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首页> 外文期刊>Journal of Computational Physics >ESTIMATING EFFECTIVE PROPERTIES OF COMPOSITES FROM CROSS-SECTIONAL PHOTOGRAPHS
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ESTIMATING EFFECTIVE PROPERTIES OF COMPOSITES FROM CROSS-SECTIONAL PHOTOGRAPHS

机译：从断面照片估计复合材料的有效性能

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An algorithm is presented for the rapid evaluation of certain functionals of three-point correlation functions, measured in a plane. This simplifies the estimation of effective physical properties of composite materials from cross-sectional photographs via bounds. More precisely, Fourier coefficients of a reduced three-point correlation function are expressed as inner products of polyharmonic fields. The polyharmonic fields are evaluated with a polyharmonic version of the fast multipole method with a CPU requirement proportional to the number p of fields included and to the number N of points in a discretization of the component interfaces. The Fourier coefficients are related to structural parameters which are used in third-order bounds on conductivity and elastic properties. Inclusion of p polyharmonic fields gives structural parameters with an error decaying at least as 1/p(3). In a simple application for disks with p = 10, superalgebraic convergence in 1/N, and a high-order Gaussian quadrature rule for the inner products, the algorithm gives an error of typically 0.05%. A previous algorithm, involving Monte Carlo integration, gives structural parameters with an error of typically 2%. (C) 1995 Academic Press, Inc. [References: 19]
机译：提出了一种算法，用于快速评估在平面中测量的三点相关函数的某些函数。这简化了从横截面照片通过边界估计复合材料的有效物理性能的过程。更精确地，将减少的三点相关函数的傅立叶系数表示为多谐波场的内积。使用快速多极方法的多谐波版本评估多谐波场，其CPU要求与所包含的场数p和组件接口离散化中的点数N成正比。傅里叶系数与在电导率和弹性特性的三阶边界中使用的结构参数有关。包含p个多谐场会给出结构参数，其误差衰减至少为1 / p（3）。在p = 10的磁盘，1 / N的超代数收敛以及内积的高阶高斯正交规则的简单应用中，该算法的误差通常为0.05％。以前涉及Monte Carlo积分的算法给出的结构参数的误差通常为2％。 （C）1995 Academic Press，Inc. [参考：19]

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