CAREER: A Parallel and Efficient Computational Framework for Unified Volumetric Meshing in Large-Scale 3D/4D Anisotropy

该提案开发了一个计算框架，可以帮助采用先进网络基础设施生态系统的领域科学家（例如，用于工程、制造、医疗保健等）真实有效地重建、可视化和分析具有复杂几何结构和高度各向异性特性（这些特性的特征在于系统中存在指定的方向和纵横比）的3D和4D（时空）体积对象。例如，在机械工程中，有必要使用用户要求的高质量措施和标准交互式地设计和建模机械零件。计算框架使得能够制造具有特定微观结构的机械部件，与不赋予这些特性的机械部件相比，这些机械部件可以有效地生产以承受更强的应力和应变，这对下一代机械部件设计产生了重大影响。作为PI职业发展的一个组成部分，教育计划强调通过PI为K-12，本科生和研究生提供的新的“3D动手”教育理念，在不同方面整合教育和研究。因此，该项目符合国家利益，正如NSF的使命所述：促进科学进步;促进国家健康，繁荣和福利。该项目的研究目标侧重于各向异性体积网格的计算框架，这是一项影响广泛科学领域的基础和转化研究。 的能力和可用性的网格框架进行评估，通过调查制造的内部微观结构和各向异性的体积模型，以捕捉器官和组织的形状的对象。（1）基于Nash定理的高维几何嵌入的并行计算：高维几何嵌入的计算实现使得具有多个张量特征的复杂对象的建模可以在一个大型线性系统中并行建立和求解。(2)在统一的粒子框架中建模多种形状的网格单元：粒子系统灵活有效地生成高质量的蜂窝、四面体和六面体（网格）图案，这些图案是为网格结构而设计的。优化过程是很容易制定在高维空间中的并行性。(3)并行生成3D/4D各向异性网格：最终的多形状各向异性网格在高维空间中并行计算，在各向同性度量下使用简单的欧几里得计算。该项目的主要成果是3D/4D-ParaAnisoMesh系统。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This proposal develops a computational framework that helps the domain scientists who employ advanced cyberinfrastructure ecosystem (e.g., for engineering, manufacturing, healthcare, etc.) to realistically and efficiently reconstruct, visualize, and analyze 3D and 4D (space-time) volumetric objects with complex geometric structures and highly anisotropic properties (such properties are characterized by the presence of specified orientations and aspect ratios in the system). For example, in mechanical engineering, it is necessary to interactively design and model mechanical parts with user-required high-quality measures and standards. The computational framework enables fabrication of such mechanical parts with specified microstructure that can be efficiently produced to sustain much stronger stress and strain compared with those without endowing such properties, which leads to significant impact on the next-generation mechanical component design. As an integral part of the PI's career development, the educational plan emphasizes on the integration of education and research in different aspects through the PI's new "3D hands-on" education philosophy for K-12, undergraduate and graduate students. This project thus serves the national interest, as stated by NSF's mission: to promote the progress of science; to advance the national health, prosperity and welfare. The research goal of this project focuses on a computational framework for anisotropic volumetric meshing, a foundational as well as translational research impacting a broad range of scientific domains. The capability and usability of the meshing framework are evaluated by investigating fabrication of objects with internal microstructures and construction of anisotropic volumetric models to capture the organ and tissue shape. This work has the following primary components: (1) Computing high-dimensional geometric embedding based on Nash theorem in parallel: the computational realization of high-dimensional geometric embedding makes modeling complex objects with multiple tensor features being built and solved in parallel in a large linear system. (2) Modeling multi-shape of mesh element in a unified particle framework: the particle system flexibly and effectively generates high-quality honeycomb, tetrahedral, and hexahedral (grid) patterns, which are exactly designed for meshing structure. The optimization procedure is easily formulated for parallelism in the high-dimensional space. (3) Generating 3D/4D anisotropic mesh in parallel: the final multi-shape anisotropic meshes are computed in parallel in the high-dimensional space with simple Euclidean computations under the isotropic metric. The primary outcome of this project is a 3D/4D-ParaAnisoMesh system.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.