a.Energy(gfu) - elementwise possible?

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1

Hello,

is there a possibility to receive the energy of each element in an elegant way?
For the global energy, I know the a.Energy(gfu) function which is very handy.

Thanks in advance!

2

Update:

I built a workaround to get the Energy per Element.
My BilinearForm a is non-linear. How can I say at which point the ElementMatrices are built?

e_int_list = list()
a.AssembleLinearization(gfu.vec)

for el in fes.Elements(VOL):
    elmat = a.integrators[0].CalcElementMatrix (el.GetFE(), el.GetTrafo())
    el_dofs = el.dofs
    u_el = np.array([gfu.vec[i] for i in el_dofs])
    e = 0.5 * u_el.T@elmat.NumPy()@u_el
    e_int_list.append(e)

elwise_vol = Integrate(CoefficientFunction(1),mesh,VOL, element_wise=True)

W2 = sum(e_int_list)
print('Energy sum Element energy: ', W2)

fesL2 = L2(mesh, order=0)
energy_gf = GridFunction(fesL2)
vol_gf = GridFunction(fesL2)
energy_gf.vec.FV().NumPy()[:] = np.array(e_int_list)
vol_gf.vec.FV().NumPy()[:] = elwise_vol.NumPy()

energy_cf1 = CoefficientFunction(energy_gf/vol_gf)

W1 = Integrate(energy_cf1,mesh)
print('Energy: 1*', W1)

Still the question: Is there any function to directly get the energy distribution as a CoefficientFunction?

3

Hi,

You can use

elwise_energy = Integrate(energy(gfu), mesh, VOL, element_wise=True)

It will provide a vector of dimension of number of elements, where every entry has the contribution of that element

An example is here:
https://ngsolve.org/docu/latest/i-tutorials/unit-1.6-adaptivity/adaptivity.html

best,
Joachim

4

Hello,

thanks for your respond. My question was more into the direction whether there is a inbuilt CF “energy”?

Best

5

Hello,

some update from my side: I searched in the C++ Code and found the function “ApplyElementMatrix” or “ApplyLinearizedElementMatrix”. I think this is exactly what I would need to call from Python.
Also the function “CalcLinearizedElementMatrix” would be neat to have access to.

6

Hi, may I ask for any comment of the developers about future integration of the showed functions? Or is there already a python interface to it which I didn’t find?