The use of curl-conforming basis functions for the magnetic-field integral equation

Divergence-conforming Rao-Wilton-Glisson (RWG) functions are commonly used in integral-equation formulations to model the surface current distributions on planar triangulations. In this paper, a novel implementation of the magnetic-field integral equation (MFIE) employing the curl-conforming (n) over tilde x RWG basis and testing functions is introduced for improved current modelling. Implementation details are outlined in the contexts of the method of moments, the fast multipole method, and the multilevel fast multipole algorithm. Based on the examples of electromagnetic modelling of conducting scatterers, it is demonstrated that significant improvement in the accuracy of the MFIE can be obtained by using the curl-conforming (n) over tilde x RWG functions.


Generalized Hybrid Surface Integral Equations for Finite Periodic Perfectly Conducting Objects
Karaosmanoglu, Bariscan; Ergül, Özgür Salih (2017-01-01)
Hybrid formulations that are based on simultaneous applications of diversely weighted electric-field integral equation (EFIE) and magnetic-field integral equation (MFIE) on periodic but finite structures involving perfectly conducting surfaces are presented. Formulations are particularly designed for closed conductors by considering the unit cells of periodic structures as sample problems for optimizing EFIE and MFIE weights in selected regions. Three-region hybrid formulations, which are designed by geneti...
On the accuracy of MFIE and CFIE in the solution of large electromagnetic scattering problems
Ergül, Özgür Salih (null; 2006-11-10)
We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving large scatterers. MFIE and CFIE with the conventional Rao-Wilton-Glisson (RWG) basis functions are significantly inaccurate even for large and smooth geometries, such as a sphere, compared to the solutions by the electric-field integral equation (EFIE). By using the LL funct...
Improving the accuracy of the MFIE with the choice of basis functions
Ergül, Özgür Salih (2004-06-26)
In the method-of-moments (MOM) and the fast-multipole-method (FMM) solutions of the electromagnetic scattering problems modeled by arbitrary planar triangulations, the magnetic-field integral equation (MFIE) can be observed to give less accurate results compared to the electric-field integral equation (EFIE), if the current is expanded with the Rao-Wilton-Glisson (RWG) basis functions. The inaccuracy is more evident for problem geometries with sharp edges or tips. This paper shows that the accuracy of the M...
An Application of the rayleigh-ritz method to the integral-equation representation of the one-dimensional schrödinger equation
Kaya, Ruşen; Taşeli, Hasan; Department of Mathematics (2019)
In this thesis, the theory of the relations between differential and integral equations is analyzed and is illustrated by the reformulation of the one-dimensional Schrödinger equation in terms of an integral equation employing the Green’s function. The Rayleigh- Ritz method is applied to the integral-equation formulation of the one-dimensional Schrödinger equation in order to approximate the eigenvalues of the corresponding singular problem within the desired accuracy. The outcomes are compared with those r...
Optimizations of EFIE and MFIE Combinations in Hybrid Formulations of Conducting Bodies
Karaosmanoglu, B.; Onol, C.; Ergül, Özgür Salih (2015-09-11)
We present generalized hybrid surface integral-equation formulations for three-dimensional conductors with arbitrary shapes. The proposed formulations are based on flexible applications of the electric-field integral equation and the magnetic field integral equation with varying combinations on different regions of the given objects. As a proof of concept, we demonstrate hybrid formulations using two-region maps and their parametric analysis. We show that hybrid formulations may enable optimal solutions in ...
Citation Formats
Ö. S. Ergül, “The use of curl-conforming basis functions for the magnetic-field integral equation,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, pp. 1917–1926, 2006, Accessed: 00, 2020. [Online]. Available: