Optimal Triangulations for Scientific Computing

科学计算的最佳三角测量

• 批准号: 0830209
• 负责人: Alper Ungor
• 金额: $ 12.52万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0830209&HistoricalAwards=false
• 关键词: Optimal; Triangulations; Scientific; Computing

OPTIMAL TRIANGULATIONS FOR SCIENTIFIC COMPUTINGABSTRACT FOR PROPOSAL#0830209Recent progress in scientific computing motivates new triangulationproblems. As new numerical methods being developed, new geometricconstraint formulations that are key in the accuracy and convergenceanalysis of these methods emerge. In this two-year project, practicaland theoretically sound algorithmic solutions for a number oftriangulation problems will be studied. More importantly, new softwarebased on these solutions will be developed and made available to thepublic. In particular, first ever software for computing acute andnon-obtuse triangulation problems will be deployed. Such software aresought for in scientific computing as a geometric tool to be coupledwith the widely used finite volume methods as well as in graphicsapplications. Practical algorithmic solutions for other triangulationproblems such as minimum weight Steiner triangulations which isexpected to find use in networking applications, will also be studied.In addition, parallelization of the aformentioned algorithmicsolutions will be studied within this project. The project will ensureits broader impact through distribution and integration of new robustsoftware. Project personnel consists of one graduate student that willbe selected among underrepresented groups in engineering.____________________________________________

科学计算的最佳三角剖分问题科学计算的最新进展激发了新的三角剖分问题。随着新的数值方法的发展，新的几何约束公式，这些方法的精度和收敛性分析的关键出现。在这个为期两年的项目中，将研究一些三角测量问题的实际和理论上合理的算法解决方案。更重要的是，基于这些解决方案的新软件将被开发并提供给公众。特别是，第一个软件计算急性和非钝角三角问题将部署。这样的软件在科学计算中应该作为几何工具与广泛使用的有限体积法以及图形应用相结合。其他三角测量问题的实际算法解决方案，如最小权Steiner三角测量，预计将在网络应用中使用，也将进行研究。此外，上述算法解决方案的并行化将在本项目中进行研究。该项目将通过分发和整合新的强大软件来确保其更广泛的影响。项目人员由一名研究生组成，将从代表性不足的工程学群体中选出。