Elements:Software:Open-Source Robust Geometry Toolkit for Black-Box Finite Element Analysis

Elements：软件：用于黑盒有限元分析的开源稳健几何工具包

• 批准号: 1835712
• 负责人: Daniele Panozzo
• 金额: $ 60万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-09-01 至 2023-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1835712&HistoricalAwards=false
• 关键词: Elements; Software; Open; Source; Robust

The numerical solution of partial differential equations (PDEs) is ubiquitous in science and engineering applications, including simulation of elastoplastic deformations, fluids, and light scattering. The finite element method (FEM) is the most commonly used discretization of PDEs, especially in the context of structural and thermal analysis, due to its generality and rich selection of off-the-shelf commercial implementations. Ideally, a PDE solver should be a ``black box'': the user provides as input the domain boundary, boundary conditions, and the governing equations, and the code computes the value of the solution at a set of user-specified points of the input domain. This is surprisingly far from being the case for all existing open-source or commercial software, despite the research efforts in this direction and the large academic and industrial interest. To a large extent, this is due to treating meshing and FEM basis construction as two disjoint problems, often exposing the user to the technical issues of interfacing the meshing software with FEM basis construction, both of which, strictly speaking, are technical issues internal to the solver. This state of matters presents a fundamental problem for applications that require fully automatic, robust processing of large collections of meshes of varying sizes, an increasingly common situation as large collections of geometric data become available. This proposal introduces an integrated pipeline, considering meshing and element design as a single challenge, and developing a software platform to enable black box analysis on complex geometric models represented as point clouds, triangle meshes, or CAD (Computer Aided Design) models, opening the door to new shape design technique to a wide range of new applications in sciences and engineering.This project proposes to develop a set of software components based on a set of novel approaches the investigators have developed combined with "filtered" use of rational or multi-precision numerical representations to handle robustness problems while maintaining practical performance. The proposed set of geometry processing techniques, while slower than existing ones, are fully robust in a sense of always produce a valid result with minimal assumptions on the input. The geometric toolkit will allow to automatically convert geometrical data in the form of range scans, CAD models, or voxel grids into a surface or volumetric representation, directly usable in widely used open-source finite element method (FEM) packages. It will include mesh generation, in addition to tetrahedral meshes, for other common types of discretizations: hexahedral meshes, and hex-dominant hybrid meshes. The key innovation is to achieve numerical robustness with minimal added algorithmic complexity by carefully mixing higher precision representations for the critical part, while relying on standard fixed-precision floating point representation for the rest and designing algorithms amenable to this approach. As in overwhelming majority of cases higher accuracy is needed for a vanishingly small fraction of computation, this approach allows the users to achieve sensible running time while ensuring output validity and algorithmic correctness on imperfect, real world data. Secondly, the invetigators will integrate FEM basis construction with meshing decoupling accuracy from mesh quality. The software toolkit developed in this proposal has potential for a major impact in all domains that require computational simulation of physical phenomena in complex geometries, enabling the automation of data acquisition, reconstruction, and simulation pipelines. The expectation of this project is that the outcome will not only be a reduction in human time, but the opportunity to fully automate this pipeline will open new research venues. The release of all the software with a MPL2 license will facilitate integration of the results of the work into commercial software, in addition to academic/non-profit research use.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.

偏微分方程组的数值解在科学和工程应用中普遍存在，包括弹塑性变形、流体和光散射的模拟。有限元方法是偏微分方程组最常用的离散化方法，特别是在结构和热分析方面，因为它的普遍性和现成的商业实现的丰富选择。理想情况下，PDE求解器应该是一个“黑盒”：用户提供域边界、边界条件和控制方程作为输入，代码在输入域的一组用户指定的点处计算解的值。令人惊讶的是，这远远不是所有现有的开源或商业软件的情况，尽管在这个方向上做出了研究努力，并引起了学术界和工业界的广泛兴趣。这在很大程度上是因为将网格划分和有限元基础构造视为两个互不相交的问题，经常使用户面临网格划分软件和有限元基础构造之间的接口技术问题，严格地说，这两者都是求解器内部的技术问题。对于需要对各种大小的大网格集合进行全自动、健壮处理的应用程序来说，这种情况是一个基本问题，随着大的几何数据集合变得可用，这是一种越来越常见的情况。该方案引入了一个集成的管道，将网格划分和元素设计视为单一挑战，并开发了一个软件平台，以实现对表示为点云、三角形网格或CAD(计算机辅助设计)模型的复杂几何模型的黑盒分析，为新的形状设计技术在科学和工程中的广泛应用打开了大门。该项目建议开发一套基于研究人员开发的一套新方法的软件组件，结合有理或多精度数值表示的过滤使用，在保持实用性能的同时处理健壮性问题。所提出的一套几何处理技术，虽然比现有的慢，但在一定意义上是完全健壮的，因为它总是在输入假设最少的情况下产生有效的结果。几何工具包将允许自动将距离扫描、CAD模型或体素网格形式的几何数据转换为表面或体积表示，直接用于广泛使用的开放源代码有限元(FEM)包。除了四面体网格外，它还将包括其他常见离散化类型的网格生成：六面体网格和六角占主导的混合网格。关键的创新是通过仔细混合关键部分的高精度表示法，而其余部分依赖于标准的固定精度浮点表示法，并设计符合这种方法的算法，以最小的算法复杂性实现数值稳健性。由于在绝大多数情况下，对于极小的计算量需要更高的精度，这种方法允许用户获得合理的运行时间，同时确保对不完美的真实世界数据的输出有效性和算法正确性。其次，研究人员将有限元基础施工与网格划分精度与网格质量相结合。本提案中开发的软件工具包可能在所有需要对复杂几何中的物理现象进行计算模拟的领域产生重大影响，从而实现数据采集、重建和模拟管道的自动化。这个项目的期望是，结果不仅是人类时间的减少，而且这条管道完全自动化的机会将打开新的研究场所。所有具有MPL2许可证的软件的发布将促进将工作结果整合到商业软件中，以及学术/非营利性研究用途。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

DHFSlicer: Double Height-Field Slicing for Milling Fixed-Height Materials

DHFSlicer：用于铣削固定高度材料的双高度场切片

• 发表时间: 2020
• 期刊: ACM transactions on graphics
• 影响因子: 6.2
• 作者: Yang, Jinfan;Araujo, Chrystiano;Vining, Nicholas;Ferguson, Zachary;Rosales, Enrique;Panozzo, Daniele;Lefebvre, Sylvain;Cignoni, Paolo;Sheffer, Alla
• 通讯作者: Sheffer, Alla

Hardware Design and Accurate Simulation for Benchmarking of 3D Reconstruction Algorithms

3D 重建算法基准测试的硬件设计和精确仿真

• 发表时间: 2022
• 期刊: Neural Information Processing Systems (NeurIPS 2021
• 作者: Sebastian Koch, Yurii Piadyk

Decoupling simulation accuracy from mesh quality

• DOI: 10.1145/3272127.3275067
• 发表时间: 2018-12
• 期刊: ACM Transactions on Graphics (TOG)
• 作者: T. Schneider;Yixin Hu;Jérémie Dumas;Xifeng Gao;Daniele Panozzo;D. Zorin

A Cross-Platform Benchmark for Interval Computation Libraries

区间计算库的跨平台基准

• 发表时间: 2022
• 期刊: PPAM 2022
• 作者: Tang Xuan;Ferguson, Zachary;Schneider, Teseo;Zorin, Denis;Kamil, Shoaib;Panozzo, Daniele
• 通讯作者: Panozzo, Daniele

Deformation Capture via Soft and Stretchable Sensor Arrays

• DOI: 10.1145/3311972
• 发表时间: 2019-04-01
• 期刊: ACM TRANSACTIONS ON GRAPHICS
• 影响因子: 6.2
• 作者: Glauser, Oliver;Panozzo, Daniele;Sorkine-Hornung, Olga
• 通讯作者: Sorkine-Hornung, Olga