♒

Descomposició de Helmholtz

En aquesta pàgina encara no hi ha res escrit. Si vols començar, endavant!

Magatzem temporal

Video preview

www.sci.utah.edu

http://www.sci.utah.edu/~hbhatia/pubs/2013_TVCG_survey.pdf

Python:

Helmholtz-Hodge decomposition in the ball » Chebfun

In the subject of vector calculus, Helmholtz's theorem states that any sufficiently smooth function in the unit ball can be expressed as a sum of a curl-free, a divergence-free, and a harmonic vector field [4]. In this Example, we show how this decomposition is computed by Ballfun and introduce the command HelmholtzDecomposition [3].

Helmholtz-Hodge decomposition in the ball » Chebfun

https://www.chebfun.org/examples/sphere/HelmholtzDecompositionBall.html

Proof

Helmholtz decomposition

In physics and mathematics, in the area of vector calculus, Helmholtz's theorem,[1][2] also known as the fundamental theorem of vector calculus,[3][4][5][6][7][8][9] states that any sufficiently smooth, rapidly decaying vector field in three dimensions can be resolved into the sum of an irrotational (curl-free) vector field and a solenoidal (divergence-free) vector field; this is known as the Helmholtz decomposition or Helmholtz representation. It is named after Hermann von Helmholtz.

Helmholtz decomposition

https://en.wikipedia.org/wiki/Helmholtz_decomposition#Derivation