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

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Abstract
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 advantages of the method as compared with 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 that are electrically more than an order of magnitude larger than those that can be handled by other techniques.