Hi everyone!
I'm trying to solve a variational problem on vector fields that has both linear and non-linear dependencies in TrialFunctions in the bilinear form. Obviously, defining the problem in FEniCS like a classic linear problem wouldn't work:
solve(a==L, sol, bcs)
So I guess I'll have to use the non-linear problem formulation:
solve(F==0, sol, bcs)
But I don't know if this will work, I tried to solve it this way but I get a "All terms in form must have same rank" error.
Here is the way the problem is defined:
Given an interval domain $\Gamma$, find the 2 vector functions of the curvilinear abscissa $s$ subject to the problem: (let the $X_s$ writing denote the derivation of $X$ with respect to $s$)
$find\ (u1,u2) \in \Omega = \mathbb{R}^3 \times \mathbb{R}^3\ such\ as\ \forall (v1,v2) \in \Omega,$
$\int_\Gamma u1_s\cdot v1_s ds+ u1 \times u2_s \cdot v2\ ds = \int_\Gamma f \cdot v1 + c \cdot v2 ds$
Where $f$ and $c$ are given vectors (loads). Here we can see that the bilinear form, which is the left hand side of the equation, has both linear ($u1_s\cdot v1_s$) and non linear ($u1 \times u2_s \cdot v2$) terms in TrialFunctions. Basically, I want to know if this problem can be solved defining $u1$ and $u2$ as Functions and using the non-linear formulation in the solver.
Thanks for the help!
(edited several times hoping it would be more understandable, don't hesitate to tell me if some more information is needed.)
