Algebraically Smooth 3D Print

Are you the proud owner of a 3D printer who has often thought to themselves, I wish that my prints were algebraically smooth? I imagine the answer is probably not, but on the off chance that you're a multigrid nerd with a 3D printer lying around, I have just the remedy.

A 3D-printed multigrid error, based on Figure 8.2 from A Multigrid Tutorial.

This is a model of Figure 8.2 from A Multigrid Tutorial (Briggs et al., 2000) showing error that is algebraically smooth, yet not geometrically smooth on an example PDE problem that is solved using 8 iterations of Gauss-Seidel relaxation. The top-left, top-right, and bottom-right quadrants (wrt to the above figure) have strong anisotropy in specific directions, leading to the interesting error patterns that are shown.

Figure 8.2 from A Multigrid Tutorial, included for illustrative purposes.

You can grab the .obj file as well as the reference Jupyer notebook used to generate the model here. The resulting mesh can be different based on the random seed used to initialize the error; though, in practice these differences are very slight.

References

Briggs, W. L., Henson, V. E., and McCormick, S. F. A Multigrid Tutorial, Second Edition. Society for Industrial and Applied Mathematics, second edition, 2000. doi: 10.1137/1.9780898719505. URL https://epubs.siam.org/doi/abs/10.1137/1.9780898719505.