Optimal Triangulations for Scientific Computing

科学计算的最优三角剖分最近的科学计算进展激发了新的三角剖分问题。随着新的数值方法的发展，新的几何约束公式是这些方法的准确性和收敛性分析的关键。在这个为期两年的项目中，将研究许多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出来并向公众开放。特别是，将首次部署用于计算急性和非钝角三角测量问题的软件。在科学计算中，这种软件作为一种几何工具被寻求与广泛使用的有限体积方法以及图形应用相结合。还将研究其他三角测量问题的实用算法解决方案，例如预计在网络应用中使用的最小权重斯坦纳三角测量。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集成新的健壮软件来确保更广泛的影响。项目人员由一名研究生组成，该研究生将从工程界代表性不足的群体中选出。____________________________________________

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.____________________________________________