An improved conjugate gradient FFT method for 2-D TE scattering problems

It is pointed out that the problem of two-dimensional scattering of a transverse electric (TE) polarized wave by a dielectric object can be formulated in terms of a hypersingular integral equation, in which a grad-div operator acts on a vector potential. The vector potential is a spatial convolution of the free-space Green´s function and the contrast source over the domain of interest. A weak form of the integral equation for the unknown electric flux density is obtained by testing it with roof-top functions. As the next step, the vector potential is expanded in a sequence of the roof-top functions and the grad-div operator is integrated analytically over the dielectric object domain only. Numerical results are presented for a lossy dielectric coaxially layered cylinder. The method considered shows excellent numerical performance.<>