Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 448

Variational Approach to Vector Field Decomposition

Konrad Polthier and Eike Preuss

Eurographics Workshop on Visualization, Springer Verlag 2000

For the feature analysis of vector fields we decompose a given vector field into three components: a divergence-free, a rotation-free, and a harmonic vector field. This Hodge-type decomposition splits a vector field using a variational approach, and allows to locate sources, sinks, and vortices as extremal points of the potentials of the components. Our method applies to discrete tangential vector fields on surfaces, and is of global nature. Results are presented of applying the method to test cases and a CFD flow.

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