Is there a diff operator for partial derivatives

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1

Hi,
I’m a little new to NGSolve and was looking for an operator for a simple partial derivative to solve a problem with a Bilinear form that might look like this:

[tex]\int_\Omega\frac{\partial v(x,y)}{\partial x}\frac{\partial u(x,y)}{\partial x}\mathrm{d}x\mathrm{d}y[/tex]

I found that coefficient functions have a partial derivative method called diff(), I was hoping there would be somthing similar for test and trial functions that might look something like this:

a = BilinearForm(fes)
a+=(diff(u,x)*diff(v,x))*dx

Does such an function exist in NGSolve (obviously the above doesn’t work)? Sorry if I simply haven’t read the documentation well enough

2

Hi gflower,

you can get access to the i-th partial derivative by taking the i-th entry of the full gradient.

For a scalar u and v your example would be

a = BilinearForm(fes)
a+= grad(u)[0]*grad(v)[0]*dx

Best,
Michael

3

Hi mneunteufel,

Thanks for your post. What if u and v are not scalars? In other words, if u is a vector, can we get one component of u first, then take the gradient, then pick the i th component? Thanks in advance!

4

Hi Subway,

for vector-valued functions you can compute the Jacobian matrix and then choose the j-th partial derivative of the i-th component of the vector. E.g.:

fes = HCurl(mesh, order=2)
u,v = fes.TnT()

a = BilinearForm(fes)
a += Grad(u)[0,1]*Grad(v)[0,1]*dx   #dx_2u_1*dx_2v_1

Using Grad gives always the Jacobian, grad gives, depending on the finite element space, the Jacobian or the transpose of the Jacobian.

Best,
Michael

5

Hi Michael,

That makes sense. Thanks a lot for your help!