Numerical Manifold Method (NMM) has gained widespread application in engineering practice due to its capacity to effectively address both continuous and discontinuous problems in a unified framework. With the advancement of 3D-NMM, there remains a deficiency in ready-made preprocessing tools. Hence, the generation of 3D manifold elements (MEs) is the primary prerequisite for 3D-NMM. In this study, a parallel algorithm to generate the MEs is proposed. Firstly, a novel 3D block identification algorithm is developed to improve the modeling efficiency. Then, 3D joint networks are simulated using the geological statistical results. Thirdly, the mathematical cover system is constructed using uniformly regular hexahedral meshes. Subsequently, the physical domain is cut using the Boolean algorithm to generate the related manifold blocks (MBs) and the Union-Find algorithm is used to determine the relationship of MBs with mathematical patches (MPs) and physical patches (PPs). The proposed program incorporates the OpenMP parallel library for CPU parallelization to enhance its efficiency and the OpenGL library is used to build a real-time visualization program. Finally, the proposed program is validated using several representative examples, and the obtained results demonstrate its efficient capability in generating MEs.

中文翻译：

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三维数值流形元素生成的并行算法

数值流形方法（NMM）由于能够在统一的框架下有效解决连续和不连续问题，在工程实践中获得了广泛的应用。随着3D-NMM的进步，现成的预处理工具仍然存在不足。因此，3D流形单元（ME）的生成是3D-NMM的首要前提。在本研究中，提出了一种生成 ME 的并行算法。首先，开发了一种新颖的3D块识别算法以提高建模效率。然后，使用地质统计结果模拟 3D 关节网络。第三，使用均匀正六面体网格构建数学覆盖系统。随后，使用布尔算法对物理域进行切割，生成相关的流形块（MB），并使用并查算法确定MB与数学补丁（MP）和物理补丁（PP）的关系。所提出的程序结合了用于CPU并行化的OpenMP并行库以提高其效率，并且使用OpenGL库来构建实时可视化程序。最后，使用几个代表性示例对所提出的程序进行了验证，获得的结果证明了其生成 ME 的高效能力。