The application of the conjugate gradient method to the solution of transient electromagnetic scattering from thin wires

Previous approaches to the problem of computing scattering by conducting bodies have utilized the well-known marching-on-in-time solution procedures. However, these procedures are very dependent on discretization techniques and sometimes lead to instabilities as the time progresses. Moreover, the accuracy of the solution cannot be verified easily, and usually there is no error estimation. In this paper we describe the conjugate gradient method for solving transient problems. For this method, the time and space discretizations are independent of one another. The method has the advantage of a direct method as the solution is obtained in a finite number of steps and also of an iterative method since the roundoff and truncation errors are limited only to the last stage of iteration. The conjugate gradient method converges for any initial guess; however, a good initial guess may significantly reduce the computation time. Also, explicit error formulas are given for the rate of convergence of this method. Hence any problem may be solved to a prespecified degree of accuracy. The procedure is stable with respect to roundoff and truncation errors and simple to apply. As an example, we apply the method of conjugate gradient to the problem of scattering from a thin conducting wire illuminated by a Gaussian pulse. The results compare well with the marching-on-in-time procedure.