ABSTRACT We present a fast algorithm for generating Laguerre diagrams with cells of given volumes, which can be used for creating RVEs of polycrystalline materials for computational homogenisation, or for fitting Laguerre diagrams to EBSD or XRD measurements of metals. Given a list of desired cell volumes, we solve a convex optimisation problem to find a Laguerre diagram with cells of these volumes, up to any prescribed tolerance. The algorithm is built on tools from computational geometry and optimal transport theory which, as far as we are aware, have not been applied to microstructure modelling before. We illustrate the speed and accuracy of the algorithm by generating RVEs with user-defined volume distributions with up to 20,000 grains in 3D. We can achieve volume percentage errors of less than 1% in the order of minutes on a standard desktop PC. We also give examples of polydisperse microstructures with bands, clusters and size gradients, and of fitting a Laguerre diagram to 3D EBSD measurements of an IF steel.

中文翻译：

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Laguerre 镶嵌和多晶微结构：生成给定体积晶粒的快速算法

摘要 我们提出了一种使用给定体积单元生成拉盖尔图的快速算法，该算法可用于创建多晶材料的 RVE 以进行计算均质化，或用于将拉盖尔图拟合到金属的 EBSD 或 XRD 测量。给定所需细胞体积的列表，我们解决凸优化问题以找到具有这些体积的细胞的拉盖尔图，达到任何规定的容差。该算法建立在计算几何和最优输运理论的工具之上，据我们所知，这些工具以前还没有应用于微观结构建模。我们通过在 3D 中生成具有用户定义的体积分布的 RVE 来说明算法的速度和准确性，最多 20,000 粒。我们可以在标准台式 PC 上以分钟为单位实现小于 1% 的体积百分比误差。我们还给出了具有带、簇和尺寸梯度的多分散微观结构的示例，以及将拉盖尔图拟合到 IF 钢的 3D EBSD 测量值的示例。