Improved testing of the magnetic-Field integral equation

An improved implementation of the magnetic-field integral equation (MFIE) is presented in order to eliminate some of the restrictions on the testing integral due to the singularities. Galerkin solution of the MFIE by the method of moments employing piecewise linear Rao-Wilton-Glisson basis and testing functions on planar triangulations of arbitrary surfaces is considered. In addition to demonstrating the ability to sample the testing integrals on the singular edges, a key integral is rederived not only to obtain accurate results, but to manifest the implicit solid-angle dependence of the MFIE as well.

[1]  R. Coifman,et al.  The fast multipole method for the wave equation: a pedestrian prescription , 1993, IEEE Antennas and Propagation Magazine.

[2]  L. Gurel,et al.  Solid-angle factor in the magnetic-field integral equation , 2005 .

[3]  Andrew J. Poggio,et al.  CHAPTER 4 – Integral Equation Solutions of Three-dimensional Scattering Problems , 1973 .

[4]  L. Gurel,et al.  Singularity of the magnetic-field Integral equation and its extraction , 2005, IEEE Antennas and Wireless Propagation Letters.

[5]  A. Stroud.  Approximate calculation of multiple integrals , 1973 .

[6]  Yahya Rahmat-Samii,et al.  The evaluation of MFIE integrals with the use of vector triangle basis functions , 1997 .

[7]  Jian-Ming Jin,et al.  Fast and Efficient Algorithms in Computational Electromagnetics , 2001 .

[8]  Jiming Song,et al.  Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects , 1997 .

[9]  Roberto D. Graglia,et al.  On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle , 1993 .

[10]  Nagayoshi Morita,et al.  Integral Equation Methods for Electromagnetics , 1991 .

[11]  R. Mittra,et al.  Computational Methods for Electromagnetics , 1997 .

[12]  Roger F. Harrington,et al.  Field computation by moment methods , 1968 .

[13]  L. Gurel,et al.  Investigation of the inaccuracy of the MFIE discretized with the RWG basis functions , 2004, IEEE Antennas and Propagation Society Symposium, 2004..

[14]  D. A. Dunavant.  High degree efficient symmetrical Gaussian quadrature rules for the triangle , 1985 .

[15]  D. Wilton,et al.  Electromagnetic scattering by surfaces of arbitrary shape , 1980 .