AMG vs. GMG Solver Inconsistency in 3D Elasticity Models in Spherical Domains

ASPECT
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Hi Ninghui, Timo and John,

Alright, so the problematic case is GMG + iterated Stokes. I can confirm that this case, for the viscoelastic bending beam, leads to anomalous velocities and stresses (see orange solid line in figure below). I’ve tested applying the material averaging to the viscosity used in the reaction rates as well (dashed pink line), and that leads to stable velocities and stresses, much more similar to the Newton/AMG cases. I have to do some more testing/discussing before I can be sure - this change is not in the fix_stresses_elasticity branch yet.

5_viscoelastic_bending_beam_smooth25_dte_isnot_dtc_depth_dtcisdte_AMG_GMG
5_viscoelastic_bending_beam_smooth25_dte_isnot_dtc_depth_dtcisdte_AMG_GMG3000×1800 385 KB

5_viscoelastic_bending_beam_smooth25_dte_isnot_dtc_velocity_dtcisdte_AMG_GMG
5_viscoelastic_bending_beam_smooth25_dte_isnot_dtc_velocity_dtcisdte_AMG_GMG3000×1800 347 KB

That said, the GMG solver is sensitive to the number of mesh refinement levels, and we’ve experienced in some viscoplastic models that it sometimes doesn’t converge, where AMG does. Reducing the viscosity ratio and/or the timestep can help there according to John.

Also, when elasticity is included, the Stokes equations are assembled differently for the Newton and the Picard nonlinear solvers, and for the GMG and AMG solvers (if I remember correclty). Here @YiminJin will know more.

@tjhei, not having to material average could be useful when trying to match benchmark results or in simulations with limited resolution, where you don’t want to lose the in-element variation. However, I think we should first look into those cases that people in John’s and my group have come across where GMG doesn’t converge, but could provide large speed up, like in 3D setups. What do you think @jbnaliboff ?

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Hi Anne, John and all,

Alright, so the problematic case is GMG + iterated Stokes. I can confirm that this case, for the viscoelastic bending beam, leads to anomalous velocities and stresses (see orange solid line in figure below). I’ve tested applying the material averaging to the viscosity used in the reaction rates as well (dashed pink line), and that leads to stable velocities and stresses, much more similar to the Newton/AMG cases.

Thanks a lot for the detailed testing and for sharing the results! I’m glad to see that you’ve identified the GMG + iterated Stokes combination as the problematic case, and that applying material averaging to the viscosity used in the reaction rates seems to stabilize the solution.

Please do let me know if there’s anything I can help with regarding further testing or analysis. I’m happy to assist in any way I can.

Best,
Ninghui

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I’ve tested applying the material averaging to the viscosity used in the reaction rates as well (dashed pink line), and that leads to stable velocities and stresses, much more similar to the Newton/AMG cases.

Great news, fingers crossed that change helps improve convergence behavior across a range of models.

@tjhei, not having to material average could be useful when trying to match benchmark results or in simulations with limited resolution, where you don’t want to lose the in-element variation. However, I think we should first look into those cases that people in John’s and my group have come across where GMG doesn’t converge, but could provide large speed up, like in 3D setups. What do you think @jbnaliboff ?

I agree. Having a ‘no material averaging’ for GMG may certainly be useful in some cases, but I think sorting out why the GMG performance breaks for some complicated models would be beneficial to a wider class of simulations.

Please do let me know if there’s anything I can help with regarding further testing or analysis. I’m happy to assist in any way I can.

Thanks for the offer @tiannh7. If you don’t mind sharing, posting the results of your testing/benchmarking to the forum (or via github issues) is certainly helpful. Longer term, contributing any new benchmarks or cookbooks repository would likewise be very helpful.

Please let us know how further testing goes (I would use AMG in the interim), and we can update here as well once further testing is done on our side with the changes Anne implemented.

Cheers,
John

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@anne-glerum My apologies for the late reply. As far as I remember, there is no difference between AMG and GMG in assembling the Stokes equation. But it is highly possible that I am wrong, for otherwise there should not be differences in the results. Besides, I have not fully understood the modifications made by Rene in computing the viscosity derivatives.

I am currently working on a new idea in viscosity averaging and I am going through all these stuffs. I hope I could get some conclusion before the next VEP meeting.