Hi all,
As this is my first message in this group, I will first introduce myself,
my actual question starts in the next paragraph. I am a PhD student in
physics. I am working on the modelling of organic solar cells by the
so-called drift-diffusion approach, hence I plan on using sympy to deal
with PDE and some systematic manipulations of them that I do by hand for
now. I am quite familiar with python and its mainstream scientific
libraries (I teach it as a TA) but I am new to sympy.
One of the first thing I tried to write in sympy was an equation of the
following form, where the divergence of some vector appears:
$$\frac{\partial c }{\partial t} - \vec\nabla . \vec{j_c} = 0 $$
However I found no way of writing this properly in sympy.
Indeed, using the vector module does not take into account derivatives the
way I expect it to, consider the following code:
import sympy as sp
import sympy.vector as spv
# Initialise coordinate system
S = spv.CoordSysCartesian('S')
delop = spv.Del(S)
# Create a new field without explicit expression
u0, u1, u2 = sp.symbols('u0:3')
J1 = u0*S.i + u1*S.j + u2* S.k
J2 = S.x*S.i + S.y*S.j + S.z* S.k
# Derivatives surprised me
print('div(J1) = ', delop.dot(J1))
print('div(J2) = ', delop.dot(J2))
It's output goes as follow:
> div(J1) = 0
> div(J2) = Derivative(S.x, S.x) + Derivative(S.y, S.y) + Derivative(S.z, S.z)
>
>
I assumed, however that the output would look like this:
> div(J1) = Derivative(u0, S.x) + Derivate(u1, S.y) + Derivative(u2, S.z)
> div(J2) = Derivative(S.x, S.x) + Derivative(S.y, S.y) + Derivative(S.z, S.z)
>
>
Is there a misunderstanding somewhere on my part or was sympy.vector not
designed for this kind of purposes?
Right now I am planning on writing my own set of classes and method to
handle these vectorial expressions, but before I do so I would like to be
sure that I haven't misunderstood the issue.
Thank you very much for reading through,
Best regards,
Alexis Prel
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