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.

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来推动。 该提案的主要创新之一是中央计划的制定。虽然中心方案被认为是时间相关偏微分方程最强大的数值方法之一，特别是在求解输运方程方面，但如果要充分发挥其潜力，仍有几个基本问​​题需要解决。该提案还集中研究水平集方法各向异性的威力、隐式方法的实现以及数据同化中多尺度技术的威力。大多数现实世界问题都是由计算机解决的。许多此类问题非常复杂，现有的计算方法不足以提供所需的精度。 这种情况不能通过简单地构建更快的计算机来解决。 事实上，对更精细分辨率和更准确模型的追求远远超过了计算能力的提升。 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更大的红利。 该项目的研究旨在在计算机程序（所谓的数值算法）背后的数学方面取得创新进展，这将显着加快计算速度，从而解决该国面临的许多科学和工程问题，例如跟踪沿海污染物领域或开发用于医学成像的快速、准确的传感器。