CSDL Home IEEE Transactions on Visualization & Computer Graphics 2010 vol.16 Issue No.02 - March/April

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Issue No.02 - March/April (2010 vol.16)

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

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TVCG.2009.61

ABSTRACT

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.

INDEX TERMS

Helmholtz-Hodge decomposition, smoothed particles hydrodynamics, vector field, features visualization, multiphase fluids, incompressible flow.

CITATION

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

*IEEE Transactions on Visualization & Computer Graphics*, vol.16, no. 2, pp. 338-349, March/April 2010, doi:10.1109/TVCG.2009.61REFERENCES

- [4] K. Polthier and E. Preuss, “Variational Approach to Vector Field Decomposition,”
Proc. Eurographics Workshop Scientific Visualization, 2000.- [5] K. Polthier and E. Preuss, “Identifying Vector Fields Singularities Using a Discrete Hodge Decomposition,”
Visualization and Mathematics III, pp. 113-134, Springer, 2003.- [9] A. Chorin and J. Marsden,
A Mathematical Introduction to Fluid Mechanics. Springer, 1992.- [10] G.R. Liu and M.B. Liu,
Smoothed Particle Hydrodynamics. World Science, 2005.- [11] M. Müller, D. Charypar, and M. Gross, “Particle-Based Fluid Simulation for Interactive Applications,”
Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 154-159, 2003.- [13] F. Petronetto, “Equação de Poisson e a Decomposição de Helmholtz-Hodge usando SPH,” PhD dissertation, PUC-Rio, 2008.
- [14] S. Li and W.K. Liu,
Meshfree Particle Methods. Springer, 2004.- [15] D. Dunbar and G. Humphreys, “A Spatial Data Structure for Fast Poisson-Disk Sample Generation,”
Proc. ACM SIGGRAPH, pp.503-508, 2006.- [16] M. Lage, F. Petronetto, A. Paiva, H. Lopes, T. Lewiner, and G. Tavares, “Vector Field Reconstruction from Sparse Samples with Applications,”
Proc. Brazilian Symp. Computer Graphics and Image Processing (SIBGRAPI '06), pp. 297-304, 2006.- [17] R. Pozo and K. Remington, SparseLib++ Sparse Matrix Class Library, http://math.nist.govsparselib++, 2009.
- [18] J. Dongarra, A. Lumsdaine, R. Pozo, and K. Remington, IML++ Iterative Methods Library, http://math.nist.goviml++, 1996.
- [19] Y. Saad,
Iterative Methods for Sparse Linear Systems. SIAM, 2003.- [25] R. Bridson, J. Houriham, and M. Nordenstam, “Curl-noise for Procedural Fluid Flow,”
ACM Trans. Graphics, vol. 26, no. 3, 2007.- [26] M. Becker and M. Teschner, “Weakly Compressible SPH for Free Surface Flows,”
Proc. ACM SIGGRAPH/Eurographics Symp. Computer Animation, pp. 209-217, 2007.- [27] R. Keiser, B. Adams, D. Gasser, P. Bazzi, P. Dutré, and M. Gross, “A Unified Lagrangian Approach to Solid-Fluid Animation,”
Proc. Eurographics/IEEE VGTC Symp. Point-Based Graphics, pp. 125-134, 2005.- [28] M. Müller, B. Solenthaler, R. Keiser, and M. Gross, “Particle-Based Fluid-Fluid Interaction,”
Proc. ACM SIGGRAPH '05 Symp. Computer Animation, pp. 237-244, 2005.- [29] A. Paiva, F. Petronetto, T. Lewiner, and G. Tavares, “Particle-Based Non-Newtonian Fluid Animation for Melting Objects,”
Proc. Brazilian Symp. Computer Graphics and Image Processing (SIBGRAPI '06), pp. 78-85, 2006. |