A homogeneous anisotropic conductive medium with a set of anisotropic heterogeneities of arbitrary shapes is considered. Calculation of local fields in the medium subjected to arbitrary external fields is reduced to systems of volume integral equations. For numerical solution, these equations are discretized using Gaussian approximating functions concentrated at the nodes of a regular grid. The elements of the matrices of the discretized problems have form of 1D-integrals that can be tabulated. For regular node grids, these matrices have Teoplitz’ structures, and fast Fourier transform algorithms can be used for iterative solution of the discretized problems. The method is applied to calculation of fields around isolated anisotropic spherical and cylindrical inclusions in an anisotropic homogeneous host medium. The results are used for calculation of the tensor of effective conductivity of the medium containing random sets of cylindrical inclusions. The self-consistent effective field method is used for solution of the homogenization problem. Dependencies of the components of the tensor of the effective conductivity on the volume fraction and orientations of the inclusions are presented.

考虑具有一组任意形状的各向异性异质性的均质各向异性导电介质。将介质中受到任意外部场影响的局部场的计算简化为体积积分方程组。对于数值解，这些方程使用集中在规则网格的节点上的高斯逼近函数离散化。离散问题矩阵的元素具有可以列表化的一维积分形式。对于常规节点网格，这些矩阵具有Teoplitz结构，并且快速傅里叶变换算法可用于迭代解决离散化问题。该方法适用于各向异性均质宿主介质中孤立的各向异性球形和圆柱形夹杂物周围的场的计算。该结果用于计算包含任意组圆柱形夹杂物的介质的有效电导率张量。自洽有效场法用于解决均质化问题。提出了有效电导率张量分量对夹杂物的体积分数和取向的依赖性。