Discretizing Functionals

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1

Hello,

I am new to NGSolve and FEM, so I apologize if this is a simple question. I am reading The Finite Element Method in Electromagnetics and the author formulates the PDE’s using functionals, which I have not seen in any of the NGSolve tutorials. Is there a way to translate the functionals in the book into forms that can be used in NGSolve? Specifically, I would like to find the stationary point of the attached functional.

Any help would be greatly appreciated

Attachment: Functional.gif

2

you could use a Variation integrator, see here:

https://ngsolve.org/docu/latest/i-tutorials/unit-3.8-nonlmin/nonlmin.html

But I would say it’s a bit of overkill for the linear problem.