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Meshless Helmholtz-Hodge Decomposition
March/April 2010 (vol. 16 no. 2)
pp. 338-349
Fabiano Petronetto, Universidad Federal do Espírito Santo, Brazil
Afonso Paiva, Universidade Federal de Uberlândia, Minas Gerais
Marcos Lage, PUC-Rio, Rio de Janeiro
Geovan Tavares, PUC-Rio, Rio de Janeiro
Hélio Lopes, PUC-Rio, Rio de Janeiro
Thomas Lewiner, PUC-Rio, Rio de Janeiro
Vector fields analysis traditionally distinguishes conservative (curl-free) from mass preserving (divergence-free) components. The Helmholtz-Hodge decomposition allows separating any vector field into the sum of three uniquely defined components: curl free, divergence free and harmonic. This decomposition is usually achieved by using mesh-based methods such as finite differences or finite elements. This work presents a new meshless approach to the Helmholtz-Hodge decomposition for the analysis of 2D discrete vector fields. It embeds into the SPH particle-based framework. The proposed method is efficient and can be applied to extract features from a 2D discrete vector field and to multiphase fluid flow simulation to ensure incompressibility.

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Index Terms:
Helmholtz-Hodge decomposition, smoothed particles hydrodynamics, vector field, features visualization, multiphase fluids, incompressible flow.
Fabiano Petronetto, Afonso Paiva, Marcos Lage, Geovan Tavares, Hélio Lopes, Thomas Lewiner, "Meshless Helmholtz-Hodge Decomposition," IEEE Transactions on Visualization and Computer Graphics, vol. 16, no. 2, pp. 338-349, March-April 2010, doi:10.1109/TVCG.2009.61
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