M. Griebel, T. Preußer, M. Rumpf, A. Schweitzer, and A. Telea.
Flow field clustering via algebraic multigrid.
In Visualization. IEEE CS Press, 2004.
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A novel multiscale approach for flow visualization is presented. We define a local alignment tensor that encodes a measure for alignment to the direction of a given flow field. These tensors induce 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's meshing. We use an algebraic multigrid algorithm to generate a hierarchy of descriptions for the above coupling data, ranging from fine to coarse representations of the initial finest coupling. This hierarchy comes along with a corresponding multiscale of basis functions and domains, yielding a multilevel decomposition of the flow structure. Finally, we use standard streamline icons 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 in 3D.