On Wed, Apr 23, 2025 at 2:20 PM Blaise Bourdin <bour...@mcmaster.ca>
wrote:
Hi,
Typically, phase-field models are formulated as rate independent
unilateral minimization problems of the form
u_i,\alpha_i = \argmin_{u,\alpha \le \alpha_{i-1}} F(u,\alpha)
Where i denotes the time step. These are technically neither DAE nor
ODE since there is the only time derivative in the limit model would
be a constraint in the form \dot{\alpha} = 0.
The most common numerical scheme is for each time step, to alternate
minimization with respect to u and \alpha. The main reason is that
while F is not convex jointly in u and \alpha, it is separately
convex and quadratic with respect to each variable, and because in
the simpler models.
Alternate minimization is technically block Gauss-Seidel, I think.
It is not particularly efficient but very robust and unconditionally
stable. Joint minimization in (u,\alpha) is typically fragile (most
of the interesting physics in fracture mechanics corresponds to
situation where a family of critical points looses stability, i.e.
the pair (u,\alpha) has to evolve through a region of non-convexity
of F.
In general, is there an advantage in implementing a steady-state
problem as a TS vs. Solving its optimality conditions as a SNES, or
minimizing the associated energy using TAO?
I think TAO would actually be the better route here, unless you are
using time as a sort of continuation variable.
Thanks,
Matt
Regards,
Blaise
On Apr 23, 2025, at 11:22 AM, PERRIER-MICHON Augustin
<augustin.perrier-mic...@ensma.fr> wrote:
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Dear Mr Bourdin,
thank you for your answer and the remarks.
I will performed time dependent multi-physics analysis including
crack
propagation afterward. To anticipate this time dependency, I chose
to
use TS solver instead of SNES or TAO. Plus, I thought that TS solver
can
be used for quasi-static problems as well.
In my previous simulations with a monolithic TS solver, I controlled
the
time step during all the calculation. In my opinion I could do the
same
in this framework and not let TS solvers adapt the step time. A
synchronization of the two solvers is necessary.
With these informations, is this framework and especially TSSTEP
function compatible with my problem ?
Thanks a lot
Augustin
Le 2025-04-23 16:58, Blaise Bourdin a écrit :
Augustin,
Out of curiosity, why TS and not SNES? At the very least the damage
problem should be a constrained minimization problem so that you can
model criticality with respect to the phase-field variable.
Secondly, I would be very wary about letting TS adapt the time step
by
itself. In quasi-static phase-field fracture, the time step affects
the crack path, not the order of the approximation in time. I doubt
that any of the mechanisms in TS are appropriate here.
You are welcome to dig into my implementation for inspiration, or
reuse it for your problems
https://urldefense.us/v3/__https://github.com/bourdin/mef90__;!!G_uCfscf7eWS!avkeFItwEAey6K_gtfFmi47RGpcntWLEnHYooiJLUAsD7p4k7c6bRKuEFgeKamuzP-HAjZNz-BldqS-LQaVh_oBU4V5nLW2neA$
[2]
Blaise
On Apr 23, 2025, at 10:20 AM, PERRIER-MICHON Augustin
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Dear Petsc users,
I am currently dealing with finite element fracture analysis using
phase
field model. To perform such simulations, I have to develop a
staggered
solver : mechanical problem is solved at constant damage and damage
problem is solved at constant displacement.
I created 2 TS solver and 2 DMPLEX for each "physics".
Each physics's system is built using TSSetIFunction and
TSSetIJacobian
with associated functions.
The TS calls are performed with TSSTEP in order to respect staggered
solver scheme in iterative loops.
My question : Is the using of TSSTEP function adapted to a staggered
solver ? How to use this function in my framework ? Have you got any
other suggestions or advices ?
Thanks a lot
Best regards
--
Augustin PERRIER-MICHON
PhD student institut PPRIME
Physics and Mechanics of materials department
ISAE-ENSMA
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