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

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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.