Meshless Helmholtz-Hodge decomposition

Meshless Helmholtz-Hodge decomposition
Fabiano Petronetto, Afonso Paiva, Marcos Lage, Geovan Tavares, Hélio Lopes, Thomas Lewiner


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.


PDF paper (20.2 MB)
Meshless Helmholtz-Hodge decomposition


    author = {Fabiano Petronetto and Afonso Paiva and Marcos Lage and Geovan Tavares and Hélio Lopes and Thomas Lewiner},
    title = {Meshless Helmholtz-Hodge decomposition},
    year = {2010},
    month = {march},
    journal = {Transactions on Visualization and Computer Graphics},
    volume = {16},
    number = {2},
    pages = {338--342},
    publisher = {IEEE},
    doi = {10.1109/TVCG.2009.61},
    url = {\url{}}

Last modifications on July 3rd, 2013