MSPA-MCS: Automatic Geometric Simplification

MSPA-MCS：自动几何简化

• 批准号: 0434338
• 负责人: Stephen Vavasis
• 金额: $ 50万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0434338&HistoricalAwards=false
• 关键词: MSPA; MCS; Automatic; Geometric; Simplification

ABSTRACTPI: Stephen Vavasis proposal: 0434338The team members investigate new algorithms for automatic simplification of complex geometries arising in solution of boundary and initial value problems from engineering and biomedical applications. Geometric simplification allows the use of finite-element meshes with many fewer elements, which greatly speeds up the solution time of partial differential equations. Powerful new tools from hyperbolic geometry are applied to the simplification problem. These tools enable linear-time estimation of the effect on the solution of a change in the boundary using purely geometric analysis and without prior information about the solution. The simplification algorithm is based on a partitioning of the original geometry into simpler shapes.Brain injury is an enormous medical problem in the U.S., with 1.5 million new cases per year, $56 billion spent on medical expenses, and countless lives affected adversely. Life prediction for composite materials like concrete, asphalt and laminates, similarly have significant public-safety and economic consequences. These two disparate problems share in common the property that they are amenable to computer modeling and analysis. Furthermore, for accurate results, both applications require computer modeling of complex geometric shapes. Unfortunately, complex geometric shapes require time-consuming computations on large high-performance computers and thus limit the practical applicability of computer modeling. The project invents computer methods that can quickly and accurately simplify complex geometries. "Accurately" in this context means that the simplification is guaranteed not to change the outcome of the simulation by more than a small percentage. Therefore, the research project leads to much faster analysis of problems with complex geometry. In the long run, this leads to better understanding of the consequences and perhaps therapy for traumatic brain injury and better life-prediction capability for complex structural materials.

摘要：Stephen Vavasis建议：0434338团队成员研究了用于自动简化工程和生物医学应用中边界和初始值问题解决方案中出现的复杂几何形状的新算法。几何简化允许使用具有更少元素的有限元网格，这大大加快了偏微分方程的求解时间。 强大的新工具，从双曲几何的简化问题。 这些工具能够使用纯几何分析并且在没有关于解决方案的先验信息的情况下对边界变化对解决方案的影响进行线性时间估计。 简化算法基于将原始几何体分割成更简单的形状。脑损伤在美国是一个巨大的医疗问题，每年有150万新病例，560亿美元用于医疗费用，无数人的生命受到不利影响。 混凝土、沥青和层压板等复合材料的寿命预测同样具有重大的公共安全和经济后果。 这两个完全不同的问题有一个共同点，即它们都可以用计算机建模和分析。 此外，为了获得准确的结果，这两种应用都需要对复杂的几何形状进行计算机建模。 不幸的是，复杂的几何形状需要在大型高性能计算机上进行耗时的计算，从而限制了计算机建模的实用性。 该项目发明了计算机方法，可以快速准确地简化复杂的几何形状。 在此上下文中，“准确地”意味着保证简化不会使模拟结果改变超过很小的百分比。 因此，该研究项目可以更快地分析复杂几何问题。 从长远来看，这将导致更好地理解创伤性脑损伤的后果，并可能治疗创伤性脑损伤，以及更好地预测复杂结构材料的寿命。