SGER: Three-Dimensional Generalized Parallel Delaunay Mesh Generation for the Numerical Solution of Partial Differential Equations

本建议的目标是研究新的和高效的并行保证质量和三维（3D）网格生成方法的实时有限元计算当前和新兴的并行体系结构的发展。 具体而言，我们将：（1）将点插入理论推广到三维Delaunay网格生成中，（2）建立了一个并行的理论框架，该框架可以在有限的额外工作量下将该方法从顺序处理器部署到多核/多线程处理器上，甚至部署到具有多核/多线程处理器的多处理器节点集群上，（3）利用LogP模型进行复杂度分析;（4）利用现有的网格生成技术，实现了第一个三维并行高质量网格生成方法。我们将开发一个全功能的顺序软件和并行框架。这个建议的智力价值是在外接球体内导出整个3D区域，用于选择Steinerpoint插入。 该方法的新奇在于，我们可以灵活地使用许多新的位置来插入Delaunay方法的点，而不是过去使用的一个或两个选择;另外， 选择创造更多 的机会 与其他以应用为中心标准（多种组织/材料）一起改进尺寸优化沿着。 此外，有史以来第一次，我们可以实现3D几何图形的代码重用。 该项目将产生更广泛的影响 在几个科学 计算和工程社区 比如网格生成和生物工程。

The goal of this proposal is to study the development of new andefficient class of parallel guaranteed quality and three-dimensional(3D) mesh generation methods for real-time finite element computationson current and emerging parallel architectures. Specifically, wewill: (1) generalize the point insertion theory for 3D guaranteedquality Delaunay mesh generation, (2) develop a parallel theoreticalframework that can deploy this method with limited additional effortfrom sequential to multicore/multithreaded processors and eventuallyon clusters of multiprocessor nodes with multicore/multithreadedprocessors, (3) perform complexity analysis using the practical LogPmodel and (4) finally implement the first ever 3D parallel guaranteedquality mesh generation method using existing state-of-the-art fullyfunctional sequential software and the parallel framework we willdevelop.The intellectual merit of this proposal is to derive an entire 3Dregion inside the circumscribed sphere, for the selection of Steinerpoint insertion. The novelty of the approach is that we have theflexibility to use many new positions for point insertion of Delaunaymethods rather than one or two choices were used in the past; theadditional choices create more opportunities to improve sizeoptimality along with other application-centric criteria (multipletissues/materials). In addition, for the first time ever, we canachieve code re-use for 3D geometries. The project will have broaderimpact on several scientific computing and engineering communities like mesh generation and bioengineering.