Derivative of derivative

variational formulation
1

Sometime I like to solve the variational problem directly by setting up an energy functional energy = H*dx and then solving with a residual

R=derivative(H,u,du)

If I want to get the ‘exact’ Jacobian of then taking

derivative(R,u,du)

leads to

ValueError: Can only create arguments automatically for non-indexed coefficients.

What is the right way to do this? I want to solve a time-dependent problem so it would be good to not build the solver in each time step and calculate this jacobian first. My hope is to let ufl/fenicsx do this all without me calculating the derivative myself.

2

You need to make a minimal reproducible example.

For documentation, see for instance:
http://jsdokken.com/FEniCS-workshop/src/applications/optimal_control.html#the-forward-problem

3

That’s a nice resource. It has given me some ideas. I’ll get back to you if my question still makes sense. Thanks for the link… very helpful info there.

4

ok so that resource was very helpful and it solves my issue. The ordering of my operations has led to nice speedups. Thanks. I guess I’d just delete this question?

5

You can keep the question as other people might have the same question in the future.