How to use PETSc SNES (scalable nonlinear equation solver), when the solution is not a vector but a user defined state?
I am implementing a non-linear mechanics problem (geometrically exact shell 5-paramter model), the update
$$X^{(k+1)} = X^{(k)} + \Delta_X$$
is not additive and requires the use of exponential maps.
More specifically, the state I mentioned above stores $ X $ : $$ X = \left \{ \Phi , \Lambda \right \} $$ $ \Phi $ (vector of size 3) is mid-surface coordinates and have direct updates i.e $$ \Phi _{n+1} = \Phi_{n} + \Delta \Phi $$ While $ \Lambda $, the rotation matrix (correpondiong to director at mid surface), is updated through exponential map (the update increment is a vector of size 2, which is obtained after exploiting the one to one connection between tangent space of SO3 and S2 and fixing a reference vector). The residual at each point of mid surface(node) is a vector of size 5 and consists of $ \Lambda $ , $ \Phi $ and their derivatives.
I am using Newton-Raphson and many times the solution couldn't converge using a complete step size. Consequently, I thought of resorting to PETSc SNES (line search).
At any state, I know the residual vector and stiffness matrix. I could not figure how to make sense of solution vector that I get from SNES solver (or to send data to SNES), given that I have my own update procedure.
