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

Abstract

[1] Basis functions with linear variations are investigated in terms of the accuracy of the magnetic field integral equation (MFIE) and the combined-field integral equation (CFIE), on the basis of recent reports indicating the inaccuracy of the MFIE. Electromagnetic scattering problems involving conducting targets with arbitrary geometries, closed surfaces, and planar triangulations are considered. Specifically, two functions with linear variations along the triangulation edges in both tangential and normal directions (linear normal and linear tangential (LN-LT) type) are defined. They are compared to the previously employed divergence-conforming Rao-Wilton-Glisson (RWG) and curl-conformingn  RWG functions. Examples are presented to demonstrate the significant improvement in the accuracy of the MFIE and the CFIE gained by replacing the commonly used RWG functions with the LN-LT type functions.Citation: Ergül, Ö ., and L. Gürel (2006), Improving the accuracy of the magnetic field integral equation with the linear-linear basis functions, Radio Sci., 41, RS4004,

Numerical Analysis of Combined Field Integral Equation Formulations for Electromagnetic Scattering by Dielectric and Composite Objects

“…In particular, the solution accuracy of JM-CFIE1(0) and rsJM-CFIE1(0) formulations improve significantly. A similar phenomenon has been observed previously in the case of PEC-CFIE [11]. In comparing the results with the RWG and LL functions it is important to remember that for the same mesh the LL functions double the number of unknowns compared to the RWG functions.…”

“…Recent studies have shown that surface integral equation formulations may have very different accuracy, see e.g., [11][12][13][14]. In particular, the choice of a formulation is important if the surface is non-smooth [12] or the material contrast is very low [17] or very high [16].…”

“…Many studies have indicated that the optimal value of α giving rise to the best conditioned matrix equation is between 0.2 and 0.3, see e.g., [10,11]. If the surface is sufficiently smooth, by increasing the order of the basis functions the solution accuracy can be made only weakly dependent on the choice of α [11,12] and the condition of the matrix becomes the sole criterion for the choice of α in PEC-CFIE.…”

Improving the accuracy of the surface integral equations for low-contrast dielectric scatterers

“…However, since the N formulations contain well-tested identity operators, their results are usually contaminated with a persistent error compared to T formulations [1]. This inaccuracy problem is extensively investigated [7] for the solutions of perfectly conducting objects with the magnetic-field integral equation (MFIE) using the conventional Rao-Wilton-Glisson (RWG) [8] basis functions. Although S-CNF is more stable than CNF, it still includes the identity term.…”

Fast and accurate solutions of large-scale scattering problems with parallel multilevel fast multipole algorithm

“…To obtain accurate results, the size of the triangles are set to approximately λ/10, where λ is the wavelength. Then, the unknown surface current density is expanded in a series of Rao-Wilton-Glisson (RWG) [3] or linear-linear (LL) [4] basis functions. The triangulation data is read from a file and the tree structure …”