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Comments on the "Meshless Helmholtz-Hodge Decomposition"
March 2013 (vol. 19 no. 3)
pp. 527-528
H. Bhatia, Sci. Comput. & Imaging Inst., Univ. of Utah, Salt Lake City, UT, USA
G. Norgard, Numerica, Fort Collins, CO, USA
V. Pascucci, Sci. Comput. & Imaging Inst., Univ. of Utah, Salt Lake City, UT, USA
P. Bremer, Center of Appl. Sci. Comput., Lawrence Livermore Nat. Lab., Livermore, CA, USA
The Helmholtz-Hodge decomposition (HHD) is one of the fundamental theorems of fluids describing the decomposition of a flow field into its divergence-free, curl-free, and harmonic components. Solving for the HHD is intimately connected to the choice of boundary conditions which determine the uniqueness and orthogonality of the decomposition. This article points out that one of the boundary conditions used in a recent paper “Meshless Helmholtz-Hodge Decomposition” [5] is, in general, invalid and provides an analytical example demonstrating the problem. We hope that this clarification on the theory will foster further research in this area and prevent undue problems in applying and extending the original approach.
Index Terms:
Boundary conditions,Harmonic analysis,Computational modeling,Helmholtz-Hodge decomposition.,Vector fields,boundary conditions
H. Bhatia, G. Norgard, V. Pascucci, P. Bremer, "Comments on the "Meshless Helmholtz-Hodge Decomposition"," IEEE Transactions on Visualization and Computer Graphics, vol. 19, no. 3, pp. 527-528, March 2013, doi:10.1109/TVCG.2012.62
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