CHS: Small: Collaborative Research: Robust High Order Meshing and Analysis for Design Pipeline Automation

许多现实世界现象的模拟（如弹塑性变形、声音传播和热扩散）依赖于空间的显式离散化，这允许存储物理量并在其上进行计算。然而，用于设计形状的计算机辅助设计（CAD）工具依赖于不同的离散化，通常是一组断开的高阶多项式补丁，这不能用于模拟。因此，有必要将CAD模型转换为仿真网格，这一过程可能由于使用线性元素而引入几何误差，并且需要人工交互，这限制了其用于高端应用。本研究将开发一种新颖的自动方法，通过使用高阶元素“精确”地处理这种转换，从而避免不必要的几何近似。该项目将研究高阶网格生成和模拟作为一个单一的问题，建立在鲁棒线性网格和开发新的有限元方法技术的最新进展，这将允许非专业用户从模拟中受益，目前完成该任务所需的时间和成本的一小部分，这反过来将为医学和数字制造的新应用打开大门。该项目将涉及在大量实际CAD模型上对开发的算法进行广泛测试。在这个项目中收集的数据和算法的参考实现都将在公共领域发布，以促进新技术的采用以及未来在这个方向上的研究。该项目的目标是开发一个强大的网格划分管道，生成曲线元素，可以高保真地再现CAD模型和细分表面，使用近似误差的直接测量，导致粗网格的设计与应用程序所需的仿真精度相匹配，并且可以健壮地自动处理现实世界CAD模型的大量集合。对于交互式应用，生成的曲面元素和新的误差估计的结合将导致非常粗糙的模型，非常适合快速仿真。在CAD设置中，它将首次实现复杂场景的精确建模，例如螺杆的驱动或圆角上应力集中的模拟。该方法将缩小设计工具之间的差距，提供曲面几何到适合分析的曲面网格的自动转换。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。

The simulation of many real-world phenomena (such as elastoplastic deformations, sound propagation, and heat diffusion) relies on an explicit discretization of the space, which allows storage of physical quantities and performance of computations upon them. However, the Computer Aided Design (CAD) tools used to design shapes rely on a different discretization, usually a collection of disconnected high-order polynomial patches, which cannot be used in simulations. It is thus necessary to convert CAD models into simulation meshes, a procedure that can introduce geometric errors due to the use of linear elements and requires manual interaction, which limits its use to high-end applications. This research will develop a novel, automatic approach to tackle this conversion "exactly" by using high order elements, thereby avoiding unnecessary geometric approximations. The project will study high-order mesh generation and simulation as a single problem, building upon recent advances in robust linear meshing and developing new finite element method techniques that will allow non-expert users to benefit from simulation at a fraction of the time and cost currently needed to accomplish that task, which in turn will open the doors to new applications in medicine and digital fabrication. The project will involve extensive testing of the developed algorithms on a large collection of real-world CAD models. Both the data collected during this project and the reference implementation of the algorithms will be released in the public domain to foster adoption of the new technique as well as future research in this direction.The goal of this project is to develop a robust meshing pipeline that generates curvilinear elements that can reproduce both CAD models and subdivision surfaces with high fidelity, uses a direct measure of approximation errors, leading to coarse meshes that are designed to match the simulation accuracy required by applications, and can robustly and automatically process large collections of real-world CAD models. For interactive applications, the combination of the generated curved elements and the new error estimate will lead to extremely coarse models ideal for fast simulation. In CAD settings, it will for the first time enable precise modeling of complex scenarios such as the driving of a screw or the simulations of the stress concentration on fillets. The approach will close the gap between design tools, providing an automatic conversion of curved geometry to analysis-suitable curved meshes.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.