In this article, we develop an extension of the Fourier transform solution method in order to solve conduction equation with nonperiodic boundary conditions (BC). The periodic Lippmann–Schwinger equation for porous materials is extended to the case of non-periodicity with relevant source terms on the boundary. The method is formulated in Fourier space based on the temperature as unknown, using the exact periodic Green function and form factors to describe the boundaries. Different types of BC: flux, temperature, mixed and combined with periodicity can be treated by the method. Numerical simulations show that the method does not encounter convergence issues due to the infinite contrast and yields accurate results for both local fields and effective conductivity.

中文翻译：

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多孔导电介质中非周期边值问题的傅里叶变换方法

在本文中，我们开发了傅立叶变换求解方法的扩展，以求解具有非周期边界条件 (BC) 的传导方程。多孔材料的周期性 Lippmann-Schwinger 方程被扩展到非周期性的情况，在边界上有相关的源项。该方法在傅立叶空间中基于未知的温度制定，使用精确的周期性格林函数和形状因子来描述边界。该方法可以处理不同类型的BC：通量、温度、混合和结合周期性。数值模拟表明，该方法不会遇到由于无限对比度而导致的收敛问题，并且对局部场和有效电导率都产生了准确的结果。