4.7 Editorial Material

Comments on the Meshless Helmholtz-Hodge Decomposition

Journal

Publisher

IEEE COMPUTER SOC
DOI: 10.1109/TVCG.2012.62

Keywords

Vector fields; boundary conditions; Helmholtz-Hodge decomposition

Funding

  1. Direct For Computer & Info Scie & Enginr
  2. Office of Advanced Cyberinfrastructure (OAC) [0904631] Funding Source: National Science Foundation

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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.

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