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

本提案的目标是研究在当前和新兴的并行体系结构中开发新的高效的并行保证质量和三维网格生成方法，用于实时有限元计算。具体来说,我们将:(1)推广用于三维保证质量Delaunay网格生成的点插入理论；(2)开发一个并行理论框架，该框架可以在从顺序到多核/多线程处理器以及最终具有多核/多线程处理器的多处理器节点集群的有限额外努力下部署该方法；(3)使用实用的logp模型进行复杂性分析；(4)最后使用现有的最先进的全功能序列软件和我们将开发的并行框架实现有史以来第一个3D并行保证质量网格生成方法。该方案的思想优点是在限定球面内推导出一个完整的三维区域，用于选择施泰纳点插入。该方法的新颖之处在于，我们可以灵活地使用delaunay方法的许多新位置来插入点，而不是过去使用一两个选择；额外的选择创造了更多的机会来改善尺寸优化以及其他以应用为中心的标准（多种组织/材料）。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。该项目将对几个科学计算和工程社区产生更广泛的影响，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.