Electrostatics of Anisotropic Inclusions in Anisotropic Media

There are many ways to solve potential problems for anisotropic mixtures. The nite element method is a popular choice with great exibility that gives the solution in the entire computational domain. EEective medium approximation is a simpler option that only estimates eeective properties. Interface integral equation methods is a third class of methods that has been studied for a long time, but only rarely been used for computations. In this paper, electrostatics of anisotropic two-dimensional composites is discussed. The geometry under consideration is a periodic composite of arbitrarily shaped anisotropic inclusions in an anisotropic matrix. The location of the inclusion interfaces are given on analytic form as to facilitate reproduction of results. Highly accurate calculations are performed with a coupled rst and second kind Fredholm integral equation method. Comparison is made with nite element method calculations.