The construction of efficient numerical algorithms for the electrostatics of locally anisotropic composites seems to be a poorly explored area. In this paper coupled first and second kind Fredholm integral equations for the electrostatics of anisotropic inclusions in an anisotropic matrix are derived. For a square array of circular cylinders the integral equations are solved to high accuracy through pointwise discretization. In the process a recent renormalization method is extended for the evaluation of lattice sums [J. Math. Phys. 35, 6036 (1994)] to encompass the calculation of sums on stretched lattices. Conditionally convergent stretched lattice sums are computed from physical considerations.

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