Comparison between three integral formulations for the 2D-TE scattering problem

The fast Fourier transform conjugate gradient method solves numerically the electric field integral equation, using the method of moments with pulse basis function and point matching, but substantial errors are found in this method for the 2-D TE case. In the present work, the authors analyze the source of errors in these approximations and show that the modified method empirically proposed by D.T. Borup, D.M. Sullivan, and O.P. Ghandi (IEEE Trans. Microwave Theory Tech., vol.MTT-35, p.383-95, Apr.1987) would not have been necessary if correct terms in the integral equation were used. With this aim, the authors propose a new integral formulation using generalized functions and compare it with two previous formulations, that of S.C. Hill, C.H. DAmey, and D.A. Christensen Radio Sci., vol.18, p.328-36, May-June 1983 and D.E. Livesay and K.M. Chen (IEEE Trans. Microwave Theory Tech., vol.MMT-22, p.1273-80, 1974). For all the numerical methods discussed, the conjugate gradient technique is used to solve the linear system, and the convolution products are computed by means of a Fourier transform. The results are of interest in connection with refining numerical methods to support biomedical applications (e.g. microwave imaging and hypothermia treatment).<>