##  [Helmholtz Decomposition](/helmholtz-decomposition) 

  ##  [Helmholtz Decomposition](https://natural.quantumdictionary.io/helmholtz-decomposition-0) 

  

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Definition

The Helmholtz decomposition expresses a sufficiently regular vector field on a suitable domain (e.g. R^n with decay at infinity or a bounded domain with boundary conditions) as the sum of an irrotational (gradient) field and a solenoidal (divergence-free) field, possibly plus a harmonic component depending on topology and boundary conditions.