Taking the adjoint of a non-linear form

If you know it is linear in u, you can use replace(F, {u:ut}), or you can use derivative(F, u, ut) to get the Jacobi in the general case.

You can also start with the Lagrangian as a functional, to do that just let the Lagrange multiplier be a Coefficient w, and apply derivative w.r.t. w to get F and w.r.t u to get the adjoint. Apply derivative again to both w.r.t. opposite arguments to get their Jacobians.

Note that adjoint() in UFL is really only the transpose, be careful if you have e.g. time dependency or non symmetric discretization like upwinding.

Martin

Den 11. okt. 2011 kl. 21:35 skrev Douglas Brinkerhoff <email address hidden>:

> New question #173964 on DOLFIN:
> https://answers.launchpad.net/dolfin/+question/173964
>
> I'd like to get the adjoint of a non-linear Form that is calculated by taking the first variation of a Lagrangian. The problem is that the adjoint() function in FEniCs expects a bilinear form, and the nonlinear form is obviously a vector, since the variables of interest are specified as Functions rather than TrialFunctions. Is there a way to algorithmically replace every instance of a Function (u, say) with a TrialFunction (u_trial, say) in a given Form, such that the form becomes bilinear?
>
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