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

本提案开发了一个计算框架，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）现实有效地重建，可视化和分析具有复杂几何结构和高度各向异性特性的3D和4D（时空）体积对象（这些特性的特征在于系统中存在指定的方向和纵横比）。例如，在机械工程中，需要使用用户要求的高质量测量和标准对机械零件进行交互设计和建模。该计算框架能够制造出具有特定微观结构的机械部件，与那些没有赋予这些特性的机械部件相比，这些机械部件可以有效地承受更强的应力和应变，这对下一代机械部件的设计产生了重大影响。作为PI职业发展的一个组成部分，该教育计划强调通过PI对K-12，本科生和研究生的新的“3D动手”教育理念，在不同方面整合教育和研究。因此，这个项目符合国家利益，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。该项目的研究目标集中在各向异性体积网格的计算框架上，这是一项影响广泛科学领域的基础研究和转化研究。通过研究具有内部微结构的物体的制造和各向异性体积模型的构建来捕获器官和组织形状，评估了网格框架的能力和可用性。本工作的主要组成部分如下：(1)基于纳什定理的高维几何嵌入并行计算：高维几何嵌入的计算实现使得在大型线性系统中对具有多个张量特征的复杂对象进行建模并并行求解。(2)在统一的粒子框架中对网格单元的多种形状进行建模：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，这些图案都是为网格结构精确设计的。对于高维空间中的并行性，优化过程很容易表述。(3)并行生成3D/4D各向异性网格：在各向同性度量下，通过简单的欧几里德计算，在高维空间中并行计算最终的多形状各向异性网格。这个项目的主要成果是3D/ 4d paraanisomesh系统。该奖项反映了美国国家科学基金会的法定使命，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.