Rapidly convergent expansion method for calculating the effective conductivity of three-dimensional lattices of symmetric inclusions

An exact method is introduced to determine the electric potential in an inf inite rectangular lattice of particles described by curvilinear coordinates in which Laplace's equation separates. The potential is expanded in harmon ic functions, and suitable auxiliary functions are used to obtain an infini te system of linear algebraic equations for the expansion coefficients. Spe cial attention is paid to lattices of spheres and prolate spheroids. For th ese cases, the truncated system converges very rapidly as the number of ter ms in the truncation series increases. The method works well for calculatin g the effective conductivity for dense or sparse inclusions, and for highly conducting lattices or lattices of cavities. Numerical results for the eff ective conductivity are given and compared with data obtained by other meth ods. (C) 1999 American Institute of Physics. [S0021- 8979(99)06019-3].