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.

本文探讨了多极膨胀法在具有各向同性成分和不完美界面的椭圆形颗粒复合材料的电导率问题中的数值实现。详细考虑了数值算法的主要步骤，包括生成几何模型，评估再膨胀系数，满足周期性和界面条件以及通过迭代求解一组线性方程来确定级数展开系数。对于每个步骤，都执行了数值测试，这些测试说明了该方法的准确性和效率。讨论了合理的计算策略和提高计算机代码性能的方法。基于算法的代码可对复合材料的局部电势场和有效电导率进行快速而准确的分析，并充分考虑了不均匀性的排列和方向。准确考虑了基体之间的不完美热接触和不均匀性。应用领域涵盖基质类型的多分散和多相复合材料。它很容易扩展到具有各向异性成分的椭圆形颗粒复合材料。合并此功能可能会产生可在分析方法框架中考虑的最通用的复合材料模型，并且所提出的数值算法是迄今为止研究这些模型的最有效方法。准确考虑了基体之间的不完美热接触和不均匀性。应用领域涵盖基质类型的多分散和多相复合材料。它很容易扩展到具有各向异性成分的椭圆形颗粒复合材料。合并此功能可能会产生可在分析方法框架中考虑的最通用的复合材料模型，并且所提出的数值算法是迄今为止研究这些模型的最有效方法。准确考虑了基体之间的不完美热接触和不均匀性。应用领域涵盖基质类型的多分散和多相复合材料。它很容易扩展到具有各向异性成分的椭圆形颗粒复合材料。合并此功能可能会产生可在分析方法框架中考虑的最通用的复合材料模型，并且所提出的数值算法是迄今为止研究这些模型的最有效方法。