There are many ways to solve potential problems for anisotropic mixtur
es. The finite element method is a popular choice with great flexibili
ty that gives the solution in the entire computational domain. Effecti
ve medium approximation is a simpler option that only estimates effect
ive properties. Interface integral equation methods is a third class o
f methods that has been studied for a long time, but only rarely been
used for computations. In this paper, electrostatics of anisotropic tw
o-dimensional composites is discussed. The geometry under consideratio
n is a periodic composite of arbitrarily shaped anisotropic inclusions
in an anisotropic matrix. The location of the inclusion interfaces ar
e given on analytic form as to facilitate reproduction of results. Hig
hly accurate calculations are performed with a coupled first and secon
d kind Fredholm integral equation method. Comparison is made with fini
te element method calculations. (C) 1995 American Institute of Physics
.