Article

Flow Field Clustering via Algebraic Multigrid

Authors:

M. A. Schweitzer,

A. TeleaAuthors Info & Claims

VIS '04: Proceedings of the conference on Visualization '04

Pages 35 - 42

https://doi.org/10.1109/VISUAL.2004.32

Published: 10 October 2004 Publication History

Abstract

We present a novel multiscale approach for flow visualization. We define a local alignment tensor that encodes a measure for alignment to the direction of a given flow field. This tensor induces an anisotropic differential operator on the flow domain, which is discretized with a standard finite element technique. The entries of the corresponding stiffness matrix represent the anisotropically weighted couplings of adjacent nodes of the domain mesh. We use an algebraic multigrid algorithm to generate a hierarchy of fine to coarse descriptions for the above coupling data. This hierarchy comprises a set of coarse grid nodes, a multiscale of basis functions and their corresponding supports. We use these supports to obtain a multilevel decomposition of the flow structure. Standard streamline icons are used to visualize this decomposition at any user-selected level of detail. The method provides a single framework for vector field decomposition independent on the domain dimension or mesh type. Applications are shown in 2D, for flow fields on curved surfaces, and for 3D volumetric flow fields.

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Cited By

Koch SKasten JWiebel AScheuermann GHlawitschka M(2016)2D Vector field approximation using linear neighborhoodsThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-015-1140-932:12(1563-1578)Online publication date: 1-Dec-2016
https://dl.acm.org/doi/10.1007/s00371-015-1140-9
Busking SBotha CPost F(2010)Technical SectionComputers and Graphics10.1016/j.cag.2010.07.00434:6(719-728)Online publication date: 1-Dec-2010
https://dl.acm.org/doi/10.1016/j.cag.2010.07.004
Reniers DTelea A(2009)Extreme simplification and rendering of point sets using algebraic multigridComputing and Visualization in Science10.5555/3220919.322123112:1(9-22)Online publication date: 1-Jan-2009
https://dl.acm.org/doi/10.5555/3220919.3221231
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Flow Field Clustering via Algebraic Multigrid
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cover image ACM Conferences

VIS '04: Proceedings of the conference on Visualization '04

October 2004

667 pages

ISBN:0780387880

Sponsors

SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

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IEEE Computer Society

United States

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Published: 10 October 2004

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Cited By

Koch SKasten JWiebel AScheuermann GHlawitschka M(2016)2D Vector field approximation using linear neighborhoodsThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-015-1140-932:12(1563-1578)Online publication date: 1-Dec-2016
https://dl.acm.org/doi/10.1007/s00371-015-1140-9
Busking SBotha CPost F(2010)Technical SectionComputers and Graphics10.1016/j.cag.2010.07.00434:6(719-728)Online publication date: 1-Dec-2010
https://dl.acm.org/doi/10.1016/j.cag.2010.07.004
Reniers DTelea A(2009)Extreme simplification and rendering of point sets using algebraic multigridComputing and Visualization in Science10.5555/3220919.322123112:1(9-22)Online publication date: 1-Jan-2009
https://dl.acm.org/doi/10.5555/3220919.3221231
Nocke TFlechsig MBöhm UTew J(2007)Visual exploration and evaluation of climate-related simulation dataProceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come10.5555/1351542.1351673(703-711)Online publication date: 9-Dec-2007
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Yu HWang CMa KVerastegui B(2007)Parallel hierarchical visualization of large time-varying 3D vector fieldsProceedings of the 2007 ACM/IEEE conference on Supercomputing10.1145/1362622.1362655(1-12)Online publication date: 16-Nov-2007
https://dl.acm.org/doi/10.1145/1362622.1362655
Hlawitschka MScheuermann GHamann B(2007)Interactive Glyph Placement for Tensor FieldsAdvances in Visual Computing10.1007/978-3-540-76858-6_33(331-340)Online publication date: 26-Nov-2007
https://dl.acm.org/doi/10.1007/978-3-540-76858-6_33
Ebling JScheuermann G(2006)Segmentation of flow fields using pattern matchingProceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization10.5555/2384796.2384819(147-154)Online publication date: 8-May-2006
https://dl.acm.org/doi/10.5555/2384796.2384819
Salzbrunn TScheuermann G(2006)Streamline PredicatesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2006.10412:6(1601-1612)Online publication date: 1-Nov-2006
https://dl.acm.org/doi/10.1109/TVCG.2006.104
McKenzie ALombeyda SDesbrun M(2005)Vector field analysis and visualization through variational clusteringProceedings of the Seventh Joint Eurographics / IEEE VGTC conference on Visualization10.5555/2384060.2384066(29-35)Online publication date: 1-Jun-2005
https://dl.acm.org/doi/10.5555/2384060.2384066

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