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The magnetic field integral equation (MFIE) is widely used in the analysis of electromagnetic scattering problems for conducting objects. Usually, the MFIE is solved by the method of moments (MoM) using the Rao–Wilton–Glisson (RWG) basis functions. In this paper, a new kind of basis function which is named the piece-wise constant vector basis function is proposed and used to solve the MFIE by MoM. Definition of this kind of basis function is given. The calculation of the impedance matrix entries is presented in detail. This kind of basis function is then used for the solution of the MFIE for electromagnetic scattering problems. The radar cross section (RCS) results and the iterative property of both kinds of basis functions are presented. It is shown that the piece-wise constant vector basis functions give similar RCS results as those of the RWG basis functions. Particularly, when iterative solver is used to solve the resultant linear system, the solution scheme using the piece-wise constant vector basis functions iterates much faster than that using the RWG basis functions.

We present a novel method to solve the magnetic field integral equation (MFIE) using the method of moments (MoM) efficiently. This method employs a linear combination of the divergence-conforming Rao–Wilton–Glisson (RWG) function and the curl-conforming n × RWG function to test the MFIE in MoM. The discretization process and the relationship of this new testing function with the previously employed RWG and n × RWG testing functions are presented. Numerical results of radar cross section (RCS) data for objects with sharp edges and corners show that accuracy of the MFIE can be improved significantly through the use of the new testing functions. At the same time, only the commonly used RWG basis functions are needed for this method.

In this paper, we study the accuracy and the efficiency of the monopolar divergence-conforming Rao–Wilton–Glisson (RWG) and the monopolar curl-conforming n×RWG basis functions for the magnetic field integral equation (MFIE). Similar to cases using RWG and n×RWG basis functions for the MFIE, there are two impedance matrix elements calculation schemes if the monopolar RWG and monopolar n×RWG basis functions are used to the MFIE, respectively. The monopolar basis functions and the implementation schemes used for the MFIE are discussed. The scattering cross section data as well as the CPU time needed to fill the corresponding impedance matrix obtained from numerical solutions of these implementation schemes using monopolar basis functions are investigated. For the monopolar basis functions and the implementation schemes considered, the first scheme of the MFIE using the monopolar curl-conforming n×RWG basis functions gives most accurate results and it is the best choice for the use of the monopolar basis functions to the MFIE.

The magnetic field integral equation (MFIE) is widely used in method of moments (MoM) for electromagnetic scattering analysis of arbitrarily shaped three-dimensional conducting objects. Besides the well-known Rao–Wilton–Glisson (RWG) basis functions, the curl-conforming n×RWG basis functions are also used in MFIE to improve its accuracy. However, there are two different impedance matrix element formulations that result from the use of the n×RWG basis and testing functions to the MFIE in the literature. Moreover, one of the formulations is more complicated than the other. This stimulates us to explore which formulation is more efficient in improving the accuracy of the MFIE. This paper investigates the efficiency of two impedance matrix element formulations resulting from the use of the curl-conforming n×RWG basis and testing functions to the MFIE. Details to calculate the impedance matrix elements are studied. Numerical results show that the radar cross section (RCS) results of the first formulation are more accurate than those of the second one while consuming only about half of the time to fill the impedance matrix for the second formulation. Thus, compared with the second formulation, the first formulation resulting from the use of the curl-conforming n×RWG basis functions to the MFIE is a better choice for scattering analysis of three-dimensional conducting objects.

We present a novel implementation of the magnetic field integral equation (MFIE) with the use of the combined Rao–Wilton–Glisson (RWG) basis and testing functions. Implementation details are outlined in the context of the method of moments. For a wide variety of small sharp-edged objects, we show that accuracy of the MFIE can be greatly improved with a combination parameter of about 0.2 for the combined RWG functions. This is achieved with relatively coarse discretization for the scatterers and with only minor modifications in the existing codes based on the RWG and n×RWG functions.

The method of moments (MoM) solution on the magnetic field integral equation (MFIE) for electromagnetic scattering problems of conducting objects with Rao–Wilton–Glisson (RWG) basis functions requires the evaluation of almost singular double surface integrals over triangular subdomains. Calculating these integrals accurately is essential for the successful solution of the MFIE by MoM especially for small sharp-edged conducting objects. This paper studies the singularity of the MFIE and uses an accurate singularity extraction technique to avoid logarithmic singularity of the integration on the testing triangles for the MFIE. Based on the numerical examples of several small sharp-edged conducting objects, it is demonstrated that the accuracy of the MFIE is improved greatly with the use of the new singularity extraction technique.