Numerical algorithm of multipole expansion method for conductivity of ellipsoidal particle composite

Abstract

The paper addresses the numerical implementation of the multipole expansion method in application to the conductivity problem for the ellipsoidal particle composite with isotropic constituents and imperfect interfaces. The main steps of the numerical algorithm are considered in detail including generation of the geometry model, evaluating the re-expansion coefficients, fulfilling the periodicity and interface conditions and determination of the series expansion coefficients by iterative solving a set of linear equations. For each step, the numerical tests are performed which illustrate an accuracy and efficiency of the method. The rational computational strategies and the ways of boosting the computer code performance are discussed. The algorithm-based code provides a fast and accurate analysis of the local potential fields and the effective conductivity of composite with an adequate account for the arrangement and orientation of inhomogeneities. The imperfect thermal contact between the matrix and inhomogeneities is taken into account accurately. The application area covers the polydisperse and multiphase composites of matrix type. Its extension to the ellipsoidal particle composites with anisotropic constituents is straightforward. Incorporation of this feature yields possibly the most general model of composite that may be considered in the framework of analytical approach, and the proposed numerical algorithm is by far the most efficient method for studying these models.