The method of conjugate gradients for the numerical solution of large-body electromagnetic scattering problems

Over the past few decades, many techniques have been developed for the numerical solution of integral equations representing electromagnetic scattering problems. However, a majority of these techniques are limited to electrically small scatterers, i.e., below the resonance range. This is primarily because the amount of CPU computer time and storage requirements become prohibitive for large body scatterers. Recent work indicates that a procedure based on the iterative conjugate gradient method can be incorporated into conventional numerical methods in order to extend the range of application of the techniques to larger geometries. In this paper we discuss the conjugate gradient method and illustrate several ways in which it can be applied to electromagnetic scattering problems. The discussion includes mention of the method as compared to conventional approaches as well as some of its limitations. In many practical scattering problems of interest at optical wavelengths, the method can provide a convenient means of treating problems which are electrically more than an order of magnitude larger than can be handled by other techniques.