GV:Small: Lagrangian Visualization Methods for Very Large Time-Dependent Vector Fields

GV:Small：非常大的时变向量场的拉格朗日可视化方法

• 批准号: 0916289
• 负责人: Kenneth Joy
• 金额: $ 44.35万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0916289&HistoricalAwards=false
• 关键词: GV; Small; Lagrangian; Visualization; Methods

Lagrangian methods assume a central role in the analysis and visualization of vector fields resulting from simulation and measurement across many application domains. These methods provide key insight into vector field structures and dynamics, but are based on the expensive computation of integral curves. Applied to large-scale problems and data sets, they are burdened heavily by enormous computational cost.To improve this situation, the problem-specific computation of integral curves employed in vector field visualization techniques is replaced by a two-stage process consisting of an adaptive pre-computation of integral curve sets and methods for interpolation within these sets, effectively transferring the vector field representation to the Lagrangian domain. Hence, the computational burden is isolated into a pre-computation stage. The obtained Lagrangian representation is stored into efficient out-of-core data structures. Integration-based visualization algorithms can leverage the resulting fast interpolation of integral curves, whose approximative characteristics are examined in detail, from this pre-computed data. This generic framework permits enhancement of existing integration-based visualization methods to become interactive and provides a basis for research into novel efficient and interactive vector field visualization for very large vector fields. Taking advantage of these properties, new visualization tools are developed to study transport processes in vector fields using Lagrangian analysis. To increase the impact of this research and distribute it to a large community of scientists and engineers, the developed algorithms are integrated with an open-source visualization package. These new techniques are integrated into coursework and student projects that enable students to study new methods of analysis of flow computations. Information concerning these new methods are found on the project website (http://idav.ucdavis.edu/~joy/NSF-IIS-0916289).

拉格朗日方法在许多应用领域的模拟和测量所产生的矢量场的分析和可视化中扮演着中心角色。这些方法提供了对矢量场结构和动力学的关键洞察，但基于昂贵的积分曲线计算。为了改善这种情况，将矢量场可视化技术中针对特定问题的积分曲线计算替换为两阶段过程，该过程包括积分曲线集合的自适应预计算和这些集合内的内插方法，有效地将矢量场表示转移到拉格朗日区域。因此，计算负担被隔离到预计算阶段。所获得的拉格朗日表示被存储到高效的核外数据结构中。基于积分的可视化算法可以利用从该预计算数据得到的积分曲线的快速内插，其近似特性被详细检查。这种通用框架允许增强现有的基于积分的可视化方法成为交互式的，并为研究针对非常大的矢量场的新颖、高效和交互的矢量场可视化提供了基础。利用这些性质，开发了新的可视化工具，利用拉格朗日分析研究矢量场中的输运过程。为了增加这项研究的影响力，并将其分发给一大批科学家和工程师，开发的算法与一个开源可视化包集成在一起。这些新技术被整合到课程作业和学生项目中，使学生能够学习分析流量计算的新方法。有关这些新方法的信息可在项目网站(http://idav.ucdavis.edu/~joy/NSF-IIS-0916289).上找到