Numerical artifacts in the form of spurious oscillations are among the critical issues of Fast Fourier Transfer (FFT) methods for solving multiphase elastic problems such as numerical homogenization, in spite of their computational simplicity and efficiency. In the first part of the present work, it is shown that the irregular discretization of the interface due to the use of a voxel-based discretization is the dominant cause of oscillations. The second part of the present work focuses on numerical artifacts reduction schemes, and in particular special treatments for dealing with the irregular discretization of the interface such as the composite voxel method and neighbor averaging methods. An improved composite voxel method by using the level-set technique is proposed, which alleviates the implementation difficulty of the composite voxel method. This improved method is particularly relevant for non-parametrized interface representations such as those obtained from three-dimensional experimental images.

杂散振荡形式的数值伪像是快速傅立叶传递（FFT）方法的关键问题，尽管这些方法计算简单且效率高，但它们却可以解决诸如数值均质化之类的多相弹性问题。在本工作的第一部分中，表明由于使用基于体素的离散化导致界面的不规则离散化是振荡的主要原因。本工作的第二部分侧重于数值伪影减少方案，尤其是用于处理界面的不规则离散化的特殊处理，例如复合体素方法和邻居平均方法。提出了一种利用水平集技术改进的复合体素方法，减轻了复合体素方法的实现难度。