[petsc-users] Staggered solver phase field

Wed Apr 23 23:43:34 CDT 2025

Dear all,

I agree that TAO or SNES should be better solutions for fracture 
analysis using phase field models alone.
In my case, the use of TS is not real a choice. It is motivating by 
later adding new time-dependent physics (like thermal or species 
diffusion).

To be fair, I chose to use gradient damage model built in the framework 
of generalized standard materials instead of phase field models 
developped as a minimization problem. I obtained a coupled system of 
strong equations in displacement and damage.

I am trying is to solve this coupled problem with a staggered scheme. I 
identified TSSTEP as a potential function to apply staggered physics 
solving. Is this promising ?

Thanks
Augustin

Le 2025-04-23 21:17, Matthew Knepley a écrit :
> On Wed, Apr 23, 2025 at 2:20 PM Blaise Bourdin <bourdin at 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-michon at ensma.fr> wrote:
>> 
>> [You don't often get email from augustin.perrier-michon at ensma.fr.
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>> 
>> Caution: External email.
>> 
>> 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
>> <augustin.perrier-michon at ensma.fr> wrote:
>> 
>> [You don't often get email from augustin.perrier-michon at ensma.fr.
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>> 
>> Caution: External email.
>> 
>> 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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>> 27243
> 
> —
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> 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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