Potential Numerical Issue?

[benhills]

I am playing around with your model to think about timescales for fabric evolution.

I can reproduce your demo result in /demo/fabric-evolution/run-fabric-evolution.py
However, if I change the number of time steps, Nt, to 500 instead of 50 (the default value) I get this oscillatory behavior which looks like a numerical artifact. It is especially apparent in the simple shear case although I have not tried all cases. I tried changing the time step which would be my normal approach for a numerical issue but that did not change anything.

I wonder if you can explain this physically (e.g. once the total strain exceeds 1 this weird behavior may be expected).

Thanks for any help! and awesome work on this, very slick model.

[nicholasmr]

Hi Ben,

I'm very pleased that you find our model useful.

The short answer is that your regularization is too weak, and that you should multiply the regularization matrix by some constant > 1. You'll see, however, that doing so effectively reduces the spectral resolution (L), limiting how strong a single maxima you can model (a1 eigenvalue). This, I guess, is hardly a problem if you are just playing around with fabric timescales etc., else try set L=20 which also comes with a default (calibrated) regularization.
See https://github.com/nicholasmr/specfab/wiki/Fabric-evolution#regularization for a pure-shear example of the effect/need for regularization.

We chose the default regularization strength weak enough to reduce its influence on the effective spectral resolution, while also providing sufficient regularization needed for typical large-scale ice-flow model implementations. Put differently, ice parcels in large-scale flow models are unlikely to experience the deformation history you are prescribing, and we can therefore allow ourselves to reduce the strength of regularization a bit in order to gain some spectral resolution (ability to model tighter c-axis distributions for a given L).

Regarding parcel strains exceeding 1, this is a good point. However, one might imagine another parcel deformation experiment with an initial fabric that is not isotropic, but rather with a preexisting strong single maximum. Modelling the fabric evolution up until strain ~1 would be equivalent to continuing the deformation experiment of an initially-isotropic fabric beyond strain = 1.

I hope this makes sense and was useful, else feel free to follow up.

[benhills]

This is very helpful, thank you.
I will keep you posted on any significant updates.