Boundary Conditions on Inverse Problem

[gabrielord]

Hello, Professor Lu Lu, I am sorry for bothering you.

I am trying to implement the following boundary condition:

Where phi and sigma are the output and n^ is the outer vector at the point where the boundary condition is defined.

My difficult is on how to derivate phi with respect to this outer vector.

I would appreciate if you could give any insight on how to implement this directional derivative.

[lululxvi]

I don't understand your question. Your problem is about boundary condition implementation, but why is it related to the inverse problem setup? You may remove those parts unrelated to your key question.

[gabrielord]

Thank you for your response and I'm sorry for my mistake.
I've updated my question.

[lululxvi]

Just compute it based on the definition.