Flow field clustering via algebraic multigrid

Griebel, Michael; Preußer, Tobias; Rumpf, Martin; Schweitzer, Marc Alexander; Telea, Alexandru

doi:10.1109/visual.2004.32

Cited by 29 publications

(30 citation statements)

References 20 publications

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“…It is noted that some conventional operations in the spatial domain, such as the distance calculation of two points, cannot be performed in the spacetime domain. However, these operations are essential for visualization calculations, such as streamline placement [10,13] and clustering [21,6]. Unlike the previous research, we achieve the spatial and temporal coherence in a high-dimensional space.…”

Section: Background and Related Workmentioning

confidence: 99%

“…Existing techniques can be classified into glyph and field-line based methods [29,16], dense texture methods [19,24], clustering-based methods [21,7,6], and topology-based methods [8,18]. Glyph or field-line visualization is particularly effective for the visualization of isolated regions in the vector field.…”

Section: Background and Related Workmentioning

confidence: 99%

“…This makes those methods computationally intensive when the size of the input vector field is large. Another category of methods, vector field clustering [21,6], is successful in finding representative streamlines based on the clustering analysis. These methods share some characteristics with traditional clustering methods in data mining.…”

Section: Streamline Generation For Large Steady Vector Fieldsmentioning

confidence: 99%

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Parallel hierarchical visualization of large time-varying 3D vector fields

Wang

2007

Proceedings of the 2007 ACM/IEEE Conference on Supercomputing

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We present the design of a scalable parallel pathline construction method for visualizing large time-varying 3D vector fields. A 4D (i.e., time and the 3D spatial domain) representation of the vector field is introduced to make a timeaccurate depiction of the flow field. This representation also allows us to obtain pathlines through streamline tracing in the 4D space. Furthermore, a hierarchical representation of the 4D vector field, constructed by clustering the 4D field, makes possible interactive visualization of the flow field at different levels of abstraction. Based on this hierarchical representation, a data partitioning scheme is designed to achieve high parallel efficiency. We demonstrate the performance of parallel pathline visualization using data sets obtained from terascale flow simulations. This new capability will enable scientists to study their time-varying vector fields at the resolution and interactivity previously unavailable to them.

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Section: Background and Related Workmentioning

confidence: 99%

Section: Background and Related Workmentioning

confidence: 99%

Section: Streamline Generation For Large Steady Vector Fieldsmentioning

confidence: 99%

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Parallel hierarchical visualization of large time-varying 3D vector fields

Wang

2007

Proceedings of the 2007 ACM/IEEE Conference on Supercomputing

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“…Our construction of a space-time hierarchy for time-dependent particle data is related to clustering methods for vector fields ?, [24][25][26][27] in that it considers similar merging criteria for clustering particles. In contrast to these techniques, however, our objective is not to approximate a given flow field by a sparse set of vector samples, but to hierarchically describe the distribution and flow of mass over time that is represented by the motion of individual particles.…”

Section: Space-time Hierarchymentioning

confidence: 99%

Motion visualization in large particle simulations

Fraedrich¹,

Westermann²

2012

Visualization and Data Analysis 2012

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Figure 1. We present a novel space-time hierarchy for large particle sets, which allows for the analysis of formation processes in astrophysical particle simulations, such as the merging of particles into clusters (middle image). Our approach can show the motion of mass at multiple levels of detail, and it allows classifying the motion dynamics based on directional information. ABSTRACTInteractive visualization of large particle sets is required to analyze the complicated structures and formation processes in astrophysical particle simulations. While some research has been done on the development of visualization techniques for steady particle fields, only very few approaches have been proposed to interactively visualize large time-varying fields and their dynamics. Particle trajectories are known to visualize dynamic processes over time, but due to occlusion and visual cluttering such techniques have only been reported for very small particle sets so far. In this paper we present a novel technique to solve these problems, and we demonstrate the potential of our approach for the visual exploration of large astrophysical particle sequences. We present a new hierarchical space-time data structure for particle sets which allows for a scale-space analysis of trajectories in the simulated fields. In combination with visualization techniques that adapt to the respective scales, clusters of particles with homogeneous motion as well as separation and merging regions can be identified effectively. The additional use of mapping functions to modulate the color and size of trajectories allows emphasizing various particle properties like direction, speed, or particle-specific attributes like temperature. Furthermore, tracking of interactively selected particle subsets permits the user to focus on structures of interest.

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“…In [34] we use the fact that the structure of the flow is completely encoded in the diffusion operator −div (A(v, ∇u)∇u) to create a multiscale representation of the flow field. Let us assume that we have discretized the diffusion operator by standard finite elements on a regular grid yielding the stiffness-matrix L introduced in Subsect.…”

Section: Multiscale Analysis With Algebraic Multigrid (Amg)mentioning

confidence: 99%