Coefficient defined on quadrature points in the form definition

I have a the coefficient function that does not belong to the same finite element space as v, but is defined for each quadrature point.

@LinearForm
def loading(v, w):
    return dot(w["sig0"], sym(grad(v)))

Is it possible?

Background In linear elasticity, sometimes the stress - strain is given by

sigma = Hooke @ eps + sig0

where sig0 is the initial stress tensor, possibly heterogeneous (different value for each Gauss point). This can be used for instance to model thermal stress.

[gdmcbain]

If you pass v to the .interpolate method of its basis, you’ll get a DiscreteField which has a .grad attribute.

[kinnala]

I wonder if there is a more “local” way to do this without doing a global solve (like LocalSolver in FEniCS)…

Unfortunately, no. I think the “correct” way to do this would be to return here a list of local stiffness matrices: https://github.com/kinnala/scikit-fem/blob/91a276ab2e7e8eda8a01b40a97d1c25d0e939ece/skfem/assembly/form/bilinear_form.py#L101

And then use np.linalg.solve or similar which supports solving multiple dense systems at one go. I can try implementing it in few days if you want.