Abstract The Fourier series method is used to solve the periodic homogenization problem for conductive materials containing voids. The problems involving voids are special cases of infinite contrast whose full field solution is not unique, causing convergence issues when iteration schemes are used. In this paper, we reformulate the problem based on the temperature field in the skeleton and derive an equation where the temperature field is connected to values on the pore boundary. Iteration schemes based on the new equation show that the convergence is fast, yielding good results both in terms of local fields and effective conductive properties.

中文翻译：

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基于FFT的多孔导电材料数值均匀化方法

摘要 傅里叶级数法用于解决含空隙导电材料的周期性均匀化问题。涉及空隙的问题是无限对比度的特殊情况，其全场解不是唯一的，在使用迭代方案时会导致收敛问题。在本文中，我们根据骨架中的温度场重新表述问题，并推导出一个方程，其中温度场与孔隙边界上的值相关联。基于新方程的迭代方案表明收敛速度快，在局部场和有效导电性能方面都产生了良好的结果。