Comments on the "Meshless Helmholtz-Hodge decomposition"
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Updated: May 24, 2026

Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects
Published on: February 8, 2014
Harsh Bhatia1, Gregory Norgard, Valerio Pascucci
1Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112, USA. hbhatia@sci.utah.edu
Abstract:
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" 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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