AF: Small: Collaborative Research: A Robust Framework for Overcoming the Tangled Mesh Problem

工程师们在很大程度上依赖计算机模拟来设计和制造产品。计算机模拟的一个关键部分是网格生成，例如飞机起落架的虚拟模型被分成大量更简单的形状，如三角形、正方形和立方体。不幸的是，对于复杂的模型，这些简单的形状可能会被缠绕和重叠，这可能会导致错误的模拟结果。这个项目将解决这个长期存在的问题：(1)可以与轻微纠缠的网格一起工作的新的模拟方法，以及(2)‘解开’糟糕的纠缠的新方法。该项目将对从生物力学到制造等学科的模拟产生重大影响，该团队将创建软件发布给科学界。PI将创建教学模块，以激发年轻学生对网格、科学计算和工程之间的互联互通的兴趣。这两所大学将为K-12学生，包括少数族裔学生，举办计算机模拟推广活动。该项目将开发一种新的有限元模拟方法，以避免某些类型的显式纠缠，在纠缠网格上计算准确的结果。因此，并行地，将开发一类新的非线性优化方法来处理四边形、六面体和高阶网格中的纠缠，这些网格明显更难解缠；其目的是通过解缠来处理任何输入网格，直到可以保证数值模拟的正确性。这一统一和强大的框架的可行性将通过有针对性的应用程序得到证明。

Engineers rely heavily on computer simulation to design and create products. A critical part of computer simulation is mesh generation, where a virtual model of, say an aircraft landing-gear, is divided into a large number of simpler shapes, such as triangles, squares, and cubes. Unfortunately, for complex models, these simple shapes can get 'entangled' and overlap, which can lead to erroneous simulation results. This project will address this long-standing problem by developing: (1) new simulation methods that can work with a mildly tangled mesh, and (2) new methods of 'untangling' bad tangles. The project will have a significant impact on simulation in disciplines from biomechanics to manufacturing, and the team will create software for release to the scientific community. The PIs will create teaching modules to excite young students on the interconnectivity between meshes, scientific computing, and engineering. Both universities will host outreach activities on computer simulation for K-12 students, including underrepresented minority students.This project will develop a novel finite-cell simulation method to compute accurate results on tangled meshes that avoid certain types of explicit tangling. Therefore, in parallel, a new class of nonlinear optimization methods will be developed to handle tangling in quadrilateral, hexahedral, and high-order meshes that are significantly more difficult to untangle; the aim is to handle any input mesh by untangling until a numerically correct simulation can be guaranteed. The viability of this unified and robust framework will be demonstrated through targeted applications.