are observed to be plagued with an inaccuracy problem persistent for a wide variety of scattering problems, even for the solution of simple geometries, such as the sphere [Ergül and Gürel, 2006].…”

Novel Monopolar MFIE MoM-Discretization for the Scattering Analysis of Small Objects

“…However, it has been reported some clear disagreement of the conventional MoM-MFIE respect to the MoM-EFIE [6], [12] in the analysis of moderately small objects in scattering problems. This discrepancy, for which a heuristical correction is provided in [6], becomes especially evident in the analysis of moderately small sharp-edged objects.…”

Fast Converging Cfie-Mom Analysis of Electromagnetic Scattering From Pec Polygonal Cross-Section Closed Cylinders

“…To do this, for a given number of expansion functions used, the parameters 0 < α, β < 1 in Equations (12) and (20) are suitably chosen in order to minimize the condition number of the truncated coefficients' matrix.…”

“…Unfortunately, the discretization and truncation of CFIE when its EFIE component contains a hypersingular term leads to "approximate solutions" which do not necessarily converge to the exact solution of the problem, and in any case, the sequence of condition numbers of truncated systems is divergent due to the unboundedness of the involved operator [19]. On the other hand, it has been widely noted that classical discretization schemes (such as, Rao-Wilton-Glisson discretization) applied to MFIE produced worse results than EFIE, and more sophisticated approaches have to be employed in order to achieve more accurate solutions [20][21][22][23][24][25][26]. The problem is even worse for scatterers with edges or corners due to the divergence of the fields on geometrical singularities.…”