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于计算机模拟来设计和制造产品。计算机仿真的一个关键部分是网格生成，其中一个虚拟模型，比如飞机起落架，被分成大量的简单形状，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“纠缠”和重叠，从而导致错误的模拟结果。该项目将通过开发：(1)可以处理轻度缠结网格的新模拟方法，以及(2)“解开”严重缠结的新方法来解决这个长期存在的问题。该项目将对从生物力学到制造业等学科的模拟产生重大影响，该团队将开发软件发布给科学界。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相互联系的兴趣。两所大学将为K-12学生（包括代表性不足的少数民族学生）举办计算机模拟拓展活动。该项目将开发一种新的有限单元模拟方法来计算缠结网格的准确结果，从而避免某些类型的显式缠结。因此，与此同时，一类新的非线性优化方法将被开发出来，以处理四边形、六面体和高阶网格中的缠结，这些网格的缠结很难解开；其目的是通过解结来处理任何输入网格，直到可以保证数值正确的模拟。这个统一而健壮的框架的可行性将通过有针对性的应用程序来展示。

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.