Optimal Triangulations for Scientific Computing

科学计算的最优三角测量提案#0830209最近科学计算的进步激发了新的三角测量问题。随着新的数值方法的发展，出现了新的几何约束公式，这些公式是这些方法的精度和收敛分析的关键。在这个为期两年的项目中，将研究一些三角测量问题的实用和理论上合理的算法解决方案。更重要的是，将开发基于这些解决方案的新软件并向公众提供。特别是，将部署有史以来第一个用于计算尖锐和非钝化三角问题的软件。这种软件在科学计算中作为一种几何工具与广泛使用的有限体积法相结合，在图形应用中也是如此。还将研究其他三角测量问题的实用算法解决方案，例如有望在网络应用中使用的最小权重Steiner三角剖分。此外，将在该项目中研究上述算法解决方案的并行化。该项目将通过分发和整合新的健壮软件来确保其更广泛的影响。项目人员由一名研究生组成，该研究生将从engineering.____________________________________________代表性不足的群体中挑选出来

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.____________________________________________