Computational Challenges in Fluid Transport and Imaging

流体传输和成像的计算挑战

• 批准号: 0810869
• 负责人: Guergana Petrova
• 金额: $ 15.65万
• 依托单位: Texas A&M Research Foundation
• 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: 2008-08-15 至 2012-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0810869&HistoricalAwards=false
• 关键词: Computational; Challenges; Fluid; Transport; Imaging

The proposed research emphasizes that dramatic advances in computation must be driven by a fundamental understanding of the theory behind numerical methods. One of the main innovations in this proposal is the development of central schemes. While central schemes are considered to be among the most powerful numerical methods for time dependent PDEs, in particular for solving transport equations, there are still several fundamental issues to be resolved if they are to reach their full potential. This proposal also concentrates on the investigation of the power of anisotropy of level set methods, the implementation of implicit methods, and the power of multi-scale techniques in data assimilation.Most real world problems are solved by computers. Many such problems are so complicated that the existing computational methods are insufficient to provide the accuracy needed. This situation cannot be solved by simply building faster computers. Indeed, the quest for finer resolution and more accurate models far outstrips gains in computational power. Moreover, as has been demonstrated often in the past, innovations in computer algorithms and software pay larger dividends than advances in computational power. The research in this project seeks to make innovative advances in the mathematics behind computer programs (so-called numerical algorithms) which will have the effect of significantly speeding up computation and thereby solving many scientific and engineering problems facing this country such as tracking pollutants in coastal areas or developing fast and accurate sensors for medical imaging.

这项拟议的研究强调，计算的巨大进步必须由对数值方法背后的理论的基本理解推动。这项提议的主要创新之一是制定中央计划。虽然中心格式被认为是求解含时偏微分方程组的最强大的数值方法之一，特别是对于求解输运方程，但如果要充分发挥它们的潜力，仍有几个基本问题需要解决。该方案还重点研究了水平集方法各向异性的能力、隐式方法的实现以及多尺度技术在数据同化中的能力。许多这样的问题是如此复杂，以至于现有的计算方法不足以提供所需的精度。这种情况不是简单地建造更快的计算机就能解决的。事实上，对更精细的分辨率和更精确的模型的追求远远超过了计算能力的增长。此外，正如过去经常证明的那样，计算机算法和软件的创新比计算能力的进步带来的红利更大。这个项目的研究试图在计算机程序(所谓的数值算法)背后的数学方面取得创新性的进展，这些程序将大大加快计算速度，从而解决这个国家面临的许多科学和工程问题，如跟踪沿海地区的污染物或开发快速而准确的医学成像传感器。