Is there a function that could be used for calculation of the divergence of the vectorial field? (in matlab) I would expect it exists in numpy/scipy but I can not find it using Google.
I need to calculate div[A * grad(F)]
, where
F = np.array([[1,2,3,4],[5,6,7,8]]) # (2D numpy ndarray)
A = np.array([[1,2,3,4],[1,2,3,4]]) # (2D numpy ndarray)
so grad(F)
is a list of 2D ndarray
s
I know I can calculate divergence like this but do not want to reinvent the wheel. (I would also expect something more optimized) Does anyone have suggestions?
but we need define func divergence as : divergence ( f) = dfx/dx + dfy/dy + dfz/dz +… = np. gradient( fx) + np. gradient(fy) + np.
The numerical divergence of a vector field is a way to estimate the values of the divergence using the known values of the vector field at certain points. div F = ∇ · F = ∂ F x ∂ x + ∂ F y ∂ y + ∂ F z ∂ z .
Formulas for divergence and curl For F:R3→R3 (confused?), the formulas for the divergence and curl of a vector field are divF=∂F1∂x+∂F2∂y+∂F3∂zcurlF=(∂F3∂y−∂F2∂z,∂F1∂z−∂F3∂x,∂F2∂x−∂F1∂y).
The divergence computes a scalar quantity from a vector field by differentiation. We can write this in a simplified notation using a scalar product with the ∇ vector differential operator: div a = ( ˆı ∂ ∂x + ˆ ∂ ∂y + k ∂ ∂z ) · a = ∇ · a (5.17) Notice that the divergence of a vector field is a scalar field.
Just a hint for everybody reading that:
the functions above do not compute the divergence of a vector field. they sum the derivatives of a scalar field A:
result = dA/dx + dA/dy
in contrast to a vector field (with three dimensional example):
result = sum dAi/dxi = dAx/dx + dAy/dy + dAz/dz
Vote down for all! It is mathematically simply wrong.
Cheers!
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