面向全空间有限元数值模拟的四面体网格并行生成算法研究

With the development of high performance computers, the models that can be processed by finite element numerical simulation are becoming more and more complex, and the scale of the required meshes can reach a number of billions. However, most large-scale finite element simulations still depend on a squential meshing procedure nowadays, although the solvers may be able to run in a massiavely parallel computer efficiently. Not surprisingly, it remains a main performance bottleneck in the aspect of memory and efficiency when generating large-scale meshes. The finite element numerical simulation of the whole space not only need to generate the mesh of the model, but also need to generate the mesh of the outer computational space of the model. The scale of the whole model is large. So, further requirements for mesh generation are put forward. Therefore, a key approach to overcome this bottleneck is developing efficent parallel mesh generators.. This project aims to solve the problem of parallel tetrahedral mesh generation for finite element numerical simulation in whole computational space . We try to design and implement a geometric adaptive mesh size control technology, and combine the advanced front method with Delaunay triangulation method to solve the two key problems in this project, including the domain decomposition method for the whole model and the mesh generation for interfaces between sub-regions. We are going to develop a convergent and robust parallel tetrahedral mesh generation method for the numerical simulation in whole computational space. The method is applicatable to tens of thousands of processors and provides high-quality large scale meshes for high performance numerical simulations.

随着并行计算机的发展，有限元数值模拟可处理的模型越来越复杂，需要的网格数可达数十亿规模。目前，数值模拟大都采用“串行网格生成+并行求解”的“准并行”计算模式，在生成大规模网格单元时存在严重的内存和时间性能瓶颈。而全空间的有限元数值模拟不仅要生成模型的网格，还要生成模型外部计算空间的网格，整体模型尺度跨度大，对复杂问题的网格生成提出了进一步的要求。因此，发展有效的并行网格生成方法，实现全过程并行计算模式，是提高全空间数值模拟计算能力的关键所在。. 本项目面向全空间有限元数值模拟的四面体网格并行生成问题，拟建立几何特征自适应的网格尺寸控制技术，结合前沿推进思想和Delaunay算法，重点突破复杂几何模型的全空间区域分解和子区域交界面网格生成两个关键问题，实现具有良好收敛性和鲁棒性的、适应数万处理器核的全空间四面体网格并行生成算法，为全空间的高性能有限元数值模拟提供高质量、大规模的四面体网格。

本项目致力于研究四面体网格并行生成方法，并研制相关程序，为电磁辐射和散射以及计算流体力学中三维全空间/半空间的数值模拟提供大规模计算网格。本项目发展了一种全空间/半空间自动构建方法，避免了几何模型的布尔运算；进而发展了一种分布式和共享内存耦合的全自动四面体网格多级并行生成方法，该方法可以更好的适应目前超级计算机的体系结构，且适用于复杂精细CAD模型的大规模网格生成。为了生成用于粘性流体模拟问题的网格，本项目还发展了边界层网格生成算法，与四面体网格生成组合形成混合网格生成算法。本项目发展的方法已成功应用于舰船、电路板、天线系统等大型工程模型的电磁仿真和燃烧室等复杂工程模型的流体仿真中，验证了本项目发展的网格生成方法的有效性。