To do a decent stabilized problem with nonlinearities on the time
derivative term, our mass_residual() functions ought to have access to
the current element solution u(t) at the simulation-time being
evaluated, a fixed element solution u_f which is constant from t_n to
t_{n+1}, and some measure of the rate of change du/dt at t.
We currently pack the rate of change (as deltat * du/dt) into
elem_solution (a woefully confusing decision originally made for
backwards compatibility reasons), we pack a u_f into
elem_fixed_solution, and nonlinear mass_residual calls can reuse
elem_fixed_solution as u(t) so long as they're not doing any time
integration more complicated than the single-evaluation theta method.
We currently can't add more accurate time integrators (or even use a
simple trapezoidal rule!) on problems with nonlinear mass matrices
without the results being inaccurate.
I'd like to change this, by:
Adding an elem_solution_rate (or elem_solution_derivative? opinions
welcome) to FEMContext which holds du/dt.
Making elem_solution consistently hold u(t).
The problem is that this will thoroughly break the results of anyone
with a FEMSystem-based code complicated enough to require overriding
mass_residual(). I've talked to the few developers who I personally
know to be in such a situation, and so far there's unanimous support
for "just break it and we'll update", but if any other users disagree
I'd like to know about it. Adding a "transition release" with
forwards and backwards compatibility for this change would be a pain
in the neck, but it can be done if someone really wants it.
---
Roy
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