An analytical convolution method combined with the conformal fourier transform for solving 1-D integral equations

A new solver, the analytical convolution method (ACM) combined with the conformal Fourier transform (CFT), is proposed for 1-D integral equations in electromagnetics. ACM directly obtains the convolution between the Green's function and the induced current density in a closed form. CFT provides a highly accurate Fourier transform of the discontinuous current density. Numerical results show that the ACM-CFT solver is several orders of magnitude more accurate than the traditional methods such as the conjugate-gradient fast Fourier transform (FFT) method, and its CPU time is significantly shorter.