Understanding and optimizing effective properties of porous functional materials, such as permeability or conductivity, is one of the main goals of materials science research with numerous applications. For this purpose, understanding the underlying 3D microstructure is crucial since it is well known that the materials' morphology has a significant impact on their effective properties. Because tomographic imaging is expensive in time and costs, stochastic microstructure modeling is a valuable tool for virtual materials testing, where a large number of realistic 3D microstructures can be generated and used as geometry input for spatially-resolved numerical simulations. Since the vast majority of numerical simulations is based on solving differential equations, it is essential to have fast and robust methods for generating high-quality volume meshes for the geometrically complex microstructure domains. The present paper introduces a novel method for generating volume-meshes with periodic boundary conditions based on an analytical representation of the 3D microstructure using spherical harmonics. Due to its generality, the present method is applicable to many scientific areas. In particular, we present some numerical examples with applications to battery research by making use of an already existing stochastic 3D microstructure model that has been calibrated to eight differently compacted cathodes.

了解和优化多孔功能材料的有效特性（例如渗透性或电导率）是材料科学研究具有许多应用程序的主要目标之一。为此，了解底层3D微观结构至关重要，因为众所周知材料的形态对其有效性能具有重大影响。由于层析成像的时间和成本昂贵，因此随机微观结构建模是用于虚拟材料测试的有价值的工具，其中可以生成大量逼真的3D微观结构并将其用作空间解析数值模拟的几何输入。由于绝大多数数值模拟都基于求解微分方程，必须有快速而强大的方法来为几何复杂的微结构域生成高质量的体积网格。本文基于使用球谐函数的3D微观结构的解析表示，介绍了一种生成具有周期性边界条件的体积网格的新方法。由于其通用性，本方法可应用于许多科学领域。特别是，我们利用已经存在的随机3D微结构模型（已针对八个不同压紧的阴极进行了校准），提供了一些数值示例，并应用于电池研究。本文基于使用球谐函数的3D微观结构的解析表示，介绍了一种生成具有周期性边界条件的体积网格的新方法。由于其通用性，本方法可应用于许多科学领域。特别是，我们利用已经存在的随机3D微结构模型（已针对八个不同压紧的阴极进行了校准），提供了一些数值示例，并应用于电池研究。本文基于使用球谐函数的3D微观结构的解析表示，介绍了一种生成具有周期性边界条件的体积网格的新方法。由于其通用性，本方法可应用于许多科学领域。特别是，我们利用已经存在的随机3D微结构模型（已针对八个不同压紧的阴极进行了校准），提供了一些数值示例，并应用于电池研究。