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
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> Blaise
>
> On Apr 23, 2025, at 10:20 AM, PERRIER-MICHON Augustin
> <augustin.perrier-mic...@ensma.fr> wrote:
>
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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
> Téléport 2
> 1 Avenue Clément ADER
> 86361 Chasseneuil du Poitou- Futuroscope
> Tel : +33-(0)-5-49-49-80-97
>
>
> —
> Canada Research Chair in Mathematical and Computational Aspects of
> Solid Mechanics (Tier 1)
> Professor, Department of Mathematics & Statistics
> Hamilton Hall room 409A, McMaster University
> 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada
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> —
> Canada Research Chair in Mathematical and Computational Aspects of
> Solid Mechanics (Tier 1)
> Professor, Department of Mathematics & Statistics
> Hamilton Hall room 409A, McMaster University
> 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada
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