The application of the conjugate gradient method for the solution of operator equations arising in electromagnetic scattering from wire antennas

Abstract

In this paper the method of conjugate gradient is presented for the solution of operator equations arising in electromagnetics. The particular problem to which the conjugate gradient method has been applied is the electromagnetic scattering from arbitrary oriented wire antennas. With this iterative technique, it is possible to solve electromagnetic problems involving electrically large structures without storing any matrices as is conventionally done in the method of moments. The basic difference between the proposed method and the matrix methods (Rayleigh‐Ritz, Galerkin's, method of moments) for the same expansion functions is that for the iterative technique we are solving a least squares problem. Hence, as the order of the approximation is increased, the proposed technique guarantees a monotonic convergence for the residuals AI‐Y, whereas matrix methods, in general, do not yield monotonic convergence. The conjugate gradient method converges for any initial guess; however, a good one may significantly lower the computation time. Also, explicit error formulas are given for the rate of convergence. Numerical results are presented for electromagnetic scattering from arbitrary oriented thin‐wire antennas.