A polarization-based fast numerical method for computing the effective conductivity of composites

Abstract

Purpose

The paper deals with the development of an improved fast Fourier transform (FFT)-based numerical method for computing the effective properties of composite conductors. The convergence of the basic FFT-based methods is recognized to depend drastically on the contrast between the phases. For instance, the primal formulation is not suited for solving the problems with high conductivity whereas the dual formulation is computationally costly for problems with high resistivity. Consequently, it raises the problem of computing the properties of composites containing both highly conductive and resistive inclusions.

Design/methodology/approach

In the present work, the authors' propose a new iterative scheme for solving that kind of problems which is formulated in term of the polarization.

Findings

The capability and relevance of this iterative scheme is illustrated through numerical implementation in the case of composites containing squared inclusions. It is shown that the rate of convergence is increased and thus, particularly when the case of high contrasts is considered. The predominance of the polarization based iterative scheme (PBIS) over existing ones is also illustrated in the case of a composite containing both highly conductive and highly resistive inclusions.

Originality/value

The method is easy to implement and uses the same ingredients as the basic schemes: the FFT and the exact expression of the Green tensor in the Fourier space. Moreover, its convergence conditions do not depend on the conductivity properties of the constituents, which then constitutes the main difference with other existing iterative schemes. The method can then be applied for computing the effective properties of composites conductors with arbitrary contrasts.

Citation

Monchiet, V. and Bonnet, G. (2013), "A polarization-based fast numerical method for computing the effective conductivity of composites", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 7, pp. 1256-1271. https://doi.org/10.1108/HFF-10-2011-0207