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Meshless Helmholtz-Hodge Decomposition
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 decompo...
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| Published in: | IEEE transactions on visualization and computer graphics 2010-03, Vol.16 (2), p.338-349 |
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| Main Authors: | , , , , , |
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| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c402t-a1f58259f761c31d83a25a8289987734b255d99728aebb2d4513de19821456593 |
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| cites | cdi_FETCH-LOGICAL-c402t-a1f58259f761c31d83a25a8289987734b255d99728aebb2d4513de19821456593 |
| container_end_page | 349 |
| container_issue | 2 |
| container_start_page | 338 |
| container_title | IEEE transactions on visualization and computer graphics |
| container_volume | 16 |
| creator | Petronetto, F. Paiva, A. Lage, M. Tavares, G. Lopes, H. Lewiner, T. |
| description | 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. |
| doi_str_mv | 10.1109/TVCG.2009.61 |
| format | article |
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| fulltext | fulltext |
| identifier | ISSN: 1077-2626 |
| ispartof | IEEE transactions on visualization and computer graphics, 2010-03, Vol.16 (2), p.338-349 |
| issn | 1077-2626 1941-0506 |
| language | eng |
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| source | IEEE Electronic Library (IEL) Journals |
| subjects | Algorithms Application software Computational fluid dynamics Computational modeling Computer Graphics Computer Simulation Decomposition Feature extraction features visualization Finite difference methods Finite element method Finite element methods Fluid flow Helmholtz-Hodge decomposition Hydrodynamics incompressible flow Mathematical analysis Mathematics Meshless methods Models, Theoretical multiphase fluids Poisson equations Rheology - methods smoothed particles hydrodynamics Two dimensional vector field Vectors (mathematics) Visualization |
| title | Meshless Helmholtz-Hodge Decomposition |
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