Discrete Anisotropy Caused by Cell Aspect Ratio

[U U]

Hello everyone,

I recently read an article stating that the aspect ratio of the simulation cells can also lead to significant discretization anisotropy. Does this mean that even if all my mesh sizes are below the exchange length, using a mesh with a cell aspect ratio not equal to 1 will still introduce discretization anisotropy?

Suppose I need to simulate a magnetic thin film (where the film thickness is much smaller than the film dimensions). To reduce the simulation time, I need to use flattened rectangular prism cells (high aspect ratio cells) for the simulation. Is it possible to reduce the effect of this discretization anisotropy by adjusting parameters (e.g., setting anisotropy parameters or using tensor formulation for parameters)?

Alternatively, are there any papers or references that address this specific issue?

Thank you in advance for your help!

[Vlad Kuchkin]

Hi,

We had a similar problem when studying skyrmion dynamics.

What has helped us is using the 4th order finite-difference scheme.

You can have a look at the Mumax3 script in Appendix C:

 https://doi.org/10.1103/PhysRevB.104.165116

Best,

Vlad

чт, 16 окт. 2025 г. в 08:55, U U <zxwe...@gmail.com>:

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[U U]

Hi，

I referenced the code in your article, and the fourth-order finite difference scheme is indeed effective in reducing the error caused by discrete anisotropy. However, it seems that your dx and dy values are both 1nm. I am not sure if this is sufficient to demonstrate the additional discrete anisotropy and computational error caused by the mesh aspect ratio. If my model is a 3D model and the values of dx, dy, and dz are not equal, would a simple fourth-order finite difference scheme still be effective?

Thank you for your reply!

[Vlad Kuchkin]

I believe that if you have different dx, dy, and dz, using the 4th-order finite difference scheme will give an error of order O(max(dx,dy,dz)^4).

Or in the 2D case, for fixed dz, one gets O(max(dx,dy)^4).

However, I haven't personally investigated such a case.

Perhaps you need to implement even higher-order schemes to reduce numerical artifacts further.

Depends on the problem you are trying to solve.

Cheers,

Vlad

чт, 16 окт. 2025 г. в 10:49, U U <zxwe...@gmail.com>:

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