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

许多真实世界现象（如弹塑性变形，声音传播和热扩散）的模拟依赖于空间的显式离散化，这允许存储物理量并对其进行计算。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，通常是不连续的高阶多项式贴片的集合，其不能用于模拟。因此，有必要将CAD模型转换为模拟网格，这是一个由于使用线性元件而可能引入几何误差的过程，并且需要手动交互，这限制了其在高端应用中的使用。 这项研究将开发一种新的，自动的方法来解决这个转换“确切”使用高阶元素，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，建立在强大的线性网格和开发新的有限元方法技术的最新进展，将允许非专家用户受益于模拟在一小部分的时间和成本目前需要完成该任务，这反过来又将打开大门，在医学和数字制造的新应用。该项目将涉及在大量真实世界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该方向的未来研究。这个项目的目标是开发一个强大的网格管道，生成曲线元素，可以高保真地再现CAD模型和细分曲面，使用逼近误差的直接测量，这导致粗网格被设计为匹配应用所需的模拟精度，并且可以鲁棒地自动处理大量真实世界的CAD模型。对于交互式应用程序，生成的曲线元素和新的误差估计的组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，例如螺钉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，提供曲线几何形状到适合分析的曲线网格的自动转换。该奖项反映了NSF的法定使命，并通过使用基金会的智力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.