The conjugate gradient spectral iterative technique for planar structures

It is shown that using the spectral iterative technique (SIT) to solve the first-kind integral equation is equivalent to the Neumann iterative solution of a related second-kind integral equation. It is thus shown that SIT only converges when the norm of the operator in the second-kind equation is small enough. Applying a conjugate gradient technique to the second-kind equation results in a convergent iterative scheme. Some representative numerical results show a superiority in the rate of convergence of the conjugate gradient scheme for the second-kind equation (CGSIT-scheme) when compared with the convergence of the conjugate scheme for the original first-kind equation (CG-scheme). The CGSIT-scheme combines the advantages of the conjugate gradient method with those of the spectral iterative technique.< >