A Method of Images for the Evaluation of Electrostatic Fields in Systems of Closely Spaced Conducting Cylinders

A long-standing area of materials science research has been the study of electrostatic, magnetic, and elastic fields in composites with densely packed inclusions whose material properties differ markedly from that of the background. While powerful tools exist for dilute suspensions, accurate calculations in the close-to-touching case have been carried out largely by asymptotic methods and only for simple geometries such as regular arrays of cylinders or spheres. In this paper, we develop a hybrid numerical method for the evaluation of electrostatic fields in composites consisting of arbitrary dispersions of cylinders. Our approach is based on an integral equation formulation of the governing interface problem combined with a new method of images. High accuracy is achieved using only a small number of degrees of freedom for each inclusion.