Method of Conjugate Gradient and Fast Fourier Transformed for Numerical Solution of Conducting Plate of Resonant Size

Simple and efficient novel combination of the conjugate gradient (CG) method with the fast Fourier transform technique (FFT) is presented. With this combination, the computational time required to solve electromagnetic scattered problems is much less than the time required by the ordinary (CG) method and the method of moments (MOM). Also, applied computational electromagnetics (ACE) require the computation of potential functions given in terms of convolution integrals which can be calculated very efficiently by using the (CG-FFT). The procedure is made easy and systematic by using a sampling process with roof-top functions to represent the induced current and pulses to average the fields. The scheme is an efficient numerical tool since the spatial derivatives are replaced with simple multiplications in the transformed domain, some of the computational difficulties present in the ordinary (CG) method and the (MOM) do not exist here. Therefore, electrically small structures can also be handled more easily. In comparison with(MOM), this scheme avoids the storage of large matrices and reduces the copter time by orders of magnitude. Finally, since the method is iterative, it is possible to know the accuracy in a problem solution. A perfectly conducting square plate is analyzed. Results are presented and compared with analytical, numerical, or measured values that appear in the literature. The details of the formulation and the computational procedure are presented along with the numerical results for the problem